78 results on '"HYPERGEOMETRIC functions"'
Search Results
2. Binary dusty plasma Coulomb balls.
- Author
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Apolinario, S. W. S. and Peeters, F. M.
- Subjects
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COULOMB functions , *HYPERGEOMETRIC functions , *PHYSICAL sciences , *PARABOLIC differential equations , *PARABOLIC operators - Abstract
We investigated the mixing and segregation of a system consisting of two different species of particles, having different charges, interacting through a pure Coulomb potential, and confined in a three-dimensional parabolic trap. The structure of the cluster and its normal mode spectrum are analyzed, as a function of the relative charge and the relative number of different types of particles. We found that (a) the system can be in a mixed or segregated state depending on the relative charge ratio parameter and (b) the segregation process is mediated by a first or second order structural phase transition which strongly influences the magic cluster properties of the system. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
3. Yangian bootstrap for conformal Feynman integrals.
- Author
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Loebbert, Florian, Müller, Dennis, and Münkler, Hagen
- Subjects
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FEYNMAN integrals , *HYPERGEOMETRIC functions , *HEXAGONS , *SPECIAL functions - Abstract
We explore the idea to bootstrap Feynman integrals using integrability. In particular, we put the recently discovered Yangian symmetry of conformal Feynman integrals to work. As a prototypical example we demonstrate that the D-dimensional box integral with generic propagator powers is completely fixed by its symmetries to be a particular linear combination of Appell hypergeometric functions. In this context the Bloch-Wigner function arises as a special Yangian invariant in four dimensions. The bootstrap procedure for the box integral is naturally structured in algorithmic form. We then discuss the Yangian constraints for the six-point double box integral as well as for the related hexagon. For the latter we argue that the constraints are solved by a set of generalized Lauricella functions, and we comment on complications in identifying the integral as a certain linear combination of these. Finally, we elaborate on the close relation to the Mellin-Barnes technique and argue that it generates Yangian invariants as sums of residues. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
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4. Constant potentials in 6D Einstein-Gauss-Bonnet theory.
- Author
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Hansraj, Sudan, Maharaj, Sunil D., and Chilambwe, Brian
- Subjects
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COMPACT objects (Astronomy) , *HYPERGEOMETRIC functions , *FRIEDMANN equations , *RADIUS (Geometry) , *SPHERES , *CURVATURE - Abstract
The qualitative physical behavior of six-dimensional perfect fluid spheres is studied in the context of Einstein-Gauss-Bonnet (EGB) gravity theory, and a contrast is drawn with the associated Einstein model. At first we seek an analogue of the defective Einstein universe by setting the temporal potential to be constant. The equation of state ρ+5/3p= a constant multiple of the Gauss-Bonnet coupling α is obtained, and in the case of vanishing α the six-dimensional Einstein universe is recovered. More significantly the case of a constant spatial potential generated an exact solution in terms of hypergeometric functions. No solution in terms of elementary functions was located; however it was still possible to construct a compact star with finite radius for a specific choice of potential and suitable parameter values obtained by fine-tuning. It emerged that the EGB model was singularity free and displayed a number of pleasing physical features which were extrapolated from the usual restrictions placed on Einstein spheres. It was found that the EGB higher curvature terms allowed for the existence of stellar radius some 20 times larger than its Einstein counterpart. Moreover, the Einstein model suffered the permanent defect of a central singularity. In many respects the Gauss-Bonnet offered corrections to the corresponding Einstein model. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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- View/download PDF
5. Algebraic Structure of Cut Feynman Integrals and the Diagrammatic Coaction.
- Author
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Abreu, Samuel, Britto, Ruth, Duhr, Claude, and Gardi, Einan
- Subjects
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FEYNMAN integrals , *HYPERGEOMETRIC functions , *DIFFERENTIAL equations - Abstract
We study the algebraic and analytic structure of Feynman integrals by proposing an operation that maps an integral into pairs of integrals obtained from a master integrand and a corresponding master contour. This operation is a coaction. It reduces to the known coaction on multiple polylogarithms, but applies more generally, e.g., to hypergeometric functions. The coaction also applies to generic one-loop Feynman integrals with any configuration of internal and external masses, and in dimensional regularization. In this case, we demonstrate that it can be given a diagrammatic representation purely in terms of operations on graphs, namely, contractions and cuts of edges. The coaction gives direct access to (iterated) discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they admit. In particular, the differential equations for any one-loop integral are determined by the diagrammatic coaction using limited information about their maximal, next-to-maximal, and next-to-next-to-maximal cuts. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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6. Fractional dynamics using an ensemble of classical trajectories.
- Author
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Zhaopeng Sun, Hao Dong, and Yujun Zheng
- Subjects
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HYPERGEOMETRIC functions , *PHASE space trajectory , *LEVY processes - Abstract
A trajectory-based formulation for fractional dynamics is presented and the trajectories are generated deterministically. In this theoretical framework, we derive a new class of estimators in terms of confluent hypergeometric function (1F1) to represent the Riesz fractional derivative. Using this method, the simulation of free and confined Lévy flight are in excellent agreement with the exact numerical and analytical results. In addition, the barrier crossing in a bistable potential driven by Lévy noise of index α is investigated. In phase space, the behavior of trajectories reveal the feature of Lévy flight in a better perspective. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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7. Hypergeometric resummation of self-consistent sunset diagrams for steady-state electron-boson quantum many-body systems out of equilibrium.
- Author
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Mera, Héctor, Pedersen, Thomas G., and Nikolić, Branislav K.
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HYPERGEOMETRIC functions , *ELECTRON-phonon interactions , *GREEN'S functions - Abstract
A newly developed hypergeometric resummation technique [H. Mera et al., Phys. Rev. Lett. 115, 143001 (2015)] provides an easy-to-use recipe to obtain conserving approximations within the self-consistent nonequilibrium many-body perturbation theory. We demonstrate the usefulness of this technique by calculating the phonon-limited electronic current in a model of a single-molecule junction within the self-consistent Born approximation for the electron-phonon interacting system, where the perturbation expansion for the nonequilibrium Green's function in powers of the free bosonic propagator typically consists of a series of noncrossing sunset diagrams. Hypergeometric resummation preserves conservation laws and it is shown to provide substantial convergence acceleration relative to more standard approaches to self-consistency. This result strongly suggests that the convergence of the self-consistent sunset series is limited by a branch-cut singularity, which is accurately described by Gauss hypergeometric functions. Our results showcase an alternative approach to conservation laws and self-consistency where expectation values obtained from conserving divergent perturbation expansions are summed to their self-consistent value by analytic continuation functions able to mimic the convergence-limiting singularity structure. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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8. Superintegrability of d-Dimensional Conformal Blocks.
- Author
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Isachenkov, Mikhail and Schomerus, Volker
- Subjects
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CONFORMAL field theory , *HYPERGEOMETRIC functions , *EIGENFUNCTIONS - Abstract
We observe that conformal blocks of scalar four-point functions in a d-dimensional conformal field theory can be mapped to eigenfunctions of a two-particle hyperbolic Calogero-Sutherland Hamiltonian. The latter describes two coupled Pöschl-Teller particles. Their interaction, whose strength depends smoothly on the dimension d, is known to be superintegrable. Our observation enables us to exploit the rich mathematical literature on Calogero-Sutherland models in deriving various results for conformal field theory. These include an explicit construction of conformal blocks in terms of Heckman-Opdam hypergeometric functions. We conclude with a short outlook, in particular, on the consequences of integrability for the theory of conformal blocks. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
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9. Nonresonant two-photon transitions in length and velocity gauges.
- Author
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Jentschura, U. D.
- Subjects
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GAUGE invariance , *HYPERGEOMETRIC functions , *PHOTON-photon interactions - Abstract
We reexamine the invariance of two-photon transition matrix elements and corresponding two-photon Rabi frequencies under the "gauge" transformation from the length to the velocity gauge. It is shown that gauge invariance, in the most general sense, only holds at exact resonance, for both one-color as well as two-color absorption. The arguments leading to this conclusion are supported by analytic calculations which express the matrix elements in terms of hypergeometric functions, and ramified by a "master identity" which is fulfilled by off-diagonal matrix elements of the Schrödinger propagator under the transformation from the velocity to the length gauge. The study of the gauge dependence of atomic processes highlights subtle connections between the concept of asymptotic states, the gauge transformation of the wave function, and infinitesimal damping parameters for perturbations and interaction Hamiltonians that switch off the terms in the infinite past and future [of the form exp(-ε|t|)]. We include a pertinent discussion. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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10. Moran model as a dynamical process on networks and its implications for neutral speciation.
- Author
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de Aguiar, Marcus A. M. and Bar-Yam, Yaneer
- Subjects
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POPULATION genetics , *HAPLOIDY , *HYPERGEOMETRIC functions , *CHAOS theory , *CHEMICAL speciation - Abstract
In population genetics, the Moran model describes the neutral evolution of a biallelic gene in a population of haploid individuals subjected to mutations. We show in this paper that this model can be mapped into an influence dynamical process on networks subjected to external influences. The panmictic case considered by Moran corresponds to fully connected networks and can be completely solved in terms of hypergeometric functions. Other types of networks correspond to structured populations, for which approximate solutions are also available. This approach to the classic Moran model leads to a relation between regular networks based on spatial grids and the mechanism of isolation by distance. We discuss the consequences of this connection for topopatric speciation and the theory of neutral speciation and biodiversity. We show that the effect of mutations in structured populations, where individuals can mate only with neighbors, is greatly enhanced with respect to the panmictic case. If mating is further constrained by genetic proximity between individuals, a balance of opposing tendencies takes place: increasing diversity promoted by enhanced effective mutations versus decreasing diversity promoted by similarity between mates. Resolution of large enough opposing tendencies occurs through speciation via pattern formation. We derive an explicit expression that indicates when speciation is possible involving the parameters characterizing the population. We also show that the time to speciation is greatly reduced in comparison with the panmictic case. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
11. Massive one-loop conformal Feynman integrals and quadratic transformations of multiple hypergeometric series.
- Author
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Ananthanarayan, B., Banik, Sumit, Friot, Samuel, and Ghosh, Shayan
- Subjects
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FEYNMAN integrals , *HYPERGEOMETRIC series , *HYPERGEOMETRIC functions , *MATHEMATICAL physics , *LOGICAL prediction , *INTEGRALS - Abstract
The computational technique of N-fold Mellin-Barnes (MB) integrals, presented in a companion paper by the same authors, is used to derive sets of series representations of the massive one-loop conformal three-point Feynman integral in various configurations. This shows the great simplicity and efficiency of the method in nonresonant cases (generic propagator powers) as well as some of its subtleties in the resonant ones (for unit propagator powers). We confirm certain results in the physics and mathematics literature and provide many new results, some of them dealing with the more general massive one-loop conformal n-point case. In particular, we prove two recent conjectures that give the massive one-loop conformal n-point integral (for generic propagator powers) in terms of multiple hypergeometric series. We show how these conjectures, that were deduced from a Yangian bootstrap analysis, are related by a tower of new quadratic transformations in hypergeometric functions theory. Finally, we also use our MB method to identify spurious contributions that can arise in the Yangian approach. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
12. Anisotropic spin-singlet pairings in CuxBi2Se3 and Bi2Te3.
- Author
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Lei Hao, Gui-Ling Wang, Ting-Kuo Lee, Jun Wang, Wei-Feng Tsai, and Yong-Hong Yang
- Subjects
- *
COULOMB functions , *ELECTRIC potential , *HYPERGEOMETRIC functions , *ANTIFERROMAGNETISM , *ANTIFERROMAGNETIC materials - Abstract
Possible anisotropic spin-singlet pairings in Bi2X3 (X is Se or Te) are studied. Among six pairings compatible with the crystal symmetry, two novel pairings show nontrivial surface Andreev bound states, which form flat bands and could produce zero-bias conductance peak in measurements such as point-contact spectroscopy. By considering purely repulsive short-range Coulomb interaction as the pairing mechanism, the dominant super exchange terms are all antiferromagnetic, which would usually favor spin-singlet pairing in Bi2X3. Mean field analyses show that the interorbital pairing interaction favors a mixed spatial-parity anisotropic pairing state, and one pairing channel with zero-energy surface states has a sizable component. The results provide important information for future experiments. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
13. Exact solution of the Bloch equations for the nonresonant exponential model in the presence of dephasing.
- Author
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Zlatanov, K. N., Vasilev, G. S., Ivanov, P. A., and Vitanov, N. V.
- Subjects
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BLOCH equations , *NUCLEAR magnetism , *HYPERGEOMETRIC functions , *QUANTUM mechanics , *NUCLEAR spin , *ATOMIC collisions , *ATOMIC interactions - Abstract
An exact analytic solution is presented for a two-state quantum system driven by a time-dependent external field with an exponential temporal shape in the presence of dephasing. In the absence of dephasing the model reduces to the well-known Demkov model originally introduced in slow atomic collisions. The solution is expressed in terms of the generalized hypergeometric function, 1F2{a: b1, b2x). Various limiting cases are examined in the limits of weak and strong dephasing, strong driving field, and exact resonance. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
14. Nonlinear trident in the high-energy limit: Nonlocality, Coulomb field, and resummations.
- Author
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Torgrimsson, Greger
- Subjects
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PAIR production , *LASER pulses , *HYPERGEOMETRIC functions , *ELECTROMAGNETIC fields , *ULTRASHORT laser pulses , *ELECTRONS - Abstract
We study nonlinear trident in laser pulses in the high-energy limit, where the initial electron experiences, in its rest frame, an electromagnetic field strength above Schwinger's critical field. At lower energies the dominant contribution comes from the "two-step" part, but in the high-energy limit the dominant contribution comes instead from the one-step term. We obtain new approximations that explain the relation between the high-energy limit of trident and pair production by a Coulomb field, as well as the role of the Weizsäcker-Williams approximation and why it does not agree with the high-χ limit of the locally-constant-field approximation. We also show that the next-to-leading order in the large-a0 expansion is, in the high-energy limit, nonlocal and is numerically very important even for quite large a0. We show that the small-a0 perturbation series has a finite radius of convergence, but using Padé-conformal methods we obtain resummations that go beyond the radius of convergence and have a large numerical overlap with the large-a0 approximation. We use Borel-Padé-conformal methods to resum the small-χ expansion and obtain a high precision up to very large χ. We also use newer resummation methods based on hypergeometric/Meijer-G and confluent hypergeometric functions. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
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15. Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime.
- Author
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Middleton, Chad A. and Stanley, Ethan
- Subjects
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EINSTEIN field equations , *EQUATIONS of state , *HYPERGEOMETRIC functions , *ANISOTROPY , *COMPACTIFICATION (Physics) - Abstract
We examine the time evolution of the five-dimensional Einstein field equations subjected to a flat, anisotropic Robertson-Walker metric, where the 3D and higher-dimensional scale factors are allowed to dynamically evolve at different rates. By adopting equations of state relating the 3D and higher-dimensional pressures to the density, we obtain an exact expression relating the higher-dimensional scale factor to a function of the 3D scale factor. This relation allows us to write the Friedmann-Robertson-Walker field equations exclusively in terms of the 3D scale factor, thus yielding a set of 4D effective Friedmann-Robertson-Walker field equations. We examine the effective field equations in the general case and obtain an exact expression relating a function of the 3D scale factor to the time. This expression involves a hypergeometric function and cannot, in general, be inverted to yield an analytical expression for the 3D scale factor as a function of time. When the hypergeometric function is expanded for small and large arguments, we obtain a generalized treatment of the dynamical compactification scenario of Mohammedi [Phys. Rev. D 65, 104018 (2002)] and the 5D vacuum solution of Chodos and Detweiler [Phys. Rev. D 21, 2167 (1980)], respectively. By expanding the hypergeometric function near a branch point, we obtain the perturbative solution for the 3D scale factor in the small time regime. This solution exhibits accelerated expansion, which, remarkably, is independent of the value of the 4D equation of state parameter w. This early-time epoch of accelerated expansion arises naturally out of the anisotropic evolution of 5D spacetime when the pressure in the extra dimension is negative and offers a possible alternative to scalar field inflationary theory. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
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16. Random matrix theory of quantum transport in chaotic cavities with nonideal leads.
- Author
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Jarosz, Andrzej, Vidal, Pedro, and Kanzieper, Eugene
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PROBABILITY density function , *BALLISTICS , *PFAFFIAN systems , *HYPERGEOMETRIC functions , *HOLES - Abstract
We determine the joint probability density function (JPDF) of reflection eigenvalues in three Dyson's ensembles of normal-conducting chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Expressing the JPDF in terms of hypergeometric functions of matrix arguments (labeled by the Dyson index β), we further show that reflection eigenvalues form a determinantal ensemble at β=2 and a new type of a Pfaffian ensemble at β=4. As an application, we derive a simple analytic expression for the concurrence distribution describing production of orbitally entangled electrons in chaotic cavities with tunnel point contacts when time-reversal symmetry is preserved. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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17. f(R)gravity without a cosmological constant
- Author
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Cruz Dombriz, Álvaro de la, Dobado González, Antonio, Cruz Dombriz, Álvaro de la, and Dobado González, Antonio
- Abstract
© 2006 The American Physical Society. We would like to thank J. A. R. Cembranos and very specially A. L. Maroto for useful comments and discussions. We also thank S. D. Odintsov for bringing to our attention [13], where special functions are also considered as f(R)candidates for cosmologically viable models. This work has been partially supported by the DGICYT (Spain) under the project No. FPA2005-02327., In this work we consider the possibility of describing the current evolution of the universe, without the introduction of any cosmological constant or dark energy (DE), by modifying the Einstein-Hilbert (EH) action. In the context of the f(R) gravities within the metric formalism, we show that it is possible to find an action without cosmological constant which exactly reproduces the behavior of the EH action with cosmological constant. In addition the f(R) action is analytical at the origin having Minkowski and Schwarzschild solutions as vacuum solutions. The found f(R) action is highly nontrivial and must be written in terms of hypergeometric functions but, in spite of looking somewhat artificial, it shows that the cosmological constant, or more generally the DE, is not a logical necessity., DGICYT (Spain), Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub
- Published
- 2023
18. Magnetizability of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function.
- Author
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Stefańska, Patrycja
- Subjects
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MAGNETIZABILITY , *HYDROGEN atom , *DIRAC function , *HYPERGEOMETRIC functions , *EXCITED states - Abstract
The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski. J. Phys. B 30. 825 (1997): 30. 2747(E) (1997)] is exploited to derive a closed-form expression for the magnetizability of the relativistic one-electron atom in an arbitrary discrete slate, with a pointlike, spinless, and motionless nucleus of charge Ze. The result has the form of a double finite sum involving the generalized hypergeometric functions i F of the unit argument. Our general expression agrees with formulas obtained analytically earlier by other authors for some particular states of the atom. We present also numerical values of the magnetizability for some excited states of selected hydrogenlike ions with 1 ≲ Z ≲ 137 and compare them with data available in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
19. Exact quasinormal modes for the near horizon Kerr metric.
- Author
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Cvetič, M. and Gibbons, G. W.
- Subjects
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KERR black holes , *KERR field , *SPHERICAL harmonics , *HYPERGEOMETRIC functions , *STRING theory , *ANGULAR momentum (Mechanics) - Abstract
We study the quasinormal modes of a massless scalar field in a general subextreme Kerr background by exploiting the hidden SL(2,R)×SL(2,R)×SO(3) symmetry of the subtracted geometry approximation. This faithfully models the near horizon geometry but locates the black hole in a confining asymptotically conical box analogous to the anti-de Sitter backgrounds used in string theory. There are just two series of modes, given in terms of hypergeometric functions and spherical harmonics, reminiscent of the left-moving and right-moving degrees in string theory: one is overdamped, and the other is underdamped and exhibits rotational splitting. The remarkably simple exact formulas for the complex frequencies would in principle allow the determination of the mass and angular momentum from observations of a black hole. No black hole bomb is possible because the Killing field which corotates with the horizon is everywhere timelike outside the black hole. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
20. Precise critical exponents of the O(N)-symmetric quantum field model using hypergeometric-Meijer resummation.
- Author
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Shalaby, Abouzeid M.
- Subjects
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CRITICAL exponents , *CONFORMAL mapping , *RENORMALIZATION group , *HYPERGEOMETRIC functions , *GROWTH factors , *FORECASTING - Abstract
In this work, we show that one can select different types of hypergeometric approximants for the resummation of divergent series with different large-order growth factors. Being of n! growth factor, the divergent series for the ϵ expansion of the critical exponents of the O(N)-symmetric model is approximated by the hypergeometric functions k+1Fk-1. The divergent k+1Fk-1 functions are then resummed using their equivalent Meijer-G function representation. The convergence of the resummation results for the exponents ν, η, and ω has been shown to improve systematically in going from low order to the highest known six-loop order. Our six-loop resummation results are very competitive to the recent six-loop Borel with conformal mapping predictions and to recent Monte Carlo simulation results. To show that precise results extend for high N values, we listed the five-loop results for ν which are very accurate as well. The recent seven-loop order (g series) for the renormalization group functions β,γϕ2, and γm² has been resummed too. Accurate predictions for the critical coupling and the exponents ν, η, and ω have been extracted from β, γϕ², and γm² approximants. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
21. Analytic calculation of the edge components of the angular Fock coefficients.
- Author
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Liverts, Evgeny Z.
- Subjects
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REPRESENTATION theory , *HYPERGEOMETRIC functions , *EDGES (Geometry) - Abstract
The present paper constitutes a development of our previous work devoted to calculations of the angular Fock coefficients ψk,p(α,θ). Explicit analytic representations for the edge components ψk,0(0) and ψk,0(k) with k≤8 are derived. The methods developed enable such a calculation for arbitrary k. The single-series representation for subcomponent ψ3,0(2e) missed in the author's previous paper is developed. It is also shown how to express some of the complicated subcomponents through hypergeometric and elementary functions. Using the operator FindSequenceFunction of Wolfram's Mathematica, simple explicit representations for some complicated mathematical expressions under consideration have been obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
22. Models for saccadic motion and postsaccadic oscillations.
- Author
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Del Punta, J. A., Rodriguez, K. V., Gasaneo, G., and Bouzat, S.
- Subjects
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OSCILLATIONS , *VISCOSITY , *MOTION , *HYPERGEOMETRIC functions , *ANALYTICAL solutions - Abstract
In a recent letter [S. Bouzat et al., Phys. Rev. Lett. 120, 178101 (2018)], a mathematical model for eyeball and pupil motion was developed allowing for the understanding of the postsaccadic oscillations (PSO) as inertial effects. The model assumes that the inner part of the iris, which defines the pupil, moves driven by inertial forces induced by the eyeball rotation, in addition to viscous and elastic forces. Among other achievements, the model correctly reproduces eye-tracking experiments concerning PSO profiles and their dependence on the saccade size. In this paper we propose various extensions of the mentioned model, we provide analytical solutions, and we perform an exhaustive analysis of the dynamics. In particular, we consider a more general time dependence for the eyeball velocity enabling the description of saccades with vanishing initial acceleration. Moreover, we give the analytical solution in terms of hypergeometric functions for the constant parameter version of the model and we provide particular expressions for some cases of interest. We also introduce a new version of the model with inhomogeneous viscosity that can improve the fitting of the experimental results. Our analysis of the solutions explores the dependence of the PSO profiles on the system parameters for varying saccade sizes. We show that the PSO emerge in critical-like ways when parameters such as the elasticity of the iris, the global eyeball velocity, or the saccade size vary. Moreover, we find that the PSO profiles with the first overshoot smaller than the second one, which are usually observed in experiments, can be associated to parameter regions close to criticality. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
23. Universal formula for the stress-tensor contribution to scalar four-point functions.
- Author
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Giecold, Gregory
- Subjects
- *
SCALAR field theory , *STRAINS & stresses (Mechanics) , *STATISTICAL correlation , *PHASE diagrams , *HYPERGEOMETRIC functions , *CHIRALITY of nuclear particles , *MELLIN transform - Abstract
We illustrate the power and efficiency of a recently uncovered Mellin-space approach to AdS/CFT correlation functions by providing a universal formula for the four-scalar graviton-exchange Witten diagram for arbitrary CFT-dual scaling dimensions. Our result keeps the space-time dimension generic as well, and is expressed as a combination of just 11 hypergeometric functions. Such hypergeometric functions are related to scalar-exchange diagrams. In particular, if reverse engineered in terms of D functions, this might be viewed as a first step toward proving a long-standing conjecture by Dolan, Nirschl and Osborn pertaining to four-point correlators of chiral primary operators at strong coupling. Most importantly, the technology developed herein marks an additional development toward the long-anticipated computation of the four-point function of the Ɲ = 4 sYM stress tensor. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
24. Quasinormal modes for subtracted rotating and magnetized geometries.
- Author
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Cvetič, M., Gibbons, G. W., and Saleem, Z. H.
- Subjects
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MAGNETIZATION , *WAVE equation , *SCALAR field theory , *SUPERGRAVITY , *HYPERGEOMETRIC functions - Abstract
We obtain explicit separable solutions of the wave equation of massless minimally coupled scalar fields in the subtracted geometry of four-dimensional rotating and Melvin (magnetised) four-charge black holes of the STU model, a consistent truncation of maximally supersymmetric supergravity with four types of electromagnetic fields. These backgrounds possess a hidden SL(2,R)×SL(2,R)×SO(3) symmetry and faithfully model the near-horizon geometry of these black holes, but locate them in a confining asymptotically conical box. For each subtracted geometry we obtain two branches of quasinormal modes, given in terms of hypergeometric functions and spherical harmonics. One branch is over-damped and the other under-damped and they exhibit rotational splitting. No black hole bomb is possible because the Killing field which corotates with the horizon is everywhere timelike outside the black hole. A five-dimensional lift of these geometries is given locally by the product of a Bañados-Teitelboim-Zanelli black hole with a two-sphere. This allows an explicit analysis of the minimally coupled massive five-dimensional scalar field. Again, there are two branches, both damped; however, now their oscillatory parts are shifted by the quantized wave number k along the fifth circle direction. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
25. Multicanonical distribution: Statistical equilibrium of multiscale systems.
- Author
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Salazar, Domingos S. P. and Vasconcelos, Giovani L.
- Subjects
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STATISTICAL physics , *MULTISCALE modeling , *HYPERGEOMETRIC distribution , *LAGRANGIAN points , *TURBULENCE , *HYPERGEOMETRIC functions - Abstract
A multicanonical formalism is introduced to describe the statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales, where the hierarchical structure is described as a set of nested "internal heat reservoirs" with fluctuating "temperatures." The probability distribution of states at small scales is written as an appropriate averaging of the large-scale distribution (the Boltzmann-Gibbs distribution) over these effective internal degrees of freedom. For a large class of systems the multicanonical distribution is given explicitly in terms of generalized hypergeometric functions. As a concrete example, it is shown that generalized hypergeometric distributions describe remarkably well the statistics of acceleration measurements in Lagrangian turbulence. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
26. Reaction-diffusion process driven by a localized source: First-passage properties.
- Author
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Krapivsky, P. L.
- Subjects
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DIFFUSION processes , *REACTION-diffusion equations , *PROBABILITY theory , *HYPERGEOMETRIC functions , *DIMENSIONS , *ATOMS , *COLLISIONS (Physics) - Abstract
We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We start with only immobile atoms uniformly distributed throughout the entire space. Diffusing atoms are injected at the origin by a source that is turned on at time t = 0. When a diffusing atom collides with an immobile atom, the two atoms form an immobile stable molecule. The region occupied by molecules is asymptotically spherical with radius growing as t1/d in d ≥ 2 dimensions. We investigate the survival probability that a diffusing atom has not become a part of a molecule during the time interval t after its injection. We show that, asymptotically, the survival probability (i) saturates in one dimension, (ii) vanishes algebraically with time in two dimensions (with exponent being a function of the dimensionless flux and determined as a zero of a confluent hypergeometric function), and (iii) exhibits a stretched exponential decay in three dimensions. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
27. Theory of 2D Transport in Graphene for Correlated Disorder.
- Author
-
Qiuzi Li, Hwang, E. H., Rossi, E., and Sarma, S. Das
- Subjects
- *
GRAPHENE , *POLYCYCLIC aromatic hydrocarbons , *COULOMB functions , *HYPERGEOMETRIC functions , *HYDROCARBONS - Abstract
We theoretically revisit graphene transport properties as a function of carrier density, taking into account possible correlations in the spatial distribution of the Coulomb impurity disorder in the environment. We find that the charged impurity correlations give rise to a density-dependent graphene conductivity, which agrees well qualitatively with the existing experimental data. We also find, quite unexpectedly, that the conductivity could increase with increasing impurity density if there is sufficient interimpurity correlation present in the system. In particular, the linearity (sublinearity) of graphene conductivity at lower (higher) gate voltage is naturally explained as arising solely from impurity correlation effects in the Coulomb disorder. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
28. Polarizabilities of two-electron positive ions with screened Coulomb potentials.
- Author
-
Zishi Jiang, Kar, Sabyasachi, and Ho, Y. K.
- Subjects
- *
COULOMB functions , *IONS , *ELECTRONS , *HYPERGEOMETRIC functions , *WAVE mechanics - Abstract
We have carried out calculations of the polarizabilities of the two-electron positive ions Li+, Be2+, B3+, C4+, N5+, and O6+ interacting with screened Coulomb potentials. Highly accurate correlated exponential wave functions are used to represent correlation effects on the charged particles. The dipole, quadrupole, and octupole polarizabilities for the screening parameters in the range 0-1a0-1 are reported. Reported results for the unscreened case are comparable with the available results and for the screened case show some interesting behavior with increasing nuclear charge. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
29. Explicit densities of multidimensional ballistic Lévy walks.
- Author
-
Magdziarz, Marcin and Zorawik, Tomasz
- Subjects
- *
LEVY processes , *BALLISTIC electrons , *STOCHASTIC models , *HYPERGEOMETRIC functions , *MONTE Carlo method - Abstract
Lévy walks have proved to be useful models of stochastic dynamics with a number of applications in the modeling of real-life phenomena. In this paper we derive explicit formulas for densities of the two- (2D) and three-dimensional (3D) ballistic Lévy walks, which are most important in applications. It turns out that in the 3D case the densities are given by elementary functions. The densities of the 2D Lévy walks are expressed in terms of hypergeometric functions and the right-side Riemann-Liouville fractional derivative, which allows us to efficiently evaluate them numerically. The theoretical results agree perfectly with Monte Carlo simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
30. Experimental test of the quadratic approximation in the partially correlated speed-dependent hard-collision profile.
- Author
-
De Vizia, M. D., Castrillo, A., Fasci, E., Amodio, P., Moretti, L., and Gianfrani, L.
- Subjects
- *
QUANTUM correlations , *APPROXIMATION theory , *COLLISIONS (Nuclear physics) , *HYPERGEOMETRIC functions , *ABSORPTION spectra , *PARAMETERS (Statistics) - Abstract
We report on the outcomes of a specific study on the quadratic approximation in the partially correlated speed-dependent hard-collision (pC-SDHC) model, which is currently the recommended profile to replace the Voigt convolution for the shape of an isolated line, when perturbed by neutral gas-phase molecules. In particular, we compared the quadratic approximation with the hypergeometric dependence of the collisional relaxation rate on the absorber velocity by using high-quality H218O absorption spectra, in coincidence with three vibration-rotation transitions of the ν1+ν3 band, at 1.39 µm, also by looking for possible differences in the retrieved parameters. The pC-SDHC profile was found to be quite robust, regardless of the choice of the particular speed dependence. The pressure broadening and shifting parameters, retrieved by using the quadratic and hypergeometric versions, were found to be fully consistent, provided that the velocity-changing collision frequency νvc was considered as a free parameter. Similarly, the integrated absorbance was found to be completely unaffected by the choice of the speed dependence, in the entire pressure range we have explored. It must be noted, however, that the velocity-changing collision frequency resulted to be largely overestimated compared to the expected one when using the quadratic approximation. Moreover, the νvc values from the quadratic approximation are always significantly larger than those of the hypergeometric model. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
31. The algebraic structure of cut Feynman integrals and the diagrammatic coaction
- Author
-
UCL - SST/IRMP - Institut de recherche en mathématique et physique, Duhr, Claude, UCL - SST/IRMP - Institut de recherche en mathématique et physique, and Duhr, Claude
- Abstract
We study the algebraic and analytic structure of Feynman integrals by proposing an operationthat maps an integral into pairs of integrals obtained from a master integrand and a correspondingmaster contour. This operation is a coaction. It reduces to the known coaction on multiple poly-logarithms, but applies more generally, e.g. to hypergeometric functions. The coaction also appliesto generic one-loop Feynman integrals with any configuration of internal and external masses, andin dimensional regularization. In this case, we demonstrate that it can be given a diagrammaticrepresentation purely in terms of operations on graphs, namely contractions and cuts of edges.The coaction gives direct access to (iterated) discontinuities of Feynman integrals and facilitatesa straightforward derivation of the differential equations they admit. In particular, the differen-tial equations for any one-loop integral are determined by the diagrammatic coaction using limitedinformation about their maximal, next-to-maximal, and next-to-next-to-maximal cuts.
- Published
- 2017
32. Evidence for the exchange effect in the β decay of 241Pu.
- Author
-
Mougeot, X., Bé, M.-M., Bisch, C., and Loidl, M.
- Subjects
- *
RADIOACTIVE decay , *POLYURETHANES , *NUMERICAL solutions to equations , *HYPERGEOMETRIC functions , *RADIOISOTOPES , *ELECTRONS - Abstract
The exchange effect has been previously given as a possible explanation for a significant deviation from an allowed shape observed at low energy in the 241 Pu β spectrum. Calculations set out here confirm that this atomic effect explains a large part of this deviation. The equations needed to calculate the exchange effect are detailed, as well as the evaluation of the confluent hypergeometnc function for complex arguments of large magnitudes. After a review of the possible other effects that could explain the remaining discrepancy at low energy, the screening correction using effective nuclear charges seems to be the best explanation. For radionuclides with high Z, this work has demonstrated the necessity to take into account the spatial variation of the nuclear charge experienced by the ejected electron to accurately correct for the screening effect. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
33. Wilson loops to 20th order numerical stochastic perturbation theory.
- Author
-
Horsley, R., Hotzel, G., Ilgenfritz, E.-M., Millo, R., Perlt, H., Rakow, P. E. L., Nakamura, Y., Schierholz, G., and Schiller, A.
- Subjects
- *
STOCHASTIC systems , *QUANTUM perturbations , *LATTICE dynamics , *GAUGE field theory , *HYPERGEOMETRIC functions , *GENERALIZATION - Abstract
We calculate perturbative contributions of Wilson loops of various sizes up to order 20 in SU(3) pure lattice gauge theory at different lattice sizes for the Wilson gauge action using the technique of numerical stochastic perturbation theory. This allows us to investigate the perturbative series for various Wilson loops at high orders of the perturbation theory. We observe differences in the behavior of the series as a function of the loop order n. Up to n = 20 we do not find evidence for the factorial growth of the expansion coefficients often assumed to characterize an asymptotic series. Based on the actually observed behavior we sum the series in a model parametrized by hypergeometric functions. For Wilson loops of moderate sizes the summed series in boosted perturbation theory reach stable plateaus for moderate perturbative order already. The coefficients in the boosted series become much more stable in the result of smoothing the coefficients of the original series effected by the hypergeometric model. We introduce generalized ratios of Wilson loops of different sizes. Together with the corresponding Wilson loops from standard Monte Carlo measurements they enable us to assess their nonperturbative parts. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
34. Lens partition function, pentagon identity, and star-triangle relation.
- Author
-
Bozkurt, Deniz N., Gahramanov, Ilmar, and Mullahasanoglu, Mustafa
- Subjects
- *
YANG-Baxter equation , *PARTITION functions , *HYPERBOLIC functions , *STATISTICAL mechanics , *STATISTICAL models , *HYPERGEOMETRIC functions - Abstract
We study the three-dimensional lens partition function for N=2 supersymmetric gauge dual theories on S³/Zr by using the gauge/Yang-Baxter equation correspondence. This correspondence relates supersymmetric gauge theories to exactly solvable models of statistical mechanics. The equality of partition functions for the three-dimensional supersymmetric dual theories can be written as an integral identity for hyperbolic hypergeometric functions. We obtain such an integral identity which can be written as the star-triangle relation for Ising type integrable models and as the integral pentagon identity. The latter represents the basic 2-3 Pachner move for triangulated 3-manifolds. A special case of our integral identity can be used for proving orthogonality and completeness relation of the Clebsch-Gordan coefficients for the self-dual continuous series of Uq(osp(1|2)). [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
35. Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system
- Author
-
Battista, Emmanuele, Dell' Agnello, Simone, Esposito, Giampiero, Simo, Jules, Battista, Emmanuele, Dell' Agnello, Simone, Esposito, Giampiero, and Simo, Jules
- Abstract
Recent work in the literature has shown that the one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., at the Lagrangian libration points of stable equilibrium the planetoid is not exactly at equal distance from the two bodies of large mass, but the Newtonian values of its coordinates are changed by a few millimeters in the Earth-Moon system. First, we assess such a theoretical calculation by exploiting the full theory of the quintic equation, i.e., its reduction to Bring-Jerrard form and the resulting expression of roots in terms of generalized hypergeometric functions. By performing the numerical analysis of the exact formulas for the roots, we confirm and slightly improve the theoretical evaluation of quantum corrected coordinates of Lagrangian libration points of stable equilibrium. Second, we prove in detail that also for collinear Lagrangian points the quantum corrections are of the same order of magnitude in the Earth-Moon system. Third, we discuss the prospects to measure, with the help of laser ranging, the above departure from the equilateral triangle picture, which is a challenging task. On the other hand, a modern version of the planetoid is the solar sail, and much progress has been made, in recent years, on the displaced periodic orbits of solar sails at all libration points, both stable and unstable. The present paper investigates therefore, eventually, a restricted three-body problem involving Earth, Moon and a solar sail. By taking into account the one-loop quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist.
- Published
- 2015
36. Nonperturbative Quantum Physics from Low-Order Perturbation Theory.
- Author
-
Mera, Héctor, Pedersen, Thomas G., and Nikolić, Branislav K.
- Subjects
- *
QUANTUM theory , *QUANTUM perturbations , *STARK effect , *QUANTUM tunneling , *BOREL sets , *COUPLING constants , *GROUND state energy - Abstract
The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
37. Diffusion of finite-sized hard-core interacting particles in a one-dimensional box: Tagged particle dynamics
- Author
-
Massachusetts Institute of Technology. Department of Chemistry, Ambjornsson, T., Lizana, L., Massachusetts Institute of Technology. Department of Chemistry, Ambjornsson, T., and Lizana, L.
- Abstract
We solve a nonequilibrium statistical-mechanics problem exactly, namely, the single-file dynamics of N hard-core interacting particles (the particles cannot pass each other) of size Δ diffusing in a one-dimensional system of finite length L with reflecting boundaries at the ends. We obtain an exact expression for the conditional probability density function ρT(yT,t∣yT,0) that a tagged particle T (T=1,…,N) is at position yT at time t given that it at time t=0 was at position yT,0. Using a Bethe ansatz we obtain the N-particle probability density function and, by integrating out the coordinates (and averaging over initial positions) of all particles but particle T, we arrive at an exact expression for ρT(yT,t∣yT,0) in terms of Jacobi polynomials or hypergeometric functions. Going beyond previous studies, we consider the asymptotic limit of large N, maintaining L finite, using a nonstandard asymptotic technique. We derive an exact expression for ρT(yT,t∣yT,0) for a tagged particle located roughly in the middle of the system, from which we find that there are three time regimes of interest for finite-sized systems: (A) for times much smaller than the collision time t«τcoll=1/(ϱ2D), where ϱ=N/L is the particle concentration and D is the diffusion constant for each particle, the tagged particle undergoes a normal diffusion; (B) for times much larger than the collision time t«τcoll but times smaller than the equilibrium time t«τeq=L2/D, we find a single-file regime where ρT(yT,t∣yT,0) is a Gaussian with a mean-square displacement scaling as t1/2; and (C) for times longer than the equilibrium time t«τeq, ρT(yT,t∣yT,0) approaches a polynomial-type equilibrium probability density function. Notably, only regimes (A) and (B) are found in the previously considered infinite systems., Danish National Research Foundation, Knut and Alice Wallenberg Foundation
- Published
- 2011
38. Velocity correlations of a discrete-time totally asymmetric simple-exclusion process in stationary state on a circle.
- Author
-
Yamada, Yasuyuki and Katori, Makoto
- Subjects
- *
DISCRETE-time systems , *DISTRIBUTION (Probability theory) , *INFORMATION asymmetry , *FINITE element method , *STATIONARY processes , *PARTICLES (Nuclear physics) - Abstract
The discrete-time version of totally asymmetric simple-exclusion process (TASEP) on a finite one-dimensional lattice is studied with the periodic boundary condition. Each particle at a site hops to the next site with probability 0 ≤ p ≤ 1 if the next site is empty. This condition can be rephrased by the condition that the number n of vacant sites between the particle and the next particle is positive. Then the average velocity is given by a product of the hopping probability p and the probability that n ≥ 1. By mapping the TASEP to another driven diffusive system called the zero-range process, it is proved that the distribution function of vacant sites in the stationary state is exactly given by a factorized form. We define k-panicle velocity correlation function as the expectation value of a product of velocities of k panicles in the stationary distribution. It is shown that it does not depend on positions of k particles on a circle but depends only on the number k. We give explicit expressions for all velocity correlation functions using the Gauss hypergeometric functions. Covariance of velocities of two particles is studied in detail, and we show that velocities become independent asymptotically in the thermodynamic limit. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
39. Product of Ginibre matrices: Fuss-Catalan and Raney distributions.
- Author
-
Penson, Karol A. and Zyczkowski, Karol
- Subjects
- *
DISTRIBUTION (Probability theory) , *MELLIN transform , *HYPERGEOMETRIC distribution , *GENERALIZATION , *CLEBSCH-Gordan coefficients - Abstract
Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distributions Ps(x), such that their moments are equal to the Fuss-Catalan numbers of order s. We find a representation of the Fuss-Catalan distributions Ps(x) in terms of a combination of s hypergeometric functions of the type sFs-1. The explicit formula derived here is exact for an arbitrary positive integer s, and for s=1 it reduces to the Marchenko-Pastur distribution. Using similar techniques, involving the Mellin transform and the Meijer G function, we find exact expressions for the Raney probability distributions, the moments of which are given by a two-parameter generalization of the Fuss-Catalan numbers. These distributions can also be considered as a two-parameter generalization of the Wigner semicircle law. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
40. Multiple Series Representations of N-fold Mellin-Barnes Integrals.
- Author
-
Ananthanarayan, B., Banik, Sumit, Friot, Samuel, and Ghosh, Shayan
- Subjects
- *
QUANTUM field theory , *FEYNMAN integrals , *SOLID state physics , *MATHEMATICAL physics , *INTEGRALS , *HEXAGONS - Abstract
Mellin-Barnes (MB) integrals are well-known objects appearing in many branches of mathematics and physics, ranging from hypergeometric functions theory to quantum field theory, solid-state physics, asymptotic theory, etc. Although MB integrals have been studied for more than one century, until now there has been no systematic computational technique of the multiple series representations of N-fold MB integrals for N>2. Relying on a simple geometrical analysis based on conic hulls, we show here a solution to this important problem. Our method can be applied to resonant (i.e., logarithmic) and nonresonant cases and, depending on the form of the MB integrand, it gives rise to convergent series representations or diverging asymptotic ones. When convergent series are obtained, the method also allows, in general, the determination of a single "master series" for each series representation, which considerably simplifies convergence studies and/or numerical checks. We provide, along with this Letter, a Mathematica implementation of our technique with examples of applications. Among them, we present the first evaluation of the hexagon and double box conformal Feynman integrals with unit propagator powers. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
41. Solution to urn models of pairwise interaction with application to social, physical, and biological sciences.
- Author
-
Pickering, William and Chjan Lim
- Subjects
- *
SOCIAL sciences , *LIFE sciences , *PHYSICAL sciences - Abstract
We investigate a family of urn models that correspond to one-dimensional random walks with quadratic transition probabilities that have highly diverse applications. Well-known instances of these two-urn models are the Ehrenfest model of molecular diffusion, the voter model of social influence, and the Moran model of population genetics. We also provide a generating function method for diagonalizing the corresponding transition matrix that is valid if and only if the underlying mean density satisfies a linear differential equation and express the eigenvector components as terms of ordinary hypergeometric functions. The nature of the models lead to a natural extension to interaction between agents in a general network topology. We analyze the dynamics on uncorrelated heterogeneous degree sequence networks and relate the convergence times to the moments of the degree sequences for various pairwise interaction mechanisms. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
42. Exact Mass-Coupling Relation for the Homogeneous Sine-Gordon Model.
- Author
-
Bajnok, Zoltán, Balog, János, Katsushi Ito, Yuji Satoh, and Tóth, Gábor Zsolt
- Subjects
- *
SINE-Gordon equation , *CONFORMAL field theory , *MASS (Physics) - Abstract
We derive the exact mass-coupling relation of the simplest multiscale quantum integrable model, i.e., the homogeneous sine-Gordon model with two mass scales. The relation is obtained by comparing the perturbed conformal field theory description of the model valid at short distances to the large distance bootstrap description based on the model's integrability. In particular, we find a differential equation for the relation by constructing conserved tensor currents, which satisfy a generalization of the Θ sum rule Ward identity. The mass-coupling relation is written in terms of hypergeometric functions. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
43. Thermodynamics of Asymptotically Conical Geometries.
- Author
-
Cvetič, Miijam, Gibbons, Gary W., and Saleem, Zain H.
- Subjects
- *
THERMODYNAMIC potentials , *ANGULAR momentum (Mechanics) , *GRAVITATIONAL mass , *ENERGY density , *HYPERGEOMETRIC functions - Abstract
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
44. Closed-form expression for the magnetic shielding constant of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function.
- Author
-
Stefańska, Patrycja
- Subjects
- *
MAGNETIC shielding , *GREEN'S functions , *COULOMB functions - Abstract
We present analytical derivation of the closed-form expression for the dipole magnetic shielding constant of a Dirac one-electron atom being in an arbitrary discrete energy eigenstate. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, uniform, and time independent. With respect to the atomic nucleus we assume that it is pointlike, spinless, motionless, and of charge Ze. Calculations are based on the Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); erratum R. Szmytkowski, J. Phys. B 30, 2747(E) (1997)], combined with the theory of hypergeometric functions. The final result is of an elementary form and agrees with corresponding formulas obtained earlier by other authors for some particular states of the atom. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
45. Static electric multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function.
- Author
-
Szmytkowski, Radosław and Łukasik, Grzegorz
- Subjects
- *
GREEN'S functions , *GROUND state (Quantum mechanics) - Abstract
The ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite 2L polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 825 (1997); erratum R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 2747 (1997)] is used to derive closed-form analytical expressions for various far-field and near-nucleus static electric multipole susceptibilities of the atom. The far-field multipole susceptibilities--the polarizabilities αL, the electric-to-magnetic cross susceptibilities αEL → M(L ∓ 1), and the electric-to-toroidal-magnetic cross susceptibilities αEL → TL--are found to be expressible in terms of one or two nonterminating generalized hypergeometric functions F2 with the unit argument. Counterpart formulas for the near-nucleus multipole susceptibilities--the electric nuclear shielding constants σEL → EL, the near-nucleus electric-to-magnetic cross susceptibilities σEL → M(L ∓ 1), and the near-nucleus electric-to-toroidal-magnetic cross susceptibilities σEL → TL--involve one or two terminating F2(1) series and for each L may be rewritten in terms of elementary functions. Numerical values of the far-field dipole, quadrupole, octupole, and hexadecapole susceptibilities are provided for selected hydrogenic ions. The effect of a declared uncertainty in the CODATA 2014 recommended value of the fine-structure constant α on the accuracy of numerical results is investigated. Analytical quasirelativistic approximations, valid to the second order in αZ, where Z is the nuclear charge number, are also derived for all types of the far-field and near-nucleus susceptibilities considered in the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
46. Magnetic-field-induced electric quadrupole moments for relativistic hydrogenlike atoms: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function.
- Author
-
Stefańska, Patrycja
- Subjects
- *
QUADRUPOLE moments , *DIRAC function , *GREEN'S functions - Abstract
We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength B of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); J. Phys. B 30, 2747 (1997)], We derive a closed-form expression for the electric quadrupole moment induced in the atom in an arbitrary discrete energy eigenstate. The result, which has the form of a double finite sum involving the generalized hypergeometric functions 3F2 of the unit argument, agrees with the earlier relativistic formula for that quantity, obtained by us for the ground state of the atom. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
47. Statistics of black hole radiance and the horizon area spectrum.
- Author
-
Bekenstein, Jacob D.
- Subjects
- *
BLACK holes , *KERR black holes , *QUANTUM field theory , *SPACETIME , *EIGENVALUES , *HYPERGEOMETRIC functions - Abstract
The statistical response of a Kerr black hole to incoming quantum radiation has heretofore been studied by the methods of maximum entropy or quantum field theory in curved spacetime. Neither approach pretends to take into account the quantum structure of the black hole itself. To address this last issue we calculate here the conditional probability distribution associated with the hole's response by assuming that the horizon area has a discrete quantum spectrum, and that its quantum evolution corresponds to jumps between adjacent area eigenvalues, possibly occurring in series, with consequent emission or absorption of quanta, possibly in the same mode. This "atomic model" of the black hole is implemented in two different ways and recovers the previously calculated radiation statistics in both cases. The corresponding conditional probability distribution is here expressed in closed form in terms of a hypergeometric function. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
48. Analytical approach to the two-site Bose-Hubbard model: From Fock states to Schrödinger cat states and entanglement entropy.
- Author
-
Dell'Anna, Luca
- Subjects
- *
BOSONS , *SCHRODINGER equation , *ENTROPY , *INTERPOLATION , *HYPERGEOMETRIC functions , *SYMMETRY (Physics) , *MODULES (Algebra) - Abstract
We study the interpolation from occupation number Fock states to Schrödinger cat states on systems modeled by a two-mode Bose-Hubbard Hamiltonian, like, for instance, bosons in a double well or superconducting Cooper pair boxes. In the repulsive interaction regime, by a simplified single particle description, we calculate analytically energy, number fluctuations, stability under coupling to a heat bath, entanglement entropy, and Fisher information, all in terms of hypergeometric polynomials of the single particle overlap parameter. Our approach allows us to find how those quantities scale with the number of bosons. In the attractive interaction regime we calculate the same physical quantities in terms of the imbalance parameter, and find that the spontaneous symmetry breaking, occurring at interaction Uc, predicted by a semiclassical approximation, is valid only in the limit of infinite number of bosons. For a large but finite number we determine a characteristic strength of interaction U*, which can be promoted as the crossover point from coherent to incoherent regimes and can be identified as the threshold of fragility of the cat state. Moreover, we find that the Fisher information is always in direct ratio to the variance of on-site number of bosons, for both positive and negative interactions. We finally show that the entanglement entropy is maximum close to U* and exceeds its coherent value within the whole range of interaction between 2Ucand zero. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
49. Confluent conformal blocks and the Teukolsky master equation.
- Author
-
Carneiro da Cunha, Bruno and Paulo Cavalcante, João
- Subjects
- *
RIEMANN-Hilbert problems , *KERR black holes , *EXPONENTIATION , *DIFFERENTIAL equations , *EQUATIONS , *HYPERGEOMETRIC functions , *CONFORMAL mapping - Abstract
Quasinormal modes of usual, four-dimensional, Kerr black holes are described by certain solutions of a confluent Heun differential equation. In this work, we express these solutions in terms of the connection matrices for a Riemann-Hilbert problem, which was recently solved in terms of the Painlevé V transcendent. We use this formulation to generate small-frequency expansions for the angular spheroidal harmonic eigenvalue and derive conditions on the monodromy properties for the radial modes. Using exponentiation, we relate the accessory parameter to a semiclassical conformal description and discuss the properties of the operators involved. For the radial equation, while the operators at the horizons have Liouville momenta proportional to the entropy intake, we find that spatial infinity is described by a Whittaker operator. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
50. Two-body Coulomb problems with sources
- Author
-
L. U. Ancarani and Gustavo Gasaneo
- Subjects
Physics ,Partial differential equation ,Confluent hypergeometric function ,Differential equation ,Ciencias Físicas ,Sources ,Non-homogeous problems ,purl.org/becyt/ford/1.3 [https] ,Generalized hypergeometric function ,Atomic and Molecular Physics, and Optics ,purl.org/becyt/ford/1 [https] ,Method of undetermined coefficients ,Astronomía ,Coulomb wave function ,Quantum mechanics ,Coulomb problem ,Scattering theory ,Hypergeometric function ,CIENCIAS NATURALES Y EXACTAS ,Mathematical physics - Abstract
The two-body Coulomb Schrödinger equation with different types of nonhomogeneities are studied. The particular solution of these nonhomogeneous equations is expressed in closed form in terms of a two-variable hypergeometric function. A particular representation of the latter allows one to study efficiently the solution in the asymptotic limit of large values of the coordinate and hence the associated physics. Simple sources are first considered, and a complete analysis of scattering and bound states is performed. The solutions corresponding to more general (arbitrary) sources are then provided and written in terms of more general hypergeometric functions. © 2010 The American Physical Society. Fil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Física; Argentina Fil: Ancarani, L.U.. Université Paul Verlaine-Metz; Francia
- Published
- 2010
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