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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]

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]

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]

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]

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]

I compute the contributions of the one-loop single-real-emission amplitudes, gg → Hg, qg → Hq, etc., to inclusive Higgs boson production through next-to-next-to-next-to-leading order (N³LO) in the strong coupling αs. The next-to-leading and next-to-next-to-leading order terms are computed in closed form, in terms of G functions and the hypergeometric functions 2F¹ and 3F². I compute the N³LO terms as Laurent expansions in the dimensional regularization parameter through order (ε¹). To obtain the N³LO terms, I perform an extended threshold expansion of the phase space integrals and map the resulting coefficients onto a basis of harmonic polylogarithms. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]