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Different frameworks exist to describe the flat-space limit of AdS/CFT, include momentum space, Mellin space, coordinate space, and partial-wave expansion. We explain the origin of momentum space as the smearing kernel in Poincare AdS, while the origin of latter three is the smearing kernel in global AdS. In Mellin space, we find a Mellin formula that unifies massless and massive flat-space limit, which can be transformed to coordinate space and partial-wave expansion. Furthermore, we also manage to transform momentum space to smearing kernel in global AdS, connecting all existed frameworks. Finally, we go beyond scalar and verify that $\langle VV\mathcal{O}\rangle$ maps to photon-photon-massive amplitudes., 57 pages, 12 figures, latex; comments added, refs added; the version to appear on JHEP

We obtain an analytic description of the excitation front propagation in a medium during nonstationary superdiffusive (nonlocal) transport in the case of a finite fixed velocity of perturbation carriers (so-called Levy walks with stops). This problem embraces phenomena such as resonance radiation transport in astrophysical gases and plasma, biological migration, and energy transfer by waves in a plasma. In this approach, the result obtained by integrating the exact solution to the kinetic equation for the Green function is independent of the coordinate space dimensionality. The results are compared with data obtained using another more exact method of determining the front and with the results of numerical calculations of the statistics of trajectories using the Monte Carlo method. Comparison demonstrates the applicability of our results in a wide range of parameters of the problem. We propose a universal description of the perturbation front dynamics in the medium for an arbitrary (including infinitely high) fixed velocity of perturbation carriers. This corresponds to the combination of expressions for the front in the case of transport by Levy flights and by Levy walks. We consider the criteria of transition between these regimes of the superdiffusive transport, which corresponds, in particular, to the account for the finite velocity of light in the superdiffusive transport of resonance radiation in gases and plasmas. For Levy walks, we have obtained a relation between the integral characteristic of perturbation of the medium and its carriers.

The rank of the sparse signals brought by multiple measurement vectors (MMV) augments the performance of joint sparse recovery. In general, suppose the sparsity level $ k$ is less than or equal to $ [rank(\boldsymbol{X})+spark(\boldsymbol{A})-1]/2$ , the sparsest solution of the MMV problem is unique and recoverable via various methods. It is shown in this letter that the unique solution of the sparsity level $ k$ up to $ spark(\boldsymbol{A})-1$ actually exists in a measure theoretical point of view. More specifically, even when $ [rank(\boldsymbol{X})+spark(\boldsymbol{A})-1]/2\leq k , the sparsest solution to $ \boldsymbol{A}\boldsymbol{X}=\boldsymbol{Y}$ is still unique with full Lebesgue measure in every $ k$ -sparse coordinate space. This phenomenon is fully confirmed by the MMV tail- $ \ell _{2,1}$ minimization technique. Furthermore, the phenomenon that the traditional $ \ell _{2,1}$ minimization actually fails to recover $ \boldsymbol{X}$ with $ k \geq [spark(\boldsymbol{A})-1]/2$ is investigated from the same perspective of measure theory. Extensive numerical tests conducted by the MMV tail- $ \ell _{2,1}$ minimization and $ \ell _{2,1}$ minimization are demonstrated to confirm the findings. The tail minimization procedure exhibits the most prominent effectiveness for the larger sparsity levels among all known techniques.

Electrically charged particles are trapped by the Earth’s magnetic field, forming the Van Allen radiation belts. Observations show that electrons in this region can have energies in excess of 7 MeV. However, whether electrons at these ultra-relativistic energies are locally accelerated, arise from betatron and Fermi acceleration due to transport across the magnetic field, or if a combination of both mechanisms is required, has remained an unanswered question in radiation belt physics. Here, we present a unique way of analyzing satellite observations which demonstrates that local acceleration is capable of heating electrons up to 7 MeV. By considering the evolution of phase space density peaks in magnetic coordinate space, we observe distinct signatures of local acceleration and the subsequent outward radial diffusion of ultra-relativistic electron populations. The results have important implications for understanding the origin of ultra-relativistic electrons in Earth’s radiation belts, as well as in magnetized plasmas throughout the solar system., Electrons in the Van Allen radiation belts can have energies in excess of 7 MeV, however, the energization mechanism is debated. Here, the authors show phase space density peaks in magnetic coordinate space as a way of analyzing satellite observations which demonstrates that local acceleration is capable of heating electrons up to 7 MeV.

We employ another approach to quantize electromagnetic fields in the coordinate space, instead of the mode (or Fourier) space, such that local features of photons can be efficiently, physically, and more intuitively described. To do this, coordinate-ladder operators are defined from mode-ladder operators via the unitary transformation of systems involved in arbitrary inhomogeneous dielectric media. Then, one can expand electromagnetic field operators through the coordinate-ladder operators weighted by non-orthogonal and spatially-localized bases, which are propagators of initial quantum electromagnetic (complex-valued) field operators. Here, we call them QEM-CV-propagators. However, there are no general closed form solutions available for them. This inspires us to develop a quantum finite-difference time-domain (Q-FDTD) scheme to numerically time evolve QEM-CV-propagators. In order to check the validity of the proposed Q-FDTD scheme, we perform computer simulations to observe the Hong-Ou-Mandel effect resulting from the destructive interference of two photons in a 50/50 quantum beam splitter.

Einstein-Podolsky-Rosen (EPR) entanglement involving a pair of particles entangled in their positions and momenta is of special interest in the field of quantum information. Previously, EPR entanglement has been studied in different physical systems but in fixed coordinate spaces. Here, we demonstrate an experiment of ghost imaging and ghost interference in rotated position-momentum spaces by using position-momentum entangled photons generated from a hot atomic ensemble. By using different image objects, the measured position-momentum correlations exhibit intriguing dynamics, including gradual decrease and axis-independent EPR entanglement. The reported results on manipulating the EPR entanglement in rotating coordinate spaces hold promise in quantum communication and distant quantum image processing.

A four-state diabatic potential energy matrix (DPEM), Hd, for the description of the nonadiabatic quenching of OH(A2Σ+) by collisions with H2 is reported. The DPEM is constructed as a fit to adiabatic energies, energy gradients, and derivative couplings obtained exclusively from multireference configuration interaction wave functions. A four-adiabatic-electronic-state representation is used in order to describe all energetically accessible regions of the nuclear coordinate space. Partial permutation-inversion symmetry is incorporated into the representation. The fit is based on electronic structure data at 42 882 points, described by over 1.6 million least squares equations with a root mean square (mean unsigned) error of 178(83) cm−1. Comparison of ab initio and Hd determined minima, saddle points, and energy minimized points on C2v, Cs, C∞v, and C1 (noncoplanar) portions of two conical intersection seams are used to establish the accuracy of the Hd.

With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various structures and formations such as waves, vortices, turbulent pulsations and others. Such properties of the mathematical physics equations, which are hidden (they appear only in the process of solving these equations), depend on the consistency of derivatives in partial differential equations and on the consistency of equations, if the equations of mathematical physics are a set of equations. This is due to the integrability of mathematical physics equations. It is shown that the equations of mathematical physics can have double solutions, namely, the solutions on the original coordinate space and the solutions on integrable structures that are realized discretely (due to any degrees of freedom). The transition from the solutions of the first type to one of the second type describes discrete transitions and the processes of origin of various structures and observable formations. Only mathematical physics equations, on what no additional conditions such as the integrability conditions are imposed, can possess such properties. The results of the present paper were obtained with the help of skew-symmetric differential forms.

We perform canonical analysis of a model in which gravity is coupled to a spherically symmetric dust shell in 2+1 spacetime dimensions. The result is a reduced action depending on a finite number of degrees of freedom. The emphasis is made on finding canonical variables providing the global chart for the entire phase space of the model. It turns out that all the distinct pieces of momentum space could be assembled into a single manifold which has ADS^{2}-geometry, and the global chart for it is provided by the Euler angles. This results in both non-commutativity and discreteness in coordinate space, which allows to resolve the central singularity. We also find the map between ADS^{2} momentum space obtained here and momentum space in Kuchar variables, which could be helpful in extending the present results to 3+1 dimensions., 19 pages, 3 figures, conference

We examine skyrmionic field configurations on a spherical ferromagnet with large normal anisotropy. Exploiting variational concepts of angular momentum, we find a new family of localized solutions to the Landau–Lifshitz equation that are topologically distinct from the ground state and not equivariant. Significantly, we observe an emergent spin–orbit coupling on the level of magnetization dynamics in a simple system without individual rotational invariance in spin and coordinate space.

The equation of state of neutron and symmetric matter is calculated within the lowest order constrained variational (LOCV) method using the Argonne V18 (AV18) nucleon–nucleon interaction supplemented by the local, coordinate space versions of the chiral three-nucleon force (TNF) at next-to-next-to-leading order (N2LOL). We present the first results of studying the nuclear equation of state in the LOCV framework by employing a chiral TNF. It is shown that although some calculated values of saturation properties lie well in the empirically determined ranges, all of the saturation quantities can not be predicted simultaneously. We also study other possible parametrizations of the N2LOL TNF by fitting the low-energy constants (LECs) to nuclear saturation point. It is found that by employing the proposed sets of LECs, LOCV method is able to successfully produce the equilibrium properties of symmetric nuclear matter.

We study a puzzle raised recently regarding the running coupling prescription used in the calculation of forward particle production in proton-nucleus collisions at next-to-leading order: using a coordinate space prescription which is consistent with the one used in the high energy evolution of the target leads to results which can be two orders of magnitude larger than the ones obtained with a momentum space prescription. We show that this is an artefact of the Fourier transform involved when passing between coordinate and momentum space and propose a new coordinate space prescription which avoids this problem., Comment: 4 pages, 1 figure. Quark Matter 2018 proceedings

We present a general study of 3-point functions of conformal field theory in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWI' s), introduced in recent works by Bzowski, McFadden and Skenderis (BMS). We investigate and detail the structure of the CWI's, their non-perturbative solutions and the transition to momentum space, comparing them to perturbation theory by taking QED as an example. We then proceed with an analysis of the $TJJ$ correlator, presenting independent and detailed re-derivations of the conformal equations in the reconstruction method of BMS, originally formulated using a minimal tensor basis in the transverse traceless sector. A careful comparison with a second basis introduced in previous studies shows that this correlator is affected by one anomaly pole in the graviton (T) line, induced by renormalization. The result shows that the origin of the anomaly, in this correlator, should be necessarily attributed to the exchange of a massless effective degree of freedom. Our results are then exemplified in massless QED at one-loop in $d$-dimensions, expressed in terms of perturbative master integrals. An independent analysis of the Fuchsian character of the solutions, which bypasses the 3K integrals, is also presented. We show that the combination of field theories at one-loop - with a specific field content of degenerate massless scalar and fermions - is sufficient to generate the complete non-perturbative solution, in agreement with a previous study in coordinate space. The result shows that free conformal field theories, in specific dimensions, arrested at one-loop, reproduce the general result for the $TJJ$. Analytical checks of this correspondence are presented in $d=3,4$ and $5$ spacetime dimensions[..]., 79 pages, 3 Figures. Final version, with changes in section 8. Accepted for publication in Nuclear Physics B

Background: Recently, the researches of cluster structure have attracted considerable attention. Many microscopic structure models have been applied to describe the cluster configurations.Purpose: To better analyze the cluster structure and associate with the experimental observations, comparative studies are carried out in this paper by combining the nuclear structure model with the electron scattering theory.Method: The density distributions for candidate nuclei of normal and cluster states are obtained from the deformed relativistic Hartree-Bogoliubov (RHB) model. Using some moderate approximations, the corresponding Coulomb form factors $|{F}_{C}{(q)|}^{2}$ and inclusive cross sections for different configurations are calculated by the distorted wave Born approximation (DWBA) and coherent density fluctuation model (CDFM), respectively.Results: Comparing the $|{F}_{C}{(q)|}^{2}$ and inclusive cross sections of different configurations, the effects of nuclear cluster structure can be revealed, due to the differences of nuclear charge radii ${R}_{C}$ in coordinate space and the discrepancies of Fermi momentum ${k}_{F}$ in momentum space.Conclusions: Results illustrate that the cluster structure can be reflected from the elastic and inclusive electron scattering. The studies conducted in this paper provide a new approach to analyze the cluster configurations, and are also helpful to guide future electron scattering experiments.

Multi-configurational time-dependent Hartree (MCTDH) calculations using time-dependent grid representations can be used to accurately simulate high-dimensional quantum dynamics on general ab initio potential energy surfaces. Employing the correlation discrete variable representation, sets of direct product type grids are employed in the calculation of the required potential energy matrix elements. This direct product structure can be a problem if the coordinate system includes polar and azimuthal angles that result in singularities in the kinetic energy operator. In the present work, a new direct product-type discrete variable representation (DVR) for arbitrary sets of polar and azimuthal angles is introduced. It employs an extended coordinate space where the range of the polar angles is taken to be [-pi, pi]. The resulting extended space DVR resolves problems caused by the singularities in the kinetic energy operator without generating a very large spectral width. MCTDH calculations studying the F·CH4 complex are used to investigate important properties of the new scheme. The scheme is found to allow for more efficient integration of the equations of motion compared to the previously employed cot-DVR approach [G. Schiffel and U. Manthe, Chem. Phys. 374, 118 (2010)] and decreases the required central processing unit times by about an order of magnitude.

We study the Post-Minkowskian (PM) and Post-Newtonian (PN) expansions of the gravitational three-body effective potential. At order 2PM a formal result is given in terms of a differential operator acting on the maximal generalized cut of the one-loop triangle integral. We compute the integral in all kinematic regions and show that the leading terms in the PN expansion are reproduced. We then perform the PN expansion unambiguously at the level of the integrand. Finding agreement with the 2PN three-body potential after integration, we explicitly present new $G^2v^4$-contributions at order 3PN and outline the generalization to $G^2v^{2n}$. The integrals that represent the essential input for these results are obtained by applying the recent Yangian bootstrap directly to their $\epsilon$-expansion around three dimensions. The coordinate space Yangian generator that we employ to obtain these integrals can be understood as a special conformal symmetry in a dual momentum space., Comment: 15 pages, 5 figures, 1 ancillary machine-readable file, v2: minor improvements and additions, title adapted to journal title

We investigate the prospects of combining a standard momentum space approach for ultracold three-body scattering with efficient coordinate space schemes to solve the underlying two-body problem. In many of those schemes, the two-body problem is numerically restricted up to a finite interparticle distance ${r}_{\mathrm{b}}$. We analyze the effects of this two-body restriction on the two- and three-body level using pairwise square-well potentials that allow for analytic two-body solutions and more realistic Lennard-Jones van der Waals potentials to model atomic interactions. We find that the two-body $t$ operator converges exponentially in ${r}_{\mathrm{b}}$ for the square-well interaction. Setting ${r}_{\mathrm{b}}$ to 2000 times the range of the interaction, the three-body recombination rate can be determined accurately up to a few percent when the magnitude of the scattering length is small compared to ${r}_{\mathrm{b}}$, while the position of the lowest Efimov features is accurate up to the percent level. In addition, we find that with the introduction of a momentum cutoff, it is possible to determine the three-body parameter in good approximation even for deep van der Waals potentials.

In large-momentum effective theory (LaMET), calculating parton physics starts from calculating coordinate-space-$z$ correlation functions $\tilde h(z, a,P^z)$ in a hadron of momentum $P^z$ in lattice QCD. Such correlation functions involve both linear and logarithmic divergences in lattice spacing $a$, and thus need to be properly renormalized. We introduce a hybrid renormalization procedure to match these lattice correlations to those in the continuum $\overline{\rm MS}$ scheme, without introducing extra non-perturbative effects at large $z$. We analyze the effect of ${\cal O}(\Lambda_{\rm QCD})$ ambiguity in the Wilson line self-energy subtraction involved in this hybrid scheme. To obtain the momentum-space distributions, we recommend to extrapolate the lattice data to the asymptotic $z$-region using the generic properties of the coordinate space correlations at moderate and large $P^z$, respectively., Comment: Text revised, version to appear in NPB

We apply a recently developed momentum-space semilocally regularized chiral potential to the $^{2}\mathrm{H}$ and $^{3}\mathrm{He}$ photodisintegration processes and to the (anti)neutrino induced deuteron breakup reactions. Specifically, the differential cross section, the photon analyzing power, and the final proton polarization have been calculated for deuteron photodisintegration at photon energies of 30 and 100 MeV. For $^{3}\mathrm{He}$ photodisintegration, predictions for the semi-inclusive and exclusive differential cross sections are presented for photon energies up to 120 MeV. The total cross section is calculated for (anti)neutrino disintegration of the deuteron for (anti)neutrino energies below 200 MeV. Predictions based on the Argonne V18 potential and on an older chiral force with regularization applied in coordinate space are used for comparison. Using the fifth-order chiral nucleon-nucleon potential supplemented with dominant contributions from the sixth order allows us to obtain converged predictions for observables in the investigated reactions. Our results based on the newest semilocal chiral potentials show even smaller cutoff dependence and a somewhat faster convergence for the considered electroweak observables than the previously reported ones with a coordinate-space regulator, which make them a promising tool to study electroweak processes.

We present the first Monte Carlo based global QCD analysis of spin-averaged and spin-dependent parton distribution functions (PDFs) that includes nucleon isovector matrix elements in coordinate space from lattice QCD. We investigate the degree of universality of the extracted PDFs when the lattice and experimental data are treated under the same conditions within the Bayesian likelihood analysis. For the unpolarized sector, we find rather weak constraints from the current lattice data on the phenomenological PDFs, and difficulties in describing the lattice matrix elements at large spatial distances. In contrast, for the polarized PDFs we find good agreement between experiment and lattice data, with the latter providing significant constraints on the spin-dependent isovector quark and antiquark distributions., Comment: 23 pages, 4 figures

Single-particle resonances in the continuum are crucial for studies of exotic nuclei. In this study, the Green's function approach is employed to search for single-particle resonances based on the relativistic-mean-field model. Taking $^{120}$Sn as an example, we identify single-particle resonances and determine the energies and widths directly by probing the extrema of the Green's functions. In contrast to the results found by exploring for the extremum of the density of states proposed in our recent study [Chin. Phys. C, 44:084105 (2020)], which has proven to be very successful, the same resonances as well as very close energies and widths are obtained. By comparing the Green's functions plotted in different coordinate space sizes, we also found that the results very slightly depend on the space size. These findings demonstrate that the approach by exploring for the extremum of the Green's function is also very reliable and effective for identifying resonant states, regardless of whether they are wide or narrow., Comment: 8 pages, 4 figures, and 1 table

Within this work, we derive and analyse an expression for the free energy of a single-species system in the thermodynamic limit in terms of a generalised cavity volume, that is exact in general, and in principle applicable to systems across their entire range of density, as well as to particles within a general coordinate space. This provides a universal equation of state, and can thus relate the cavity volume to classical results, such as Mayer’s cluster expansions. Through this, we are able to provide some insight into the connections between cavity volume and free energy density, as well as their consequences. We use examples which permit explicit computations to further probe these results, reclaiming the exact results for a classical Tonks gas and providing a novel derivation of Onsager’s free energy for a single species, isotropic system. Given the complexity of the problem, we also provide a local lattice ansatz, exact in one dimension, with which we may approximate the cavity volume for hard sphere systems to provide an accurate equation of state in the cases of hard disks and spheres in both dilute regimes as well as beyond the freezing transition.

The origin of weakly bound objects like clusters and hypernuclei, observed in heavy-ion collisions, is of theoretical and experimental interest. It is in the focus of the experiments at the BNL Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) since it is not evident how such weakly bound objects can survive in an environment whose hadronic decay products point to a temperature of the order of 150 MeV. It is also one of the key research topics in the future facilities of FAIR and NICA, which are under construction in Darmstadt (Germany) and Dubna (Russia), respectively. The first results on the cluster dynamics within the model-independent cluster recognition library ``phase-space minimum spanning tree'' (psMST) applied to different transport approaches: PHQMD, PHSD, SMASH, and UrQMD are presented here. The psMST is based on the ``minimum spanning tree'' (MST) algorithm for the cluster recognition which exploits correlations in coordinate space, and it is extended to correlations of baryons in the clusters in momentum space. The sensitivity of the cluster formation on the microscopic realization of the $n$-body dynamics and on the potential interactions in heavy-ion collisions is shown.

We present a new math-physics modeling approach, called canonical quantization with numerical mode-decomposition, for capturing the physics of how incoming photons interact with finite-sized dispersive media, which is not describable by the previous Fano-diagonalization methods. The main procedure is to (1) study a system where electromagnetic (EM) fields are coupled to non-uniformly distributed Lorentz oscillators in Hamiltonian mechanics, (2) derive a generalized Hermitian eigenvalue problem for conjugate pairs in coordinate space, (3) apply computational electromagnetics methods to find a countably/finite set of time-harmonic eigenmodes that diagonalizes the Hamiltonian, and (4) perform the subsequent canonical quantization with mode-decomposition. Moreover, we provide several numerical simulations that capture the physics of full quantum effects, impossible by classical Maxwell's equations, such as non-local dispersion cancellation of an entangled photon pair and Hong-Ou-Mandel (HOM) effect in a dispersive beam splitter., Comment: submitted to Physical Review A (under review)

We investigate the role of high momentum components of optical model potentials for nucleon-nucleus scattering and its incidence on their nonlocal structure in coordinate space. The study covers closed-shell nuclei with mass number in the range $4\leq A\leq 208$, for nucleon energies from tens of MeV up to 1 GeV. To this purpose microscopic optical potentials are calculated using density-dependent off-shell $g$ matrices in Brueckner-Hartree-Fock approximation and based on Argonne $v_{18}$ as well as chiral 2$N$ force up to next-to-next-to-next-to-leading order. We confirm that the gradual suppression of high-momentum contributions of the optical potential results in quite different coordinate-space counterparts, all of them accounting for the same scattering observables. We infer a minimum cutoff momentum $Q$, function of the target mass number and energy of the process, that filters out irrelevant ultraviolet components of the potential. We find that when ultraviolet suppression is applied to Perey-Buck nonlocal potential or local Woods-Saxon potentials, they also result nonlocal with similar appearance to those obtained from microscopic models in momentum space. We examine the transversal nonlocality, quantity that makes comparable the intrinsic nonlocality of any potential regardless of its representation. We conclude that meaningful comparisons of nonlocal features of alternative potentials require the suppression of their ultraviolet components., 12 pages, 15 figures. Accepted for publication in EPJA

We present two-loop results for the quark condensate in an external magnetic field within chiral perturbation theory using coordinate space techniques. At finite temperature, we explore the impact of the magnetic field on the pion-pion interaction in the quark condensate for arbitrary pion masses and derive the correct weak magnetic field expansion in the chiral limit. At zero temperature, we provide the complete two-loop representation for the vacuum energy density and the quark condensate., Comment: 27 pages, 4 figures

A coordinate-space representation for a charged scalar particle propagator in a constant magnetic field was obtained as a series over the Landau levels. Using the recently developed modified Fock-Schwinger method, an intermediate expression was constructed and symmetrized, thus, allowing for factorization of the series terms into two factors. The first one, a sum of Bessel functions, depends on time and $z$-coordinate, where the $z$-axis is chosen to be a direction of the magnetic field, and has a structure similar to the propagator of a free field. The second one, a product of a Laguerre polynomial and a damping exponential, depends on $x,y$-coordinates, which form a plane perpendicular to the direction of the magnetic field, and ensures the localized propagation in the $x,y$-plane., 4 pages, 0 figures, submitted to Proceedings of ICPPA 2020

Time-dependent covariant density functional theory with the density functional PC-PK1 is developed in a three-dimensional coordinate space without any symmetry restrictions, and benchmark calculations for the $^{16}\mathrm{O}+^{16}\mathrm{O}$ reaction are performed systematically. The relativistic kinematics, the conservation laws of the momentum, total energy, and particle number, as well as the time-reversal invariance are examined and confirmed to be satisfied numerically. Two primary applications including the dissipation dynamics and above-barrier fusion cross sections are illustrated. The obtained results are in good agreement with the ones given by the nonrelativistic time-dependent density functional theory and the data available. This demonstrates that the newly developed time-dependent covariant density functional theory could serve as an effective approach for the future studies of nuclear dynamical processes.

Quantum Monte Carlo (QMC) belongs to the most accurate simulation techniques for quantum many-particle systems. However, for fermions, these simulations are hampered by the sign problem that prohibits simulations in the regime of strong degeneracy. The situation changed with the development of configuration path integral Monte Carlo (CPIMC) by Schoof et al. [Contrib. Plasma Phys. 51, 687 (2011)] that allowed for the first ab initio simulations for dense quantum plasmas [Schoof et al., Phys. Rev. Lett. 115, 130402 (2015)]. CPIMC also has a sign problem that occurs when the density is lowered, i.e., in a parameter range that is complementary to traditional QMC formulated in coordinate space. Thus, CPIMC simulations for the warm dense electron gas are limited to small values of the Brueckner parameter—the ratio of the interparticle distance to the Bohr radius—rs=r⎯⎯⎯/aB≲1 . In order to reach the regime of stronger coupling (lower density) with CPIMC, here we investigate additional restrictions on the Monte Carlo procedure. In particular, we introduce two different versions of “restricted CPIMC”—called RCPIMC and RCPIMC+—where certain sign changing Monte Carlo updates are being omitted. Interestingly, one of the methods (RCPIMC) has no sign problem at all, but it introduces a systematic error and is less accurate than RCPIMC+, which neglects only a smaller class of the Monte Carlo steps. Here, we report extensive simulations for the ferromagnetic uniform electron gas with which we investigate the properties and accuracy of RCPIMC and RCPIMC+. Furthermore, we establish the parameter range in the density–temperature plane where these simulations are both feasible and accurate. The conclusion is that RCPIMC and RCPIMC+ work best at temperatures in the range of Θ = kBT/EF ∼ 0.1…0.5, where EF is the Fermi energy, allowing to reach density parameters up to rs ∼ 3…5, thereby partially filling a gap left open by existing ab initio QMC methods.

We investigate the properties of neutral and charged pions in a constant background magnetic field mainly at zero temperature within the Nambu--Jona-Lasinio model. In the previous calculations, the Ritus method involving Schwinger phases in a fixed gauge was employed within the momentum-space random phase approximation (RPA) [M. Coppola et al., Phys. Lett. B 782, 155 (2018).]. However, gauge invariance of the charged pion masses has not yet been examined. In this work, by adopting the linear response theory based on the imaginary-time path integral formalism, we derive the correlation functions for pions in coordinate space, where the corresponding Schwinger phases show up automatically. At sufficiently large imaginary time $\ensuremath{\tau}$, the meson correlation function approaches an exponential form $\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}{E}_{\mathrm{G}}\ensuremath{\tau})$, where ${E}_{\mathrm{G}}$ is the ground-state energy of the one-meson state and hence determined as the meson mass. Furthermore, we show that the mass of the charged pions is gauge independent, i.e., independent of the choice of the vector potential for the magnetic field. Actually, we also find that the momentum-space RPA is equivalent to the imaginary-time method used here.

Collisionless media devoid of intrinsic stresses, for example, a dispersed phase in a multiphase medium, have a much wider variety of space-time structures and features formed in them than collisional media, for example, a carrier, gas, or liquid phase. This is a consequence of the fact that evolution in such media occurs in phase space, i.e., in a space of greater dimensions than the usual coordinate space. As a consequence, the process of the formation of features in collisionless media (clustering or vice versa, a loss of continuity) can occur primarily in the velocity space, which, in contrast to the features in the coordinate space (folds, caustics, or voids), is poorly observed directly. To identify such features, it is necessary to use visualization methods that allow us to consider, in detail, the evolution of the medium in the velocity space. This article is devoted to the development of techniques that allow visualizing the degree of anisotropy of the velocity fields of collisionless interpenetrating media. Simultaneously tracking the behavior of different fractions in such media is important, as their behavior can be significantly different. We propose three different techniques for visualizing the anisotropy of velocity fields using the example of two- and three-continuum dispersed media models. We proposed the construction of spatial distributions of eccentricity fields (scalar fields), or fields of principal directions of the velocity dispersion tensor (tensor fields). In the first case, we used some simple eccentricity functions for dispersion tensors for two fractions simultaneously, which we call surrogate entropy. In the second case, to visualize the anisotropy of the velocity fields of three fractions simultaneously, we used an ordered array (3-vector) of eccentricities for the color representation through decomposition in three basic colors. In the case of a multi-stream flow, we used cluster analysis methods to identify sections of a multi-stream flow (beams) and used glyphs to visualize the entire set of beams (vector-tensor fields).

We present the generalization of recently introduced observables for the studies of correlated fluctuations of different anisotropic flow amplitudes, dubbed Symmetric Cumulants. We introduce a new set of higher order observables and outline a unique way how the genuine multi-harmonic correlations can be extracted from multi-particle azimuthal correlators. We argue that correlations among flow amplitudes can be studied reliably with the general mathematical formalism of cumulants only if that formalism is applied directly on the flow amplitudes. We have tested all the desired properties of new observables with the carefully designed Toy Monte Carlo studies. By using the realistic iEBE-VISHNU model, we have demonstrated that their measurements are feasible and we have provided the predictions for the centrality dependence in Pb--Pb collisions at LHC energies. A separate study was performed for their values in the coordinate space. The new observables contain information which is inaccessible to individual flow amplitudes and correlated fluctuations of only two flow amplitudes, and therefore they provide further and independent constraints for the initial conditions and the properties of Quark-Gluon Plasma in high-energy nuclear collisions., Comment: 30 pages, 12 figures. Major revision. This version was accepted for publication in Physical Review C

We explain the dynamics of ultracold atoms in amplitude modulated optical lattice with harmonic confinement. We show the existence of dynamical localization that manifests itself as the cold atoms exhibit quantum suppression of classical chaos in the dynamical system. The exponential localization takes place both in momentum as well as in coordinate space within certain windows on modulation amplitude. We show that inter-band transitions, taking place due to the amplitude modulation in optical lattice, play an important role in controlling the dynamical localization of matter waves. Our obtained results can be generalized to other dynamical systems and are experimentally realizable as we consider the values of parameters from the present-day available experiments.

We investigate the evolution of clustering structure through the momentum distributions in the $^{8\text{--}10}\mathrm{Be}$ isotopes. The nucleon dynamics within the intercluster antisymmetrization are discussed via the momentum distribution of a Brink type $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}$ wave function. For the state with a small $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}$ distance, we observe a significant depression with a dip structure at zero momentum and an enhanced tail in a relatively higher momentum region. In addition, we find the ``cluster structure'' in the intrinsic frame of momentum space, which is complementary to its significant $\ensuremath{\alpha}$-cluster dissolution in the coordinate space because of the strong antisymmetrization. For the physical $^{8\text{--}10}\mathrm{Be}$ isotopes, the Tohsaki-Horiuchi-Schuck-R\"opke (THSR) wave functions are adopted. The evolution from the dilute clustering state to the compact one is demonstrated by a successive depression at zero momentum of nucleon distribution for the two $\ensuremath{\alpha}$ clusters within $^{8\text{--}10}\mathrm{Be}$ isotopes. For the compact $^{10}\mathrm{Be}$ nucleus, the momentum distribution of all nucleons shows significant depression at zero momentum with a dip structure, which is found to be contributed by both the intercluster antisymmetrization and the $p$-orbit occupation of the valence neutrons. This study proposes a new window for the investigations of the $\ensuremath{\alpha}$-clustering effects via the low-momentum components of nuclei, which is expected to be extended to the heavier nuclear clustering states.

We propose the approach for a lattice investigation of light-cone distribution amplitudes (LCDA) of heavy-light mesons, such as the $B$-meson, using the formalism of parton pseudo-distributions. A basic ingredient of the approach is the study of short-distance behavior of the $B$-meson Ioffe-time distribution amplitude (ITDA), which is a generalization of the $B$-meson LCDA in coordinate space. We construct a reduced ITDA for the $B$-meson, and derive the matching relation between the reduced ITDA and the LCDA. The reduced ITDA is ultraviolet finite, which guarantees that the continuum limit exists on the lattice., 6 pages, 1 figure, version published in Phys. Rev. D

We present a lattice-QCD calculation of the pion, kaon, and ηs distribution amplitudes using large-momentum effective theory. Our calculation is carried out using three ensembles with 2+1+1 flavors of highly improved staggered quarks, generated by MILC Collaboration, at 310-MeV pion mass with 0.06, 0.09, and 0.12 fm lattice spacings. We use clover fermion action for the valence quarks and tune the quark mass to match the lightest light and strange masses in the sea. The resulting lattice matrix elements are nonperturbatively renormalized in regularization-independent momentum-subtraction scheme and extrapolated to the continuum. We use two approaches to extract the x dependence of the meson distribution amplitudes: (i) we fit the renormalized matrix elements in coordinate space to an assumed distribution form through a one-loop matching kernel and (ii) we use a machine-learning algorithm trained on pseudo lattice-QCD data to make predictions on the lattice data. We found the results are consistent between these methods with the latter method giving a less smooth shape. Both approaches suggest that as the quark mass increases, the distribution amplitude becomes narrower. Our pion distribution amplitude has broader distribution than predicted by light-front constituent-quark model, and the moments of our pion distributions agree with previous lattice-QCD results using the operator production expansion.

In this paper we study the Kotzinian-Mulders effect of a single hadron production in semi-inclusive deep inelastic scattering (SIDIS) within the framework of transverse momentum dependent (TMD) factorization. The asymmetry is contributed by the convolution of the Kotzinian-Mulders function $g_{1T}$ and the unpolarized fragmentation function $D_1$. As a TMD distribution, the Kotzinian-Mulders function in the coordinate space in the perturbative region can be represented as the convolution of the $C$-coefficients and the corresponding collinear correlation function. The Wandzura-Wilczek approximation is used to obtain this correlation function. We perform a detailed phenomenological numerical analysis of the Kotzinian-Mulders effect in the SIDIS process within TMD factorization at the kinematics of the HERMES and COMPASS measurements. It is found that the obtained $x_B$-, $z_h$- and $P_{h\perp}$-dependent Kotzinian-Mulders effect are basically consistent with the HERMES and COMPASS measurements., 8 figures, 11 pages

In the studied axisymmetric case of the central four-body problem, the axis of symmetry is defined by two unequal-mass bodies, while the other two bodies are situated symmetrically with respect to this axis and have equal masses. Here, we consider a special case of the problem and assume that three of the masses are equal. Using a recently found analytical solution of the general case, we formulate the equations of condition for three equal masses analytically and solve them numerically. A complete description of the problem is given by providing both the coordinates and masses of the bodies. We show furthermore how the three-equal-mass solutions are related to the general case in the coordinate space. The physical aspects of the configurations are also studied and discussed., 16 pages, 8 figures, appeared in the open-access journal Symmetry (special issue: Astronomy and Symmetry)

The aim of this work is to develop the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) theory based on the point-coupling density functionals and extend it to provide a unified description for all even-even nuclei in the nuclear chart by overcoming all possible challenges. The nuclear superfluidity is considered via Bogoliubov transformation. Densities and potentials are expanded in terms of Legendre polynomials to include the axial deformation degrees of freedom. Sophisticated relativistic Hartree-Bogoliubov equations in coordinate space are solved in the DiracWoods-Saxon basis to consider the continuum effects. Numerical checks are performed from light nuclei to heavy nuclei. The techniques to construct the DRHBc mass table for even-even nuclei are explored. The DRHBc theory is extended to study heavier nuclei beyond magnesium isotopes. Taking Nd isotopes as examples, the experimental binding energies, two-neutron separation energies, quadrupole deformations, and charge radii are reproduced rather well. The deformation and continuum play essential roles in the description of nuclear masses and prediction of drip-line nuclei. By examining the single-particle levels in the canonical basis and their contributions to the total density, the thickness of the neutron skin, the particles number in continuum, and the Coulomb barrier, the exotic structures including the neutron skin and the proton radioactivity are predicted., 45 pages, 17 figures, and 1 table, accepted version for Physical Review C

In order to study structure of proto-neutron stars and those in subsequent cooling stages, it is of great interest to calculate inhomogeneous hot and cold nuclear matter in a variety of phases. The finite-temperature Hartree-Fock-Bogoliubov (FT-HFB) theory is a primary choice for this purpose, however, its numerical calculation for superfluid (superconducting) many-fermion systems in three dimensions requires enormous computational costs. To study a variety of phases in the crust of hot and cold neutron stars, we propose an efficient method to perform the FT-HFB calculation with the three-dimensional (3D) coordinate-space representation. Recently, an efficient method based on the contour integral of Green's function with the shifted conjugate-orthogonal conjugate-gradient method has been proposed [Phys. Rev. C 95, 044302 (2017)]. We extend the method to the finite temperature, using the shifted conjugate-orthogonal conjugate-residual method. We benchmark the 3D coordinate-space solver of the FT-HFB calculation for hot isolated nuclei and fcc phase in the inner crust of neutron stars at finite temperature. The computational performance of the present method is demonstrated. Different critical temperatures of the quadrupole and the octupole deformations are confirmed for $^{146}$Ba. The robustness of the shape coexistence feature in $^{184}$Hg is examined. For the neutron-star crust, the deformed neutron-rich Se nuclei embedded in the sea of superfluid low-density neutrons appear in the fcc phase at the nucleon density of 0.045 fm$^{-3}$ and the temperature of $k_B T=200$ keV. The efficiency of the developed solver is demonstrated for nuclei and inhomogeneous nuclear matter at finite temperature. It may provide a standard tool for nuclear physics, especially for the structure of the hot and cold neutron-star matters., 13 pages, 9 figures

The energy density is calculated in coordinate space for 12C, 40Ca, 48Ca, and 208Pb using a dispersive optical model constrained by all relevant data including the corresponding energy of the ground state. The nuclear interior minimally contributes to the total binding energy due to the 4πr2 phase space factor. Thus, the volume contribution to the energy in the interior is not well constrained. The dispersive-optical-model energy densities are in reasonable agreement with ab initio self-consistent Green’s function calculations of infinite nuclear matter restricted to treat only short-range and tensor correlations. These results call into question the degree to which the equation of state for nuclear matter is constrained by the empirical mass formula. In particular, the results in this chapter indicate that saturated nuclear matter does not require the canonical value of 16 MeV binding per particle but only about 13–14 MeV when the interior of 208Pb is considered.

We study proximity effect of pair correlation in the inner crust of neutron stars by means of the Skyrme-Hartree-Fock-Bogoliubov theory formulated in the coordinate space. We describe a system composed of a nuclear cluster immersed in neutron superfluid, which is confined in a spherical box. Using a density-dependent effective pairing interaction which reproduces both the pair gap of neutron matter obtained in ab initio calculations and that of finite nuclei, we analyze how the pair condensate in neutron superfluid is affected by the presence of the nuclear cluster. It is found that the proximity effect is characterized by the coherence length of neutron superfluid measured from the edge position of the nuclear cluster. The calculation predicts that the proximity effect has a strong density dependence. In the middle layers of the inner crust with baryon density $5 \times 10^{-4}$ fm$^{-3} < ��_b < 2\times 10^{-2}$ fm$^{-3}$, the proximity effect is well limited in the vicinity of the nuclear cluster, i.e. in a sufficiently smaller area than the Wigner-Seitz cell. On the contrary, the proximity effect is predicted to extend to the whole volume of the Wigner-Seitz cell in shallow layers of the inner crust with $��_b < 2 \times 10^{-4}$ fm$^{-3}$, and in deep layers with $��_b > 5 \times 10^{-2}$ fm$^{-3}$., 23 pages, 8 figures

We applied the semilocal coordinate-space (SCS) regularized chiral N\(^4\)LO nucleon-nucleon (NN) potential supplemented by the chiral N\(^2\)LO three-nucleon force (3NF), regularized in the same way, to study the nucleon-deuteron (Nd) elastic scattering and deuteron breakup reaction. We checked that the elastic Nd scattering cross section can be used to fix, together with the \(^3\)H binding energy, the strengths of the contact terms of the N\(^2\)LO 3NF. We found that the N\(^2\)LO 3NF provides effects comparable to those of (semi)phenomenological \(2\pi \)-exchange 3NF’s.

We present a detailed study of the spectrum and dispersion of Bogoliubov quasiparticles in two coupled elongated Bose-Einstein condensates. We develop an analytically solvable model that approximates two infinite homogeneous condensates and compare its predictions to a numerical simulation of a realistic trapped system. While the comparisons show a reasonable agreement between the two models, they also manifest the existence of several anomalous Bogoliubov modes in the spectrum. These modes show degeneracy in both energy and momentum together with self-localization in the coordinate space.

We introduce the package SIDES (Schrodinger Integro-Differential Equation Solver) that solves the integro-differential Schrodinger equation for elastic scattering of a nonlocal optical potential in coordinate space. The code is capable of treating the Coulomb interaction without restrictions. The method is based on previous developments by Jacques Raynal in the DWBA07 code. Elastic scattering observables such as differential and integral cross sections, as well as analyzing power and spin rotation functions for both neutron and proton projectiles are evaluated, with no restriction on the type of nonlocality of the potential nor on the beam energy. The corresponding distorted wavefunctions are calculated as well. The SIDES package includes a Perey–Buck potential generator with two parametrizations. It includes as well local potential parametrizations and allows for mixing local and nonlocal contributions. Benchmarks are performed and discussed. Program summary Program Title: SIDES Program Files doi: http://dx.doi.org/10.17632/cmpjgyrngr.1 Licensing provisions: GNU General Public License, Version 2 Programming language: FORTRAN-90 Nature of problem: The description of nucleon elastic scattering off a target nucleus involves solving the Schrodinger’s wave equation for positive incident energy. The determination of scattering observables calls for accurate treatments of the continuum. The effective coupling between the projectile and the target is accounted for by an optical potential, an operator which is by nature complex, energy-dependent and nonlocal. The coupling becomes long-range in the case of charged projectiles. In a general scenario under nonlocal potentials, Schrodinger’s equation becomes an integro-differential equation. Solution method: SIDES solves the Schrodinger integro-differential equation numerically by matrix inversion using Gibbs, Numerov or a modified Numerov method with a uniform radial mesh in a box. The solution is refined by an iterative procedure until a specified precision is achieved. To obtain elastic scattering observables, the associated phase-shifts are calculated via matching of the numerical solution with its analytic asymptotic behavior.

Experimental and theoretical investigations of excitons in cuprous oxide have revealed a significant fine-structure splitting of the excitonic Rydberg states caused by a strong impact of the valence band structure. We provide a semiclassical interpretation of that splitting by investigating the classical dynamics of the excitonic electron-hole pair beyond the hydrogen-like model. Considering the slow motion of Rydberg excitons in coordinate space compared to the fast dynamics of quasispin and hole spin we use an adiabatic approach and energy surfaces in momentum space for the computation of the exciton dynamics. We observe quasi-periodic motion on near-integrable tori. Semiclassical torus quantization yields the energy regions of the fine-structure splitting of $n$-manifolds in agreement with quantum mechanical computations., Comment: 5 pages, 3 figures

The article of record as published may be found at http://dx.doi.org/10.1121/10.0000470 The small-slope approximation (SSA) for rough-interface scattering is most commonly applied to the upper bound ary of either impenetrable media or uniform half-space media, but has been recently developed for layered media in the acoustic and electromagnetic cases. The present work gives an overview of three forms of the SSA for layered media. The first has been previously presented in the acoustics literature. The second is from the electromagnetics literature and in the present work is converted to the fluid-sediment problem. A missing proof is supplied of a key consistency condition demanded of the small-slope ansatz. As is usual, these small-slope results are expressed in k-space. A third SSA for layered seafloors follows from conversion of the usual half-space formulation from k-space to coordinate space. This form turns out to be useful for reverberation simulations. The three different approaches are compared with respect to scattering strength and the coherent reflection coefficient, but an assessment of their relative merits will require comparison with exact calculations. U.S. Office of Naval Research

The leading-order equations of the $1/N$ -- expansion for a vector-matrix model with interaction $g\phi_a^*\phi_b\chi_{ab}$ in four dimensions are investigated. This investigation shows a change of the asymptotic behavior in the deep Euclidean region in a vicinity of a certain critical value of the coupling constant. For small values of the coupling the phion propagator behaves as free. In the strong-coupling region the asymptotic behavior drastically changes -- the propagator in the deep Euclidean region tend to some constant limit. The phion propagator in the coordinate space has a characteristic shell structure. At the critical value of coupling that separates the weak and strong coupling regions, the asymptotic behavior of the phion propagator is a medium among the free behavior and the constant--type behavior in strong--coupling region. The equation for a vertex with zero transfer is also investigated. The asymptotic behavior of the solutions shows the finiteness of the charge renormalization constant. In the strong-coupling region, the solution for the vertex has the same shell structure in coordinate space as the phion propagator. An analogy between the phase transition in this model and the re-arrangement of the physical vacuum in the supercritical external field due to the "fall-on-the-center" phenomenon is discussed., Comment: 7 pages

We discuss specific hypergeometric solutions of the conformal Ward identities (CWI's) of scalar 4-point functions of primary fields in momentum space, in $d$ spacetime dimensions. We determine such solutions using various dual conformal ans\"atze (DCA's). We start from a generic dual conformal correlator, and require it to be conformally covariant in coordinate space. The two requirements constrain such solutions to take a unique hypergeometric form. They describe correlators which are at the same time conformal and dual conformal in any dimension. These specific ans\"atze also show the existence of a link between 3- and 4-point functions of a CFT for such class of exact solutions, similarly to what found for planar ladder diagrams. We show that in $d=4$ only the box diagram and its melonic variants, in free field theory, satisfies such conditions, the remaining solutions being nonperturbative. We then turn to the analysis of some approximate high energy fixed angle solutions of the CWI's which also in this case take the form of generalized hypergeometric functions. We show that they describe the behaviour of the 4-point functions at large energy and momentum transfers, with a fixed $-t/s$. The equations, in this case, are solved by linear combinations of Lauricella functions of 3 variables and can be rewritten as generalized 4K integrals. In both cases the CWI's alone are sufficient to identify such solutions and their special connection with generalized hypergeometric systems of equations., Comment: Revised final version. Two sections added. To be published on Journal of High Energy Physics. 46 pages, 2 figures