Semiclassical Results Research Articles

Mixmaster chaos in an AdS black hole interior

We derive gravitational backgrounds that are asymptotically Anti-de Sitter, have a regular black hole horizon and which deep in the interior exhibit mixmaster chaotic dynamics. The solutions are obtained by coupling gravity with a negative cosmological constant to three massive vector fields, within an Ansatz that reduces to ordinary differential equations. At late interior times the equations are identical to those analysed in depth by Misner and by Belinskii-Khalatnikov-Lifshitz fifty years ago. We review and extend known classical and semiclassical results on the interior chaos, formulated as both a dynamical system of ‘Kasner eras’ and as a hyperbolic billiards problem. The volume of the universe collapses doubly-exponentially over each Kasner era. A remarkable feature is the emergence of a conserved energy, and hence a ‘time-independent’ Hamiltonian, at asymptotically late interior times. A quantisation of this Hamiltonian exhibits arithmetic chaos associated with the principal congruence subgroup Γ(2) of the modular group. We compute a large number of eigenvalues numerically to obtain the spectral form factor. While the spectral statistics is anomalous for a chaotic system, the eigenfunctions themselves display random matrix behaviour.

Geometric localization of waves on thin elastic structures.

We consider the localization of elastic waves in thin elastic structures with spatially varying curvature profiles, using a curved rod and a singly curved shell as concrete examples. Previous studies on related problems have broadly focused on the localization of flexural waves on such structures. Here, using the semiclassical WKB approximation for multicomponent waves, we show that in addition to flexural waves, extensional and shear waves also form localized, bound states around points where the absolute curvature of the structure has a minimum. We also see excellent agreement between our numerical experiments and the semiclassical results, which hinges on the vanishing of two extra phases that arise in the semiclassical quantization rule. Our findings open up novel ways to fine-tune the acoustic and vibrational properties of thin elastic structures and raise the possibility of introducing new phenomena not easily captured by effective models of flexural waves alone.

Ground state energy of twisted AdS3 × S3 × T4 superstring and the TBA

We use the lightcone AdS3 × S3 × T4 superstring sigma model with fermions and bosons subject to twisted boundary conditions to find the ground state energy in the semi-classical approximation where effective string tension h and the light-cone momentum L are sent to infinity in such a way that J\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{J} $$\\end{document} ≡ L/h is kept fixed. We then analyse the ground state energy of the model by means of the mirror TBA equations for the AdS3 × S3 × T4 superstring in the pure RR background. The calculation is performed for small twist μ with L and h fixed, for large L with μ and h fixed, and for small h with μ and L fixed. In these limits the contribution of the gapless worldsheet modes coming from the T4 bosons and fermions can be computed exactly, and is shown to be proportional to hL/(4L2 – 1). Comparison with the semi-classical result shows that the TBA equations involve only one Y0-function for massless excitations but not two as was conjectured before. Some of the results obtained are generalised to the mixed-flux AdS3× S3× T4 superstring.

Experimental and Semiclassical Stark Widths and Shifts for Spectral Lines of Neutral and Ionized Atoms (A Critical Review of Experimental and Semiclassical Data for the Period 2008 Through 2020)

This Review Article compares new experimental and corresponding semiclassical Stark broadened data for non-hydrogenic spectral lines of neutral atoms and positive ions. This Review covers the period 2008 until the end of 2020 and presents the continuation of previous critical reviews from 1976 (two), 1984 (two), 1990, 2002, and one from 2009. This Review reports the Stark broadening parameters of 1665 spectral lines belonging to 35 elements with 61 different atomic and ion species. The data are taken from 60 papers. Experimental data are arranged by elements and spectra, and these are reported in tables in alphabetical and numerical order, respectively. Each experimental Stark broadening parameter is followed with estimated accuracy. The experimental Stark broadening and shift data presented in the tables are compared with the corresponding semiclassical results available in the literature. In addition, for comparison experiments versus semiclassical theoretical Stark broadening parameters, a numerically improved theoretical approach developed based on Griem and co-workers’ theory is used to evaluate Stark widths and shifts of all studied lines whenever required atomic energy levels data and transition probabilities are available. At the end of the text report, for each analyzed neutral or ion species, the information about the location of the same species data in preceding reviews is given.

Calculation of Ionization, Excitation and Electron Capture Cross Sections for Be4+ + H(2s,2p) Collisions.

A computational study of Be4+ + H(2s,2p) collisions has been carried out employing the Classical Trajectory Monte Carlo (CTMC) method for the impact energy range from 20 keV/u to 1000 keV/u. The integral n partial cross sections for H(n) excitation and Be3+(n) electron capture and, the total ionization and electron capture cross sections are calculated and compared to recent semiclassical results. A general good agreement is observed for the n partial and total electron capture and ionization cross sections. The comparative study of the three inelastic processes show no significant differences between both excited targets.

Application of the WKB Theory to Investigate Electron Tunneling in Kek-Y Graphene

In this paper, we have constructed a WKB approximation for graphene having a Y-shaped Kekulé lattice distortion and a special folding of the K and K′ valleys, which leads to very specific linear energy dispersions with two non-equivalent pairs of subbands. These obtained semi-classical results, which include the action, electron momentum and wave functions, are utilized to analyze the dynamics of electron tunneling through non-square potential barriers. In particular, we explore resonant scattering of an electron by a potential barrier built on Kekulé-distorted graphene. Mathematically, a group of consecutive equations for a semi-classical action have been solved by following a perturbation approach under the condition of small strain-induced coupling parameter Δ0≪1 (a good fit to its actual value Δ0∽ 0.1). Specifically, we consider a generalized model for Kek-Y graphene with two arbitrary Fermi velocities. The dependence of the electron transmission amplitude on the potential profile V(x) and band parameters of Kekulé-patterned graphene has been explored and analyzed in detail.

Infrared physics of the 3D SU(2) adjoint Higgs model at the crossover transition

We study the crossover phase transition of the SU(2) Georgi-Glashow model in three dimensions. In this model, a confining condensate of topological ’t Hooft-Polyakov monopoles exists in the Higgs regime. We use lattice Monte Carlo simulations to study the monopole gas across a crossover transition, and demonstrate that gradient flow can be used to renormalize the otherwise divergent monopole number density. The condensation of the monopoles means that the theory admits also a massive photon-like excitation. We show that the renormalized monopole number density is approximately proportional to the square of the photon mass, in agreement with semiclassical results. Our results give insight into behaviour of the Higgs regime near crossover, which has boarder implications for beyond the Standard Model theories containing adjoint scalar fields.

Reflected waves and quantum gravity

In the context of canonical quantum gravity, we consider the effects of a nonstandard expression for the gravitational wave function on the evolution of inflationary perturbations. Such an expression and its effects may be generated by a sudden variation in the (nearly constant) inflaton potential. The resulting primordial spectra, up to the leading order, are affected in the short and in the long wavelength regime, where an oscillatory behavior with a non-negligible amplitude is superimposed on the standard semiclassical result. Moreover, a novel, nonperturbative, approach is used to study the evolution. Finally, a simplified application is fully illustrated and commented.

Algebraic approach to the frozen formalism problem of time

The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic reduction that avoids difficult requirements such as the computation of a complete set of Dirac observables or the construction of a physical Hilbert space. In addition, the new algebraic treatment makes it possible to implement a consistent realization of the gauge structure off the constraint surface. As a consequence, previously unrecognized consistency conditions are imposed on deparametrization---the method traditionally used to unfreeze evolution in completely constrained systems. A detailed discussion of how the new formulation extends previous semiclassical results shows that an internal time degree of freedom need not be semiclassical in order to define a consistent quantum evolution.

Perturbative understanding of nonperturbative processes and quantumization versus classicalization

In some instances of study of quantum evolution of classical backgrounds it is considered inevitable to resort to nonperturbative methods at the price of treating the system semiclassically. We show that a fully quantum perturbative treatment, in which the background is resolved as a multiparticle state, recovers the semiclassical nonperturbative results and allows going beyond. We reproduce particle creation by a classical field in a theory of two scalars as well as in scalar QED in terms of scattering processes of high multiplicity. The multiparticle treatment also gives a transparent picture of why a single-process transition from a classical to a quantum state, which we call quantumization, is exponentially suppressed, whereas the opposite process, classicalization, can take place swiftly if the microstate degeneracy of the classical state is high. An example is provided by the $N$-graviton portrait of a black hole: a black hole can form efficiently via a $2\ensuremath{\rightarrow}N$ classicalization process in the collision of high-energy particles, but its quantumization via a decay $N\ensuremath{\rightarrow}2$ is exponentially suppressed.

Quantum Chern–Simons Theories on Cylinders: BV-BFV Partition Functions

We compute partition functions of Chern–Simons type theories for cylindrical spacetimes I times Sigma , with I an interval and dim Sigma = 4l+2, in the BV-BFV formalism (a refinement of the Batalin–Vilkovisky formalism adapted to manifolds with boundary and cutting–gluing). The case dim Sigma = 0 is considered as a toy example. We show that one can identify—for certain choices of residual fields—the “physical part” (restriction to degree zero fields) of the BV-BFV effective action with the Hamilton–Jacobi action computed in the companion paper (Cattaneo et al., Constrained systems, generalized Hamilton–Jacobi actions, and quantization, arXiv:2012.13270), without any quantum corrections. This Hamilton–Jacobi action is the action functional of a conformal field theory on Sigma . For dim Sigma = 2, this implies a version of the CS-WZW correspondence. For dim Sigma = 6, using a particular polarization on one end of the cylinder, the Chern–Simons partition function is related to Kodaira–Spencer gravity (a.k.a. BCOV theory); this provides a BV-BFV quantum perspective on the semiclassical result by Gerasimov and Shatashvili.

Logarithmic corrections, entanglement entropy, and UV cutoffs in de Sitter spacetime

It has been argued that the entropy of de Sitter space corresponds to the entanglement between disconnected regions computable by switching on a replica parameter q modeled by the quotient dS/ℤq. Within this framework, we show that the centrally-extended asymptotic symmetry algebra near the cosmic horizon is a single copy of the Virasoro algebra. The resulting density of states matches the semi-classical result of Gibbons and Hawking up to an undetermined constant that is chosen to reproduce the entanglement entropy previously found in the literature. It follows that the logarithmic quantum corrections to the Cardy entropy reproduces the known one-loop result computed in the bulk in the presence of a cutoff. The resulting entanglement entropy follows the divergent area law, where the UV cutoff is now a function of the replica parameter. Thus, as the near-horizon CFT fixes the cutoff in units of the Planck scale, the model can be viewed as a probe into whether the defect Hilbert space has a finite dimension; indeed, the limit q → 0, reproduces Banks’ formula. We also study the quantum corrections of the effective description of the horizon entropy by means of Liouville field theory, where the large q limit corresponds to a realization of dS3/CFT2 correspondence matching the logarithmic corrections to three-dimensional de Sitter space obtained by computing the one-loop contribution to the quantum gravity partition function in the round three-sphere.

Surface gravity and the information loss problem

The information loss paradox is widely regarded as one of the biggest open problems in theoretical physics. Several classical and quantum features must be present to enable its formulation. First, an event horizon is needed to justify the objective status of tracing out degrees of freedom inside the black hole. Second, evaporation must be completed (or nearly completed) in finite time according to a distant observer, and thus the formation of the black hole should also occur in finite time. In spherical symmetry these requirements constrain the possible metrics strongly enough to obtain a unique black hole formation scenario and match their parameters with the semiclassical results. However, the two principal generalizations of surface gravity, the quantity that determines the Hawking temperature, do not agree with each other on the dynamic background. Neither can correspond to the emission of nearly-thermal radiation. We infer from this that the information loss problem cannot be consistently posed in its standard form.

Black holes and their horizons in semiclassical and modified theories of gravity

For distant observers, black holes are trapped spacetime domains bounded by apparent horizons. We review properties of the near-horizon geometry emphasizing the consequences of two common implicit assumptions of semiclassical physics. The first is a consequence of the cosmic censorship conjecture, namely, that curvature scalars are finite at apparent horizons. The second is that horizons form in finite asymptotic time (i.e. according to distant observers), a property implicitly assumed in conventional descriptions of black hole formation and evaporation. Taking these as the only requirements within the semiclassical framework, we find that in spherical symmetry only two classes of dynamic solutions are admissible, both describing evaporating black holes and expanding white holes. We review their properties and present the implications. The null energy condition is violated in the vicinity of the outer horizon and satisfied in the vicinity of the inner apparent/anti-trapping horizon. Apparent and anti-trapping horizons are timelike surfaces of intermediately singular behavior, which manifests itself in negative energy density firewalls. These and other properties are also present in axially symmetric solutions. Different generalizations of surface gravity to dynamic spacetimes are discordant and do not match the semiclassical results. We conclude by discussing signatures of these models and implications for the identification of observed ultra-compact objects.

Backreaction of mesonic fluctuations on the axial anomaly at finite temperature

The impact of mesonic fluctuations on the restoration of the ${U}_{A}(1)$ anomaly is investigated nonperturbatively for three flavors at finite temperature in an effective model setting. Using the functional renormalization group, the dressed, fully field-dependent Kobayashi-Maskawa-'t Hooft (KMT) anomaly coupling is computed. It is found that mesonic fluctuations strengthen this signature of the ${U}_{A}(1)$ breaking as the temperature increases. On the other hand, when instanton effects are included by parametrizing the explicit temperature dependence of the bare anomaly parameter in consistency with the semiclassical result for the tunneling amplitude, a natural tendency appears, diminishing the anomaly at high temperatures. As a result of the two competing effects, the dressed KMT coupling shows a well-defined intermediate strengthening behavior around the chiral (pseudo)transition temperature before the axial anomaly gets fully suppressed at high temperature. As a consequence, we conclude that below $T\ensuremath{\sim}200\text{ }\text{ }\mathrm{MeV}$ the ${U}_{A}(1)$ anomaly is unlikely to be effectively restored. Robustness of the conclusions against different assumptions for the temperature dependence of the bare anomaly coefficient is investigated in detail.

Coherent and incoherent superposition of transition matrix elements of the squeezing operator

We discuss the general matrix elements of the squeezing operator between number eigenstates of a harmonic oscillator (which may also represent a quantized mode of the electromagnetic radiation). These matrix elements have first been used by Popov and Perelomov (1969 Zh. Eksp. Teor. Fiz. 56 1375–90) long ago, in their thorough analysis of the parametric excitation of harmonic oscillators. They expressed the matrix elements in terms of transcendental functions, the associated Legendre functions. In the present paper we will show that these matrix elements can also be derived in a different form, expressed by the classical Gegenbauer polynomials. This new expression makes it possible to determine coherent and incoherent superpositions of these matrix elements in closed analytic forms. As an application, we describe multiphoton transitions in the system ‘charged particle + electromagnetic radiation’, induced by a (strong) coherent field or by a black-body radiation component (with a Planck–Bose photon number distribution). The exact results are compared with the semi-classical ones. We will show that in case of interaction with a thermal field, the semi-classical result (with a Gaussian stochastic field amplitude) yields an acceptable approximation only in the Rayleigh–Jeans limit, however, in the Wien limit it completely fails.

Periodic orbit evaluation of a spectral statistic of quantum graphs without the semiclassical limit

Energy level statistics of quantized chaotic systems have been evaluated in the semiclassical limit via their periodic orbits using the Gutzwiller and related trace formulae. Here we evaluate a spectral statistic of chaotic 4-regular quantum graphs from their periodic orbits without the semiclassical limit. The variance of the n-th coefficient of the characteristic polynomial is determined by the sizes of the sets of distinct primitive periodic orbits with n bonds which have no self-intersections, and the sizes of the sets with a given number of self-intersections which all consist of two sections of the pseudo orbit crossing at a single vertex. Using this result we observe the mechanism that connects semiclassical results to the total number of orbits regardless of their structure.

Coherent and incoherent superposition of transition matrix elements of the squeezing operator

Abstract We discuss the general matrix elements of the squeezing operator between number eigenstates of a harmonic oscillator (which may also represent a quantized mode of the electromagnetic radiation). These matrix elements have first been used by Popov and Perelomov (1969) long ago, in their thorough analysis of the parametric excitation of harmonic oscillators. They expressed the matrix elements in terms of transcendental functions, the associated Legendre functions. In the present paper we will show that these matrix elements can also be derived in an different form, expressed by the classical Gegenbauer polynomials. This new expression makes it possible to determine coherent and incoherent superpositions of these matrix elements in closed analytic forms. As an application, we describe multiphoton transitions in the system “charged particle + electromagnetic radiation”, induced by a (strong) coherent field or by a black-body radiation component (with a Planck-Bose photon number distribution). The exact results are compared with the semi-classical ones. We will show that in case of interaction with a thermal field, the semi-classical result (with a Gaussian stochastic field amplitude) yields an acceptable approximation only in the Rayleigh-Jeans limit, however, in the Wien limit it completely fails.

Swimmer dynamics in externally driven fluid flows: The role of noise

We theoretically investigate the effect of random fluctuations on the motion of elongated microswimmers near hydrodynamic transport barriers in externally-driven fluid flows. Focusing on the two-dimensional hyperbolic flow, we consider the effects of translational and rotational diffusion as well as tumbling, i.e. sudden jumps in the swimmer orientation. Regardless of whether diffusion or tumbling are the primary source of fluctuations, we find that noise significantly increases the probability that a swimmer crosses one-way barriers in the flow, which block the swimmer from returning to its initial position. We employ an asymptotic method for calculating the probability density of noisy swimmer trajectories in a given fluid flow, which produces solutions to the time-dependent Fokker-Planck equation in the weak-noise limit. This procedure mirrors the semiclassical approximation in quantum mechanics and similarly involves calculating the least-action paths of a Hamiltonian system derived from the swimmer's Fokker-Planck equation. Using the semiclassical technique, we compute (i) the steady-state orientation distribution of swimmers with rotational diffusion and tumbling and (ii) the probability that a diffusive swimmer crosses a one-way barrier. The semiclassical results compare favorably with Monte Carlo calculations.

Initial longitudinal velocity resolved spiderlike photoelectron momentum distributions in hydrogen

Tunneling ionization of atoms is the basis of many phenomena and techniques, which requires people to be able to comprehensively understand this crucial physical process. Recent experiments have demonstrated the existence of the nonzero initial longitudinal momentum spread at the tunnel exit. However, the initial longitudinal velocity is usually set to be zero in the adiabatic regime. In this work, we numerically study that the initial longitudinal velocity of ionized-out electrons plays the role in the spiderlike photoelectron momentum distributions in hydrogen atom by using the semiclassical rescattering model and the time-dependent Schrödinger equation. Nonzero longitudinal initial velocity, no matter whether it is an offset or an offset distribution, is considered in the semiclassical rescattering model. Longitudinal cut-plot and transverse cut-plot of the photoelectron momentum distribution are discussed. The final longitudinal momentum of the electron is found to be sensitive to the initial longitudinal velocity, which offers us a method of determining the information about the initial longitudinal velocity from a photoelectron momentum distribution according to this linear relationship. We unveil that either an offset or an offset distribution for the initial longitudinal velocity can perfectly reproduce the same spiderlike photoelectron momentum distributions. The semiclassical results are backed by the full quantum simulation. It is expected that more precise research is required to deepen the knowledge of the initial longitudinal velocity in strong field ionization of atoms.