Semiclassical Approximation Research Articles

Einstein-Dirac system in semiclassical gravity

We study the Dirac equation minimally coupled to general relativity using quantum field theory and the semiclassical gravity approximation. Previous studies of the Einstein-Dirac system did not quantize the Dirac field and required multiple independent Dirac fields to preserve spherical symmetry. We canonically quantize a single Dirac field in a static spherically symmetric curved spacetime background. Using the semiclassical gravity approximation, in which the Einstein field equations are sourced by the expectation value of the stress-energy-momentum tensor, we derive a system of equations whose solutions describe static spherically symmetric self-gravitating configurations of identical quantum spin-$1/2$ particles. We self-consistently solve these equations and present example configurations. Although limiting cases of our semiclassical system of equations reproduce the multifield system of equations found in the literature, our system of equations is derived from the excitations of a single quantum field.

Magnus effect on a Majorana zero mode

A supercurrent on the proximitized surface of a topological insulator can cause a delocalization transition of a Majorana fermion bound to a vortex core as a zero-mode. Here we study the dynamics of the deconfinement, as a manifestation of the Magnus effect (the coupling of the superflow to the velocity field in the vortex). The initial acceleration of the Majorana fermion is $\pm 2v_{\rm F}^2 K/\hbar$, perpendicular to the Cooper pair momentum $K$, for a $\pm 2\pi$ winding of the superconducting phase around the vortex. The quasiparticle escapes with a constant velocity from the vortex core, which we calculate in a semiclassical approximation and compare with computer simulations.

Asymptotic expansions for field moments of bound states

Asymptotic expansions are presented for the moments of bound states in one-dimensional anharmonic potentials. The results are derived by using the stable aggregate of flexible element (SAFE) method and include only the first non-zero wave-related correction to the familiar semi-classical approximation. Application to a couple of widely studied potentials that do not permit closed-form solutions is used to demonstrate surprising accuracy even in cases that are far from any asymptotic limit. We explore the absence of alternate terms in the asymptotic expansions as a way to explain the accuracy of the end results. Those results are expressed as definite integrals with integrands involving the parameter used in the SAFE method to control the extent of the associated elemental field contributions. Importantly, the integrals themselves are shown to be precisely independent of that parameter. Further, although the derivation proceeds by way of an asymptotic expansion for the wavefield that involves the associated classical motion, those entities do not appear in the end results which are expressed in terms of just the potential function and its first four derivatives.

Vacuum decay and Euclidean lattice Monte Carlo

The decay rate of a metastable vacuum is usually calculated using a semiclassical approximation to the Euclidean path integral. The extension to a complete Euclidean lattice Monte Carlo computation, however, is hampered by analytic continuations that are ill-suited to numerical treatment, and the nonequilibrium nature of a metastable state. In this paper we develop a new methodology to compute vacuum decay rates from Monte Carlo simulations of Euclidean lattice theories. To test the new method, we consider simple quantum mechanical systems systems with metastable vacua. This work can be extended to Euclidean field theories, which we discuss in the Conclusions.

Potential energy of a pair of identical coplanar uniformly charged circular rings

We study the features of the potential energy function for a system consisting of a pair of identical uniformly charged circular rings that are coplanar with each other. This model may emerge as a legitimate semi-classical approximation for a realistic two-dimensional electron system in a weak perpendicular magnetic field. An exact integral expression for the potential energy of the system is obtained as a function of the separation distance between the centers of the respective uniformly charged circular rings. It is found that the potential energy develops a cusp at a particular distance that corresponds to the two uniformly charged circular rings touching each other at one point. This observation has important implications for formation of clusters and/or aggregate systems.

Matsubara dynamics approximation for generalized multi-time correlation functions.

We introduce a semi-classical approximation for calculating generalized multi-time correlation functions based on Matsubara dynamics, a classical dynamics approach that conserves the quantum Boltzmann distribution. This method is exact for the zero time and harmonic limits and reduces to classical dynamics when only one Matsubara mode is considered (i.e., the centroid). Generalized multi-time correlation functions can be expressed as canonical phase-space integrals, involving classically evolved observables coupled through Poisson brackets in a smooth Matsubara space. Numerical tests on a simple potential show that the Matsubara approximation exhibits better agreement with exact results than classical dynamics, providing a bridge between the purely quantum and classical descriptions of multi-time correlation functions. Despite the phase problem that prevents practical applications of Matsubara dynamics, the reported work provides a benchmark theory for the future development of quantum-Boltzmann-preserving semi-classical approximations for studies of chemical dynamics in condensed phase systems.

Semiclassical approximations of photoabsorption cross sections beyond the continuum threshold

We develop semiclassical approximations for calculating photoabsorption cross sections beyond the continuum threshold in quantum many-body systems. These approximations use the fully quantum-mechanical Wigner function of the ground state and semiclassical expansions only for the part of the cross section depending on the continuum states, thus avoiding the difficult explicit calculation of the continuum states. Even though the approach is general, we test it in electronic-structure theory for the photoionization cross sections of the hydrogen and helium atoms. The results suggest that these semiclassical approximations can be used to obtain good estimates of cross sections at high energy.

Measuring the Vortex−Nucleus Pinning Force from Pulsar Glitch Rates

Superfluid vortex avalanches are one plausible cause of pulsar glitch activity. If they occur according to a state-dependent Poisson process, the measured long-term glitch rate is determined by the spin-down rate of the stellar crust, , and two phenomenological parameters quantifying the vortex−nucleus pinning force: a crust−superfluid angular velocity lag threshold, X cr, and a reference unpinning rate, λ 0. A Bayesian analysis of 541 glitches in 177 pulsars, with N g ≥ 1 events per pulsar, yields , , and assuming the phenomenological rate law λ 0 = λ ref[τ/(1 yr)] a , where τ denotes the characteristic spin-down age. The results are broadly similar, whether one includes or excludes quasiperiodic glitch activity, giant glitches, or pulsars with N g = 0, up to uncertainties about the completeness of the sample and the total observation time per pulsar. The X cr and λ 0 estimates are consistent with first-principles calculations based on nuclear theory, e.g., in the semiclassical local density approximation.

Comparing semiclassical mean-field and 1-exciton approximations in evaluating optical response under strong light-matter coupling conditions.

The rigorous quantum mechanical description of the collective interaction of many molecules with the radiation field is usually considered numerically intractable, and approximation schemes must be employed. Standard spectroscopy usually contains some levels of perturbation theory, but under strong coupling conditions, other approximations are used. A common approximation is the 1-exciton model in which processes involving weak excitations are described using a basis comprising the ground state and singly excited states of the molecule cavity-mode system. In another frequently used approximation in numerical investigations, the electromagnetic field is described classically, and the quantum molecular subsystem is treated in the mean-field Hartree approximation with its wavefunction assumed to be a product of single molecules' wavefunctions. The former disregards states that take long time to populate and is, therefore, essentially a short time approximation. The latter is not limited in this way, but by its nature, disregards some intermolecular and molecule-field correlations. In this work, we directly compare results obtained from these approximations when applied to several prototype problems involving the optical response of molecules-in-optical cavities systems. In particular, we show that our recent model investigation [J. Chem. Phys. 157, 114108 (2022)] of the interplay between the electronic strong coupling and molecular nuclear dynamics using the truncated 1-exciton approximation agrees very well with the semiclassical mean-field calculation.

Effect of a temperature gradient on the screening properties of ionic fluids

The electrostatic screening properties of ionic fluids are of paramount importance in countless physical processes. Yet the screening behavior of ionic conductors out of thermal equilibrium has to date mainly been studied in the context of thermoelectric phenomena by virtue of direct extensions of Debye-H\"uckel theories. We investigate how the static response of a symmetric ionic fluid is influenced by the presence of a thermal gradient by introducing a theory of electrostatic screening under a stationary temperature profile. By borrowing mathematical methods commonly used in the semiclassical approximation of quantum particles, we find analytical solutions to the asymptotic decay of the charge density which can be used to describe the nonequilibrium response of the system to external charge perturbations and for arbitrary ionic concentrations. Notably, a transition between monotonic and oscillatory screening regimes is observed as an effect of the temperature variation which generalizes known results of thermal equilibrium to out of equilibrium conditions. A final quantitative example on the screening of charged surfaces in aqueous electrolytes shows that the deviation from thermal equilibrium predicted by our solutions is generally larger than thermoelectric effects and should therefore be taken into account for a comprehensive description of the electrical double layer. Our findings pave the way to the rigorous treatment of nonequilibrium steady states in ionic systems with potential applications to the study of energy materials, nanostructured systems, and waste-heat-recovery technologies.

Ab Initio Double-Differential Ionization Cross-Section Calculations in Antiproton–Helium Collisions

We present ionization cross-sections for antiproton and helium collisions based on an ab initio time-dependent coupled channel method. In our calculations, a finite basis set of regular helium Coulomb wave packets and Slater function were used. The semiclassical approximation was applied with the time-dependent Coulomb potential to describe the antiproton–electron interaction. Three different projectile energies were considered as 10, 50 and 100 keV. We found clear evidence for the formation of the anti-cusp in the differential distributions.

Asymptotically flat vacuum solutions in order-reduced semiclassical gravity

We investigate the effects of quantum backreaction on the Schwarzschild geometry in the semiclassical approximation. The renormalized stress-energy tensor (RSET) of a scalar field is modelled via an order reduction of the analytical approximation derived by Anderson, Hiscock and Samuel (AHS). As the resulting AHS semiclassical Einstein equations are of fourth-derivative order in the metric, we follow a reduction of order prescription to shrink the space of solutions. Motivated by this prescription, we develop a method that allows to obtain a novel analytic approximation for the RSET that exhibits all the desired properties for a well-posed RSET: conservation, regularity, and correct estimation of vacuum-state contributions. We derive a set of semiclassical equations sourced by the order-reduced AHS-RSET in the Boulware state. We classify the self-consistent solutions to this set of field equations, discuss their main features and address how well they resemble the solutions of the higher-order semiclassical theory. Finally, we establish a comparison with previous results in the literature obtained through the Polyakov approximation for minimally coupled scalar fields.

Fluctuation-driven excess noise near superconducting phase transition

We discuss intrinsic mechanisms of nonequilibrium excess noise in superconducting devices and transition edge sensors. In particular, we present an overview of fluctuation-driven contributions to the current noise in the vicinity of the superconducting transition. We argue that sufficiently close to the critical temperature fluctuations of conductivity may become correlated provided that the rate of quasiparticle relaxation is slow as compared to dynamics of superconducting fluctuations. In this regime, fluctuations of conductivity adiabatically follow the fluctuations of the electron distribution. This leads to a substantial enhancement of current noise. The corresponding spectral power density of noise has a Lorentzian shape in the frequency domain while its magnitude scales proportionally to the inelastic relaxation time. It also sensitively depends on the dephasing and Ginzburg–Landau timescales. Further estimates suggest that this mechanism dominates over the conventional temperature fluctuations in the same range of parameters. To describe these effects microscopically, we use the nonequilibrium Keldysh technique in the semiclassical approximation of superconductivity with Boltzmann–Langevin random forces to account for correlations of fluctuations.

Adiabatically compressed wave dark matter halo and intermediate-mass-ratio inspirals

The adiabatic growth of a central massive black hole could compress the surrounding dark matter halo, leading to a steeper profile of the dark matter halo. This phenomenon is called adiabatic compression. We investigate the adiabatic compression of wave dark matter - a light bosonic dark matter candidate with its mass smaller than a few eV. Using the adiabatic theorem, we show that the adiabatic compression leads to a much denser wave dark matter halo similar to the particle dark matter halo in the semiclassical limit. The compressed wave halo differs from that of the particle halo near the center where the semiclassical approximation breaks down, and the central profile depends on dark matter and the central black hole mass as they determine whether the soliton and low angular momentum modes can survive over the astrophysical time scale without being absorbed by the black hole. Such a compressed profile has several astrophysical implications. As one example, we study the gravitational waves from the inspiral between a central intermediate-mass black hole and a compact solar-mass object within the wave dark matter halo. Due to the enhanced mass density, the compressed wave dark matter halo exerts stronger dynamical friction on the orbiting object, leading to the dephasing of the gravitational waves. The pattern of dephasing is distinctive from that of inspirals in the particle dark matter halo because of the difference in density profile and because of the relatively suppressed dynamical friction force, originating from the wave nature of dark matter. We investigate the prospects of future gravitational wave detectors, such as Laser Interferometer Space Antenna, and identify physics scenarios where the wave dark matter halo can be reconstructed from gravitational wave observations.

Vlasov–Maxwell equations with spin effects

We present a numerical method to solve the Vlasov–Maxwell equations for spin-1/2 particles, in a semiclassical approximation where the orbital motion is treated classically while the spin variable is fully quantum. Unlike the spinless case, the phase-space distribution function is a $2\times 2$ matrix, which can also be represented, in the Pauli basis, as one scalar function $f_0$ and one three-component vector function $\boldsymbol f$ . The relationship between this ‘vectorial’ representation and the fully scalar representation on an extended phase space first proposed by Brodin et al. (Phys. Rev. Lett., vol. 101, 2008, p. 245002) is analysed in detail. By means of suitable approximations and symmetries, the vectorial spin-Vlasov–Maxwell model can be reduced to two-dimensions in the phase space, which is amenable to numerical solutions using a high-order grid-based Eulerian method. The vectorial model enjoys a Poisson structure that paves the way to accurate Hamiltonian split-time integrators. As an example, we study the stimulated Raman scattering of an electromagnetic wave interacting with an underdense plasma, and compare the results with those obtained earlier with the scalar spin-Vlasov–Maxwell model and a particle-in-cell code.

On the applicability of the Landau-Zener formula to axion-photon conversion

Axions and photons resonantly interconvert in regions where the plasma frequency approximately equals the axion mass. This process is directly analogous to an avoided level crossing in quantum mechanics, for which the celebrated Landau-Zener (LZ) formula provides a simple, non-perturbative solution for the conversion probability. The LZ formula is commonly used in studies of axion-photon conversion; however, in this context, it relies on the assumption that the magnetic field variation is small compared to variations of the plasma frequency, which is frequently not the case in real plasmas.We derive a generalised version of the LZ formula by allowing the boundaries to be located at a scale that is similar to the inhomogeneities. We find that the LZ formula fails when the oscillation range is small compared to the resonance region. This failure is more severe in the adiabatic limit, when the plasma frequency varies slowly, resulting ina conversion probability that is not maximal as opposed to a naive application of the LZ formula.Moreover, we consider circumstances where the generalised LZ formula does not apply and present an alternative semi-classical approximation with complementary regime of validity.

Fokker-Planck treatment of nonlinearities in the dispersive coupling of an ion and an optical cavity

We complement previous studies of an ion coupled with an optical cavity in the dispersive regime, for a model which exhibits bistability of different configurations in the semiclassical description. Our approach is based on a truncated evolution in phase space and is intended to explore an especially interesting parameter region where the fully quantum-mechanical solution becomes hard but the crudest semiclassical approach fails to capture essential phenomena. We compare the results of our techniques with the ones from numerical diagonalization of the quantum evolution and find that although the treatment leads to a smoothening and a slight shift of the transitions in the system, it still provides a clear improvement over localized semiclassical approximations.

Worldline instantons for the momentum spectrum of Schwinger pair production in spacetime dependent fields

We show how to use the worldline-instanton formalism to calculate the momentum spectrum of the electron-positron pairs produced by an electric field that depends on both space and time. Using the Lehmann-Symanzik-Zimmermann (LSZ) reduction formula with a worldline representation for the propagator in a spacetime field, we make use of the saddle-point method to obtain a semiclassical approximation of the pair-production spectrum. To check the final result, we integrate the spectrum and compare with the results obtained using a previous instanton method for the imaginary part of the effective action.

Vortices number and the critical atoms number of a rotating Bose–Einstein condensates in two-dimensional optical lattice

In this paper, the vortices number and the critical atoms number are calculated. Calculations are performed for ultracold trapped Bose gas in two-dimensional deep optical lattice. Hellmann–Feynman theorem is used here to calculate the expectation values of the angular momentum and thermal average of square radius (in situ size). The above-mentioned parameters are calculated from the thermodynamic grand potential [Formula: see text]. The latter is calculated using a conventional semi-classical approximation. This thermodynamic grand potential allows us to investigate the impacts of the finite size and inter-atomic interaction effects. The obtained result for the vortices number has a peak with increase in the rate of rotation. While the critical atoms number has increase in nature with increase in the critical temperature. These parameters show a major dependence on the inter-atomic interaction, depth of optical lattice and number of particles.

All-optical polarization-state engineering in quantum cavity optomagnonics

We theoretically propose an optical polarization-state engineering based on a cavity optomagnonic platform in the full quantum regime. Here, the optomagnonic interaction can be realized in an yttrium iron garnet (YIG) sphere, which supports both two traveling-photon modes with orthogonal linear polarizations [i.e., horizontally ($H$-) and vertically ($V$-) polarized photon modes] and a Kittel magnon mode. In our scheme, the magnons mediate the photons during polarization conversions, and break the time-reversal symmetry in mutual interconversions. Through a triple resonance between the magnon mode, $H$-polarized, and $V$-polarized photon modes within the YIG optomagnonic cavity, we demonstrate an all-optical scheme to manipulate the optical polarization behaviors by adjusting an external driving laser, finding that the polarization states of the output light can be well mapped to the whole Poincar\'e sphere and a large polarization rotation of the output light with photon antibunching and superbunching can be achieved easily for a range of realistic parameters. We find the strong discrepancy in the polarization response between the exact numerical calculation using the full quantum master equation and the semiclassical approximation. In addition, we reveal the magnon-induced broken time-reversal symmetry, which connects the quantum cavity optomagnonics to the classical magneto-optical effect. Our obtained results have potential application in quantum polarization-state engineering, and also offer a further understanding for cavity optomagnonics at the quantum level.