Quasiclassical Approximation Research Articles

Polytropic spherical astrocosmic fluid stability in the EiBI gravity with strong collective correlative effects

We herein present a dynamical analysis of the Jeans (gravitational) instability in a viscoelastic polytropic astrocloud within the Eddington-inspired Born-Infeld (EiBI) gravity framework in spherical geometry. The zeroth-order material density curvature corrections to the effective self-gravitational potential are properly incorporated. The applied spherical normal mode analysis yields a unique form of monic cubic dispersion relation with multiparametric coefficients dependent on the diverse equilibrium astrofluidic conditions without invoking any kind of traditional quasi-classic approximation. It is seen that the positive EiBI gravity parameter (χ>0) acts as a stabilizing agent and a negative EiBI gravity parameter (χ<0) acts as a destabilizing agent against the inward non-local self-gravity action. Additionally, we find that larger astroclouds are more prone to gravitational collapse, irrespective of the χ-polarity, and vice-versa. It is further investigated that the cloud temperature plays a stabilizing role at larger wavenumbers and destabilizing at smaller wavenumbers for χ>0. However, for χ<0, the fluid temperature consistently exhibits a destabilizing effect. The viscoelastic relaxation time stabilizes the astrofluid against the self-gravity irrespective of the χ-polarity. The fluid density acts as a stabilizer for χ>0, destabilizer for χ<0, and so forth. This study could be potentially applicable in the EiBI-modified gravitational theory in exploring gravity-driven large-scale astrocosmic phenomena towards structure formation mechanism via the canonical Jeans condensation in diverse astrocosmic conditions.

Non-stationary quasi-classical states of a charged particle in a strong magnetic field under conditions of the dissipative medium

Based on the quasi-classical approximation, a general approach is proposed for constructing non-stationary quantum states of a charged particle in a magnetic field, when the dissipative forces of viscous friction and drag, proportional to the velocity and the square of the velocity, respectively, are also significant. The corresponding quasi-classical Green’s function is found, with the help of which the squeezed and coherent states of the particle are studied. It is shown that the dissipation and a magnetic field suppress the quantum properties of the particle. This is especially true for the transverse motion with respect to the magnetic field. Over time, the coherent and squeezed states transform into the same static state, which is characterized by a zero uncertainty of the transverse coordinates and an uncertainty of the longitudinal coordinate, which contains information about the initial velocity of the particle.

Classical and quantum gravity from the axioms of relativistic quantum mechanics

It is common practice to describe elementary particles by irreducible unitary representations of the Poincaré group. In the same way, multi-particle systems can be described by irreducible unitary representations of the Poincaré group. Representations of the Poincaré group are characterised by fixed eigenvalues of two Casimir operators corresponding to a fixed mass and a fixed angular momentum. In multi-particle systems (of massive spinless particles), fixing these eigenvalues leads to correlations between the particles. In the quasi-classical approximation of large quantum numbers, these correlations take on the structure of a gravitational interaction described by the field equations of conformal gravity. A theoretical value of the corresponding gravitational constant is calculated. It agrees with the empirical value used in the field equations of general relativity.

Quasi-Classical Approximation of Monopole Harmonics

Quasi-Classical Approximation of Monopole Harmonics

Quasi-Classical Approximation of the Data on the Ionization Potentials of Multiply Charged Ions of the Superheavy Elements

The semiempirical quasi-classical method of approximation of the ionization potentials used earlier for multiply charged ions of the elements with medium and high atomic number Z is applied to ions of elements with atomic numbers in the range of 85*z*110 and number of electrons in the range of 1*Ne*78. The discovered simple trends allow using a relatively accurate (to within 1–2%), based on two small tables, polynomial approximation of the available and lacking data on the ionization potentials in the NIST tables for all multiply charged ions in the atomic-number range under consideration. An improvement in the applicability conditions of the quasi-classical approximation with increase in the atomic number is demonstrated

Quasi-Classical Approximation of the Data on the Ionization Potentials of Multiply Charged Ions of the Superheavy Elements

Quasi-Classical Approximation of the Data on the Ionization Potentials of Multiply Charged Ions of the Superheavy Elements

Quasiclassical approach to the nonlinear Kerr dynamics

We examine the quasiclassical approximation to the self-Kerr nonlinear effect. The corresponding dynamics appears as classical trajectories, with the quantumness of the state included via its Wigner function. We obtain analytical estimates of the optimal squeezing attainable that compare fairly well with the numerical quantum solution. We delimit the range of parameters for which the quasiclassical solution retains relevant quantum features.

A Regularized Asymptotic Solution of the Cauchy Problem for the Nonhomogeneous Schroedinger Equation in the Quasiclassical Approximation in the Presence of a "strong" Turning Point of the Limit Operator

The article is devoted to the development of the regularization method by S.A. Lomov on singularly perturbed problems in the presence of spectral singularities of the limit operator. In particular, a regularized asymptotic solution is constructed for the singularly perturbed inhomogeneous Cauchy problem that arises in the quasiclassical approximation in the Schroedinger equation in the coordinate representation. The potential energy profile chosen in the paper leads to a singularity in the spectrum of the limit operator in the form of a &lt;&gt; turning point. Based on the ideas of asymptotic integration of problems with unstable spectrum, S.A. Lomov and A.G. Eliseev, it is indicated how and from what considerations regularizing functions and additional regularizing operators should be introduced, the formalism of the regularization method for the indicated type of singularity is described in detail, this algorithm is substantiated, and an asymptotic solution of any order with respect to a small parameter is constructed.

Quasiclassical theory of Th229m excitation by laser pulses via electron bridges

In the quasiclassical approximation it is studied excitation of the 8.2 eV isomer $^{229m}\mathrm{Th}$ in the electron bridges (EB), initiated by a laser pulse. While the nucleus and atomic electron are treated quantum mechanically, the laser pulse is described by a time-dependent wave packet, formed by classic electromagnetic waves. Two types of the EB are taken into consideration: via the continuous electron spectrum and via discrete atomic levels. In calculations of the excitation probability of $^{229m}\mathrm{Th}$ by a laser pulse I employ the generalized formalism of Floquet functions, which allows one to solve the time-dependent Schr\"odinger equation by the methods of stationary scattering theory. The task is solved for weak lasers as well as for the conventional lasers of arbitrary intensity. In the first case the results well correlate with those obtained previously when treating the laser pulse as a bunch of uncorrelated photons. If conventional lasers generate EB through an atomic level, its population suffers Rabi oscillations. Therefore application of the $\ensuremath{\pi}$ pulses may strongly enhance the effect of the isomer excitation. For the same EB the excitation probability of the isomer as a function of the laser carrier frequency is shown to have two peaks associated with two resonant levels.

Athermal GES-based solar plasma stability with sphero-logabarotropic special effects

A model formalism for the small-scale radial fluctuations excitable in the athermal (non-thermal) solar plasma system on the basis of the non-extensive gravito-electrostatic sheath (GES) model fabric is reported. A unique speciality here is that it intercouples the solar interior plasma (SIP) and the solar wind plasma (SWP) gravito-electrostatically via the interfacial diffused solar surface boundary (SSB). The constitutive electrons are thermostatistically framed in the κ-distribution laws via the Tsallis thermostatistics. In contrast, the heavier ions are treated as an inhomogeneous fluid. The turbulent degrees of freedom are accounted through the Larson nonlinear logabarotropic equation of state in curved geometry. A spherically symmetric wave analysis over the perturbed GES structure results in a unique pair of distinct linear dispersion laws (SIP plus SWP) without any typical quasi-classic approximation. A numerical illustrative platform for the dispersion analysis specifically shows that an antikink-type (kink-type) impulsive rarefactive (compressive) propagatory boost due to irregular dispersion is experienced by the fluctuations at the heliospheric core (photospheric SSB). We see that the thermostatistical parameter (Tsallis power-law tail index κ) acts as a unique form of acceleration agency for both the SIP and SWP instabilities to proliferate. At the last, the explorative semi-analytic results are contextually compared with the realistic domains of the collective excitation of the helioseismic waves and SSB oscillations.

Surface Resistance and Amplitude Mode under Uniform and Static External Field in Conventional Superconductors

We calculate the surface resistance of s-wave superconductors under a static external field on the basis of the quasiclassical approximation. The numerical calculations are performed both for the dirty and relatively clean cases, and the difference in the absorption spectrum between them is investigated. The amplitude mode in the dirty case, which has been previously studied in the local response function, appears also in the nonlocal response. In the clean case, there is a large discrepancy between the excitation energy of the amplitude mode and the energy of the gap edge where the coupling between the electrons and the external field is effective. Therefore, the amplitude mode exists even when the superconductor is relatively clean, but its contribution to the response function is small. These behaviors, which are qualitatively consistent with the experimental results, are obtained by taking into account the static field nonperturbatively.

Instability of Solitons and Collapse of Acoustic Waves in Media with Positive Dispersion

This article is a brief review of the results of studying the collapse of sound waves in media with positive dispersion, which is described in terms of the three-dimensional Kadomtsev-Petviashvili (KP) equation. The KP instability of one-dimensional solitons in the long-wavelength limit is considered using the expansion for the corresponding spectral problem. It is shown that the KP instability also takes place for two-dimensional solitons in the framework of the three-dimensional KP equation with positive dispersion. According to B.B. Kadomtsev this instability belongs to the self-focusing type. The nonlinear stage of this instability is a collapse. One of the collapse criteria is the Hamiltonian unboundedness from below for a fixed momentum projection coinciding with the $L_2$-norm. This fact follows from scaling transformations, leaving this norm constant. For this reason, collapse can be represented as the process of falling a particle to the center in a self-consistent unbounded potential. It is shown that the radiation of waves from a region with a negative Hamiltonian, due to its unboundedness from below, promotes the collapse of the waves. This scenario was confirmed by numerical experiments \cite{KuznetsovMusherShafarenko1983, KuznetsovMusher1986}. Two analytical approaches to the study of collapse are presented: using the variational method and the quasiclassical approximation. In contrast to the nonlinear Schr\"odinger equation (NLSE) with a focusing nonlinearity, a feature of the quasiclassical approach to describing acoustic collapse is that this method is proposed for the three-dimensional KP equation as a system with hydrodynamic nonlinearity. Within the framework of the quasiclassical description, a family of self-similar collapses is found.

Holonomic quantum manipulation in the Weyl disk

It has been shown that a Weyl point in a superconducting nanostructure may give rise to a Weyl disk where two quantum states are almost degenerate in a two-dimensional manifold in the parametric space. This opens up the possibility of a holonomic quantum manipulation: A transformation of the wave function upon an adiabatic change of the parameters within the degenerate manifold. In this paper, we investigate in detail the opportunities for holonomic manipulation in Weyl disks. We compute the connection at the manifold in quasiclassical approximation to show it is Abelian and can be used for a phase gate. To provide a closed example of quantum manipulation that includes a state preparation and readout, we augment the holonomic gate with a change of parameters that brings the system out of the degenerate subspace. For numerical illustrations, we use a finite value of quasiclassical parameter and exact quantum dynamics. We investigate the fidelity of an example gate for different execution times. We evaluate the decoherence rate and show it can be made small to ensure a wide frequency range where an adiabatic manipulation remains coherent.

Universal Hall conductivity in graphene Maxwell fish-eye quantum dot

Graphene quantum dot with Maxwell fish eye potential energy profile is studied. A quasiclassical approximation is used given that potential energy is a slowly varying function of coordinates. Near the zero energy the spectrum of electron macroscopically degenerates. All the electron trajectories are closed circles that are classified by angular momentum and an additional integral of motion. Provided the complete filling of the lower Dirac zone, a universal value for Hall conductivity is found.

On the Role of Electron Quantum Tunneling in Charging of Dust Grains in Complex Plasma

The role of the quantum tunneling effect in the electron accretion current onto a negatively charged grain immersed in isotropic plasma is analyzed, within the quasiclassic approximation, for different plasma electron distribution functions, plasma parameters, and grain sizes. It is shown that the contribution of the quantum tunneling into the grain charging is small (negligible) for relatively large (micron-sized) dust grains in plasmas with electron temperatures of the order of a few eV, but becomes important for nano-sized dust grains (tens to hundreds nm in diameter) in cold and ultracold plasmas (electron temperatures ~ tens to hundreds of Kelvin degrees), especially in plasmas with depleted high-energy "tails" in the electron energy distribution.

Density of states and interband light absorption in Y2O3 and Sc2O3 thin films

The long-wavelength edge of the fundamental absorption band of thin Y2O3 and Sc2O3 films obtained by the method of discrete evaporation in vacuum is investigated. On the basis of its temperature dependence, the excitons - phonon interaction is investigated, which made it possible to interpret the absorption edge as the absorption of self-trapped excitons. To analyze the experimental results, we used a model of a heavily doped or defective semiconductor in the quasi-classical approximation. The use of this model made it possible to estimate the radius of the ground electronic state a and the screening radius rS and the concentration of free charge carriers N in the films under study.&#x0D;

Двумерные электроны низкой плотности в магнитном поле

The photoluminescence spectrum from the two-dimensional low density electrons with the localized valence-band holes in magnetic field is studied. The ground state is considered as Wigner crystal ore the strongly correlated electron system. For the quantum Wigner crystal the Landau levels for vacancions (quasiholes appearing in the process of photoluminescence) are calculated in the quasiclassical approximation. The spectrum of single-particle excitations for a triangular lattice in the nearest-neighbor approximation is used. It is found that Landau levels for vacancions depend unusually on magnetic field. For the electron system with strong Coulomb interaction the Mahan exciton effect in the photoluminescence for the two-dimensional electrons in magnetic field is considered.

Infinite bound states and 1/n energy spectrum induced by a Coulomb-like potential of type III in a flat band system

In this work, we investigate the bound states in a one-dimensional spin-1 flat band system with a Coulomb-like potential of type III, which has a unique non-vanishing matrix element in basis ∣1〉. It is found that, for such a kind of potential, there exists infinite bound states. Near the threshold of continuous spectrum, the bound state energy is consistent with the ordinary hydrogen-like atom energy level with Rydberg correction. In addition, the flat band has significant effects on the bound states. For example, there are infinite bound states which are generated from the flat band. Furthermore, when the potential is weak, the bound state energy is proportional to the potential strength α. When the bound state energies are very near the flat band, they are inversely proportional to the natural number n (e.g., E n ∝ 1/n, n = 1, 2, 3, …). Further we find that the energy spectrum can be well described by quasi-classical approximation (WKB method). Finally, we give a critical potential strength α c at which the bound state energy reaches the threshold of continuous spectrum. After crossing the threshold, the bound states in the continuum (BIC) would exist in such a flat band system.

Two-dimensional low density electrons in high magnetic field

The photoluminescence spectrum from the two-dimensional low density electrons with the localized valence-band holes in magnetic field is studied. The ground state is considered as Wigner crystal ore the strongly correlated electron system. For the quantum Wigner crystal the Landau levels for vacancions (quasiholes appearing in the process of photoluminescence) are calculated in the quasiclassical approximation. The spectrum of single-particle excitations for a triangular lattice in the nearest-neighbor approximation is used. It is found that Landau levels for vacancions depend unusually on magnetic field. For the electron system with strong Coulomb interaction the Mahan exciton effect in the photoluminescence for the two-dimensional electrons in magnetic field is considered. Keywords: Wigner crystal, magnetic field, Mahan exciton, correlated electrons.

Reliable modeling of weak antilocalization for accurate spin-lifetime extraction

We examine models for the quantum-interference correction to the magnetoconductivity in two-dimensional electron gases (2DEGs) with both Rashba and Dresselhaus spin-orbit coupling for their applicability to experimental data fitting. In particular, we compare the Landau-quantized Cooperon approach, which is mostly only numerically treatable, and the quasiclassical approximation that was recently employed to obtain an explicit solution for arbitrary Rashba and Dresselhaus spin-orbit couplings [Marinescu et al., Phys. Rev. Lett. 112, 156601 (2019)]. It is found that the quasiclassical approximation yields significantly different results even to the lowest order in the magnetic field and appears unsuitable for reliable parameter fitting. The discrepancy emerges when a sum over Landau levels is replaced by an integral over wave vectors. Substantial improvement is achieved by supplementing the quasiclassical model with the first two corrections given by the Euler-MacLaurin formula for approximating a sum by an integral. Corresponding modifications are, however, only feasible in special spin-orbit parameter configurations where the mixing of Landau bands is negligible and a closed-form solution that accounts for Landau quantization is also available. Such a scenario appears in a parameter regime where a persistent spin helix emerges and a transition between weak localization and weak antilocalization takes place. Combining recent findings, we derive a generalized closed-form expression for the magnetoconductivity correction applicable to generic 2DEGs that are grown along a crystal direction with at least two growth-direction Miller indices equal in modulus. The result is a function of spin lifetimes of the long-lived spin textures and valid close to the persistent-spin-helix regime. The accuracy of the derived formula is validated by comparing with results from numerical diagonalization of the multiband Cooperon as well as a recently established Monte Carlo-based real-space simulation in exemplary (001)-, (113)-, and (110)-2DEGs.