Quasiclassical Parameter Research Articles

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.

Vortex charges and impurity effects based on quasiclassical theory in an s -wave and a chiral p -wave superconductor

We investigate charge densities around the vortex cores of an s-wave and a chiral p-wave superconductor (SC) in two dimension within quasiclassical theory. We consider contributions of particle-hole asymmetry through gradient expansions in first order of a quasiclassical parameter using augmented quasiclassical theory. The chiral p-wave SC has two inequivalent vortices: one is charged and the other is uncharged on the basis of Bogoliubov--de Gennes (BdG) equation. We explain this qualitatively distinct charges also by the augmented quasiclassical theory. In addition, we find that much larger charge is induced for the charged vortex of the chiral p-wave SC compared with the vortex of the s-wave SC in the clean system. We also confirm this enhancement through quantitative comparison with results based on the BdG theory. We also study effects of Born-type impurities using self-energy formalism and find that the larger charge density is rather suppressed in contrast to the s-wave's one. Furthermore we study the local density of states as another equilibrium property of particle-hole asymmetry.

Trace formulas for Wiener–Hopf operators with applications to entropies of free fermionic equilibrium states

We consider non-smooth functions of (truncated) Wiener–Hopf type operators on the Hilbert space L2(Rd). Our main results are uniform estimates for trace norms (d≥1) and quasiclassical asymptotic formulas for traces of the resulting operators (d=1). Here, we follow Harold Widom's seminal ideas, who proved such formulas for smooth functions decades ago. The extension to non-smooth functions and the uniformity of the estimates in various (physical) parameters rest on recent advances by one of the authors (AVS). We use our results to obtain the large-scale behaviour of the local entropy and the spatially bipartite entanglement entropy (EE) of thermal equilibrium states of non-interacting fermions in position space Rd (d≥1) at positive temperature, T>0. In particular, our definition of the thermal EE leads to estimates that are simultaneously sharp for small T and large scaling parameter α>0 provided that the product Tα remains bounded from below. Here α is the reciprocal quasiclassical parameter. For d=1 we obtain for the thermal EE an asymptotic formula which is consistent with the large-scale behaviour of the ground-state EE (at T=0), previously established by the authors for d≥1.

Quasi-classical asymptotics for functions of Wiener\u2013Hopf operators: smooth versus non-smooth symbols

We consider functions of Wiener–Hopf type operators on the Hilbert space {mathsf{L}^2(mathbb{R}^d)}. It has been known for a long time that the quasi-classical asymptotics for traces of resulting operators strongly depend on the smoothness of the symbol: for smooth symbols the expansion is power-like, whereas discontinuous symbols (e.g. indicator functions) produce an extra logarithmic factor. We investigate the transition regime by studying symbols depending on an extra parameter {Tge 0} in such a way that the symbol tends to a discontinuous one as {Tto 0}. The main result is two-parameter asymptotics (in the quasi-classical parameter and in T), describing a transition from the smooth case to the discontinuous one. The obtained asymptotic formulas are used to analyse the low-temperature scaling limit of the spatially bipartite entanglement entropy of thermal equilibrium states of non-interacting fermions.

Impurity Effects on Caroli–de Gennes–Matricon Mode in Vortex Core in Superconductors

We develop a scheme of Gor'kov Green's functions to treat impurity effects on Caroli-de Gennes-Matricon (CdGM) mode in superconductors (SCs) by improving the Kopnin-Kravtsov scheme with respect to the coherence factors and applicability to various SCs. We can study the impurity effects keeping the discreteness of the energy spectrum in contrast to the quasiclassical theory. We can thus apply this scheme to the SCs with the small quasiclassical parameter $k_{\mathrm{F}}\xi_{0}$ (which is the product of the Fermi wavenumber $k_{\mathrm{F}}$ and the coherence length $\xi_{0}$ in pure SC at zero temperature) and/or superclean regime $\Delta_{\mathrm{mini}} \tau \gg1$ ($\Delta_{\mathrm{mini}}$ and $\tau$ denote, respectively, the level spacing of the CdGM mode called minigap and the relaxation time for CdGM mode and we take $\hbar =1$). We investigate the impurity effects as a white noise for a vortex in an s-wave SC and two types of vortices in a chiral p-wave SC, for various values of the quasiclassical parameters and impurity strengths (from moderately clean regime to superclean regime), and confirm the validity of this scheme.

On the Stability of a Quantum Dynamics of a Bose-Einstein Condensate Trapped in a One-Dimensional Toroidal Geometry

We rigorously analyze the stability of the “quasi-classical” dynamics of a Bose-Einstein condensate with repulsive and attractive interactions, trapped in an effective 1D toroidal geometry. The “classical” dynamics, which corresponds to the Gross-Pitaevskii mean field theory, is stable in the case of repulsive interaction, and unstable (under some conditions) in the case of attractive interaction. The corresponding quantum dynamics for observables is described by using a closed system of linear partial differential equations. In both cases of stable and unstable quasi-classical dynamics the quantum effects represent a singular perturbation to the quasi-classical solutions, and are described by the terms in these equations which consist of a small quasi-classical parameter which multiplies high-order “spatial” derivatives. We demonstrate that as a result of the quantum singularity for observables a convergence of quantum solutions to the corresponding classical solutions exists only for limited times, and estimate the characteristic time-scales of the convergence.

Quantum Dynamics in the Fermi–Pasta–Ulam Problem

We study a quantum chain of oscillators with nonlinear quartic interactions, under the “narrow packet” approximation. We analyse the dynamics of quantum corrections and the conditions at which the quantum solution for average complex amplitude converges to the corresponding classical unstable solution which describes the four-wave decay processes of phonons. We develop an asymptotic theory by using a small quasiclassical parameter, and determine the characteristic time scale for which the evolution of decay processes is essentially specified by quantum effects.

Equation of state in the quasi-classical approximation

An approximate equation of state is considered that contains a correction for electron-gas inhomogeneity in the exchange-correlation and kinetic energies in the quasi-classical approximation. The problem of finding the model parameters satisfying the condition P=0 has been solved for metals at a normal density. The results of numerical solution of the model equations are presented for degrees of compression. The values of the quasi-classical parameter determining the approximation accuracy are found. The results are illustrated by the dependences on the degree of compression plotted in the range ρ/ρ0=1–106 and by the spatial dependences. Our approach to construction of the equation of state provides for a quite simple but sufficiently accurate approach to the experimental values of the model parameters. Moreover, the proposed model gives much more self-consistent information as compared to conventional approximations. In particular, the ionicity is calculated for an increase in the density. The model equation can also be used instead of the well-known effective bound-electron potential approximation.

Hierarchical structures in the phase space and fractional kinetics: II. Immense delocalization in quantized systems.

Anomalous transport due to Levy-type flights in quantum kicked systems is studied. These systems are kicked rotor and kicked Harper model. It is confirmed for a kicked rotor that there exist special "magic" values of a control parameter of chaos K=K(*)=6.908 745 em leader for which an essential increasing of a localization length is obtained. Functional dependence of the localization length on both parameter of chaos and quasiclassical parameter h is studied. We also observe immense delocalization of the order of 10(9) for a kicked Harper model when a control parameter K is taken to be K(*)=6.349 972. This "magic" value corresponds to special phase space topology in the classical limit, when a hierarchical self-similar set of sticky islands emerges. The origin of the effect is of the general nature and similar immense delocalization as well as increasing of localization length can be found in other systems. (c) 2000 American Institute of Physics.

Kinetic equations for clean superconductors: Application to the flux flow hall effect

The kinetic equations for clean superconductors (l≫ξ) are derived. Expanding the equations for the time dependent Green functions in the quasiclassical parameter, the new contributions are found which contain the derivatives of the distribution functions with respect to the quasiparticle momentum. The transition from the ultra-clean case (no relaxation) to a relaxation-dominated behavior, for which the kinetic equations coincide with the usual quasiclassical approximation, occurs for the relaxation time of the order of ℏEF/Δ2. The kinetic equations can be used for various dynamic processes in superconductors including the flux-flow Hall effect. The derived equations, after necessary modifications for the p-wave pairing, are especially suitable for nonstationary problems in the theory of superfluidity of3He.

Calculation of the exchange integrals in solid3He

Calculations are performed for two-, three-, and four-particle exchange in the quantum crystal of bcc solid3He. The quasiclassical approximation is used to find the tunneling path in the space of all atomic coordinates of the crystal. Effective potential energy is introduced by means of elasticity theory and the Lennard-Jones anharmonic interaction for exchanging atoms and their nearest neighbors. The two leading terms in the expansion of the logarithm of the exchange integrals in powers of the quasiclassical parameter given by the ratio of the zero oscillation amplitude to the lattice spacing are calculated. It is shown that all three exchange integrals are of the same order of magnitude.