Stochastic switching and dynamical freezing in nonlinear spin systems

We consider the controlled switching of individual spins in a nonlinear, interacting spin chain by means of external magnetic fields. We show analytically and by full numerical simulations that stochastic switching is achievable when the driving fields are such that the underlying semi-classical dynamics is chaotic. On the basis of random matrix theory and the geometry of quantum evolution we confirm the quantum case to follow qualitatively the semi-classical behavior.     

Unified theory of bound and scattering molecular Rydberg states as quantum maps

Using a representation of multichannel quantum defect theory in terms of a quantum Poincaré map for bound Rydberg molecules, we apply Jung's scattering map to derive a generalized quantum map, that includes the continuum. We show that this representation not only simplifies the understanding of the method, but moreover produces considerable numerical advantages. Finally we show under what circumstances the usual semi-classical approximations yield satisfactory results. In particular we see that singularities that cause problems in semi-classics are irrelevant to the quantum map.     

Fermions tunneling of higher-dimensional Kerr–Anti-de Sitter black hole with one rotational parameter

The 1/2 spin fermions tunneling at the horizon of n-dimensional Kerr–Anti-de Sitter black hole with one rotational parameter is researched via semi-classical approximation method, and the Hawking temperature and fermions tunneling rate are obtained in this Letter. Using a new method, the semi-classical Hamilton–Jacobi equation is gotten from the Dirac equation in this Letter, and the work makes several quantum tunneling theories more harmonious.     

On Semi-Classical States of Quantum Gravity and Noncommutative Geometry

We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated as a spectral triple over holonomy loops. The semi-classical limit of the spectral triple gives the Dirac Hamiltonian in 3+1 dimensions. Also, time-independent lapse and shift fields emerge from the semi-classical states. Our analysis shows that the model might contain fermionic matter degrees of freedom.     

Expansion and evaporation of hot nuclei: Comparison between semi-classical and quantal mean-field approaches

We present a general discussion of the mean field dynamics of finite nuclei prepared under extreme conditions of temperature and pressure We compare the prediction of semi-classical approximation with complete quantum simulations. Many features of the dynamics are carefully studied such as the collective expansion, the evaporation process, the different time-scale, etc. This study points out many quantitative differences between quantum and semi-classical approaches. Part of the differences are related to numerical features inherent in semi-classical simulations but most of them are a direct consequence of the non-treatment of nuclei as quantal objects. In particular, we show that because of a too strong damping in semi-classical approaches the expansion of hot nuclei is quenched and the speed of the collective motion reduced.     

The two-photon particle production mechanism. Physical problems. Applications. Equivalent photon approximation

A semi-classical theory, derived from the Feynman path-integral formalism by applying the saddle point method, is formulated for elastic and inelastic heavy ion reactions. This theory is a natural extension of earlier semi-classical methods in the sense that classical, real, trajectories are extended to complex ones by an analytic continuation of Hamilton's equations. It describes properly the role played by the complex interaction and the resulting absorptive, refractive and diffractive phenomena. The connection with the WKB-approximation is discussed. A comparison between the results of three types of calculation is made: exact (quantum mechanical), semi-classical and the earlier semi-classical approach based on real trajectories. This shows the quantitative power of the semi-classical method presented here, not only for the elastic and inelastic cross sections but it also reproduces the quantum mechanical phase shifts, reflection coefficients and excitation coefficients in quite some detail, contrary to the earlier semi-classical calculations.     

Finite-size-scaling analyses of the chiral ordert in the Josephson-junction ladder with half a flux quantum per plaquette

Chiral order of the Josephson-junction ladder with half a flux quantum per plaquette is studied by means of the exact diagonalization method. We consider an extreme quantum limit where each superconductor grain (order parameter) is represented by S=1/2 spin. So far, the semi-classical case, where each spin reduces to a plane rotator, has been considered extensively. We found that in the case of S=1/2, owing to the strong quantum fluctuations, the chiral (vortex lattice) order becomes dissolved except in a region, where attractive intrachain and, to our surprise, repulsive interchain interactions both exist. On the contrary, for considerably wide range of parameters, the superconductor (XY) order is kept critical. The present results are regarded as a demonstration of the critical phase accompanying chiral-symmetry breaking predicted for frustrated XXZ chain field-theoretically. Received 20 February 2000     

Spin damping correction to electrostatic modes in kinetic plasma theory

The effect of spin of particles is studied using a semi-classical kinetic theory for a magnetized plasma. No other quantum effects are included. We focus in the simple damping effects for the electrostatic wave modes. Besides Landau damping, we show that spin produces two new different effects of damping or instability which are proportional to ?. These corrections depend on the electromagnetic part of the wave that is coupled with the spin vector.     

The quantum spectra analysis of the circular billiards in wells

We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier-transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classical method provides a bridge between quantum and classical mechanics.     

Semi-classical approximation for a class of quantum dynamical semigroups

We determine the complex semi-classical approximation to the propagator for a class of quantum dynamical semigroups and study a simple model. The method uses functional integral techniques developed earlier.     

Predictions of quantum mechanics and stochastic electrodynamics in travelling wave second harmonic generation

We show that stochastic electrodynamics and quantum mechanics give quantitatively different predictions for the quantum nondemolition (QND) correlations in travelling wave second harmonic generation. Using phase space methods and stochastic integration, we calculate correlations in both the positive-P and truncated Wigner representations, the latter being equivalent to the semi-classical theory of stochastic electrodynamics. We show that the semi-classical results are different in the regions where the system performs best in relation to the QND criteria, and that they significantly overestimate the performance in these regions.     

Comparison of quantum,semi-classical and classical methods in the calculation of nitrogen self-broadened linewidths

We perform dynamical calculations on two robust N₂–N₂ potential energy surfaces in order to intercompare pressure broadening coefficients derived from close coupling and coupled states quantum dynamical methods, the semi-classical model of Robert and Bonamy and a full classical method. The coupled states and full classical results compare well with the experimental results or with close coupling values when available. This study confirms that the classical method is a good alternative at room and high temperatures to quantum dynamical methods. The results obtained using the semi-classical method however deviate from the other sets of data at all temperatures considered here (77–2400 K).     

Quantum dynamics of bouncing atoms in a stable gravitational cavity

Two-level atoms bouncing in a stable gravitational cavity are considered, where the atomic mirror at the bottom of the bounces is an evanescent wave caused by an internally reflected intense Gaussian-mode laser beam. We consider the broadening mechanisms of the atoms from their initially tightly spaced position distribution, using a phenomenological semi-classical model, which includes spontaneous emission. A fully quantum model, which neglects spontaneous emission, is derived, and the broadening of the atomic wave function in the quantum model is compared with the broadening of the atomic distribution in an analogous classical simulation where spontaneous emission is similarly neglected. We find that the broadening is correctly described by the classical simulations in the horizontal directions, while it significantly underestimates the broadening in the vertical direction.Dedicated to H. Walther on the occasion of his 60th birthday     

Crossover from diffusive to ballistic transport in periodic quantum maps

We derive an expression for the mean square displacement (MSD) of a particle whose motion is governed by a uniform, periodic, quantum multi-baker map. The expression is a function of both time, t, and Planck’s constant, h, and allows a study of both the long time, t→∞, and semi-classical, h→0, limits taken in either order. We evaluate the expression using random matrix theory as well as numerically, and observe good agreement between both sets of results. The long time limit shows that particle transport is generically ballistic for any fixed value of Planck’s constant. However, for fixed times, the semi-classical limit leads to diffusion. The mean square displacement for non-zero Planck’s constant, and finite time, exhibits a crossover from diffusive to ballistic motion, with crossover time on the order of the inverse of Planck’s constant. We argue that these results are generic for a large class of 1D quantum random walks, similar to the quantum multi-baker, and that a sufficient condition for diffusion in the semi-classical limit is classically chaotic dynamics in each cell. Some connections between our work and the other literature on quantum random walks are discussed. These walks are of some interest in the theory of quantum computation.     

Electron waiting times for the mesoscopic capacitor

We evaluate the distribution of waiting times between electrons emitted by a driven mesoscopic capacitor. Based on a wave packet approach we obtain analytic expressions for the electronic waiting time distribution and the joint distribution of subsequent waiting times. These semi-classical results are compared to a full quantum treatment based on Floquet scattering theory and good agreement is found in the appropriate parameter ranges. Our results provide an intuitive picture of the electronic emissions from the driven mesoscopic capacitor and may be tested in future experiments.     

Two-loop back-reaction in 2D dilaton gravity

We calculate the two-loop quantum corrections, including the back-reaction of the Hawking radiation, to the one-loop effective metric in a unitary gauge quantization of the CGHS model of 2D dilaton gravity. The corresponding evaporating black hole solutions are analyzed, and consistent semi-classical geometries appear in the weak-coupling region of the space-time when the width of the matter pulse is larger then the short-distance cutoff. A consistent semi-classical geometry also appears in the limit of a shock-wave matter. The Hawking radiation flux receives non-thermal corrections such that it vanishes for late times and the total radiated mass is finite. There are no static remnants for matter pulses of finite width, although a BPP type static remnant appears in the shock-wave limit. Semi-classical geometries without curvature singularities can be obtained as well. Our results indicate that higher-order loop corrections can remove the singularities encountered in the one-loop solutions.     

Origin of conductance oscillations in square electron billiards: A semi-classical approach

We perform semi-classical and quantum mechanical calculations on square billiards and provide a semi-classical interpretation of the conductance oscillations. We outline its relation to the Gutzwiller's picture of periodic orbits. The frequencies of the conductance oscillations are shown to be due to interference of pairs of long trajectories, which in the phase space are typically situated near the corresponding periodic orbit. We identify the pair of trajectories causing the pronounced peak in a recent experiment and from this directly extract the phase coherence length.     

Approximation semi-classique de l'equation de Heisenberg

We study the semi-classical approximation for the solution of Heisenberg equation in terms of pseudo-differential operators and establish a semi-classical version of Egorov's theorem. As an application of these results, we get the classical limit of quantum mechanical correlation functions for a class of non-bounded observables.     

Semi-classical approximation and the problem of boundary conditions in the theory of relativistic particle radiation

Abstract

The process of relativistic particle radiation in an external field has been studied in the semi-classical approximation rather extensively. The main problem arising in the studies is to express the formula of the quantum theory of radiation in terms of classical quantities, for example of the classical trajectories. However, it still remains unclear how the particle trajectory is assigned, that is which particular initial or boundary conditions determine the trajectory in semi-classical approximation quantum theory of radiation.

We shall try to solve this problem. Its importance comes from the fact that in some cases one and the same boundary conditions may give rise to two or more trajectories. We demonstrate that this fact must necessarily be taken into account on deriving the classical limit for the formulae of the quantum theory of radiation, since it leads to a specific interference effect in radiation.

The method we used to deal with the problem is similar to the method employed by Fock to analyze the problem of a canonical transformation in classical and quantum mechanics.