Quantum weak chaos in a degenerate system

Abstract

Quantum weak chaos is studied in a perturbed degenerate system: a charged particle interacting with a monochromatic wave in a transverse magnetic field. The evolution operator for an arbitrary number of periods of the external field is built and its structure is explored in terms of the quasienergy eigenstates under resonance conditions (when the wave frequency equals the cyclotron frequency) in the regime of weak classical chaos. The new phenomenon of diffusion via the quantum separatrices and the influence of chaos on diffusion are investigated and, in the quasiclassical limit, compared with its classical dynamics. We determine the crossover from purely quantum diffusion to a diffusion that is the quantum manifestation of classical diffusion along the stochastic web. This crossover results from the nonmonotonic dependence of the characteristic localization length of the quasienergy states on the wave amplitude. The width of the quantum separatrices was computed and compared with the width of the classical stochastic web. We give the physical parameters that can be realized experimentally to show the manifestation of quantum chaos in a nonlinear acoustic resonance.