Quantum weak chaos in a degenerate system

Quantum weak chaos is studied in a perturbed degenerate system: a charged p article interacting with a monochromatic wave in a transverse magnetic held . 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 e igenstates under resonance conditions (when the wave frequency equals the c yclotron frequency) in the regime of weak classical chaos. The new phenomen on 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 diff usion to a diffusion that is the quantum manifestation of classical diffusi on along the stochastic web. This crossover results from the nonmonotonic d ependence of the characteristic localization length of the quasienergy stat es on the wave amplitude. The width of the quantum separatrices was compute d and compared with the width of the classical stochastic web. We give the physical parameters that can be realized experimentally to show the manifes tation of quantum chaos in a nonlinear acoustic resonance. [S1063-651X(98)1 0412-9].