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 QE (quasienergy eigenstates) under resonance condition (wave frequency $=$ 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 quasi classical limit, compared with its classical dynamics. We determine the crossover from purely quantum diffusion to a diffusion which is the quantum manifestation of classical diffusion along the stochastic web. This crossover results from the non-monotonic dependence of the characteristic localization length of the QE 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 which can be realized experimentally to show the manifestation of quantum chaos in nonlinear acoustic resonance.

21 pages RevTex, 8 figures in GIF format. Accepted to Phys. Rev E

References in corpus (1)

• Localization of Quantum States at the Cyclotron Resonance

Cited by in corpus (5)

• Manifestation of the Arnol'd Diffusion in Quantum Systems
• Quantum Arnol'd Diffusion in a Simple Nonlinear System
• Symmetry of Quantum Phase Space in a Degenerate Hamiltonian System
• Dynamical Stability of an Ion in a Linear Trap as a Solid-State Problem of Electron Localization
• Stability of the Ground State of a Harmonic Oscillator in a Monochromatic Wave