arXiv subjects
Publications and source records attributed to D. I. Kamenev.
Using Husimi function approach, we study the ``quantum phase space'' of a harmonic oscillator interacting with a plane monochromatic wave. We show that in the regime of weak chaos, the quantum system has the same symmetry as the classical system. Analytical results agree with the results of numerical calculations.
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.
A new type of localization - localization over the quantum resonance cells - in an intrinsically degenerate system is explored by using the quasienergy eigenstates.