Influence of phase space localization on the energy diffusion in a quantum chaotic billiard

Abstract

The quantum dynamics of a chaotic billiard with moving boundary is considered in this work. We found a shape parameter Hamiltonian expansion which enables us to obtain the spectrum of the deformed billiard for deformations so large as the characteristic wave length. Then, for a specified time dependent shape variation, the quantum dynamics of a particle inside the billiard is integrated directly. In particular, the dispersion of the energy is studied in the Bunimovich stadium billiard with oscillating boundary. The results showed that the distribution of energy spreads diffusively for the first oscillations of the boundary ($<{\Delta }^{2}E>=2Dt$). We studied the diffusion contant $D$ as a function of the boundary velocity and found differences with theoretical predictions based on random matrix theory. By extracting highly phase space localized structures from the spectrum, previous differences were reduced significantly. This fact provides the first numerical evidence of the influence of phase space localization on the quantum diffusion of a chaotic system.

5 pages, 5 figures

References in corpus (1)

• Localized Structures Embedded in the Eigenfunctions of Chaotic Hamiltonian Systems

Cited by in corpus (7)

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• Sensitivity to perturbations in a quantum chaotic billiard
• Universal Response of Quantum Systems with Chaotic Dynamics
• Stadium Billiard with Moving Walls
• Dephasing due to the interaction with chaotic degrees of freedom
• The Loschmidt echo in classically chaotic systems: Quantum chaos, irreversibility and decoherence