Diffusion and localization in chaotic billiards
Fausto Borgonovi, Giulio Casati, Baowen Li
TL;DR
This paper investigates classical diffusion in chaotic billiards and explores how quantum localization phenomena can be observed, linking classical chaos with quantum statistical properties and potential experimental verification.
Contribution
It provides an analytical and numerical study of diffusion in chaotic billiards, connecting classical chaos with quantum eigenvalue statistics and localization effects.
Findings
Conditions for eigenvalue and eigenfunction statistics to follow Random Matrix Theory
Identification of quantum dynamical localization in chaotic billiards
Potential for observing localization phenomena in experiments
Abstract
We study analytically and numerically the classical diffusive process which takes place in a chaotic billiard. This allows to estimate the conditions under which the statistical properties of eigenvalues and eigenfunctions can be described by Random Matrix Theory. In particular the phenomenon of quantum dynamical localization should be observable in real experiments.
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