Quantum localization in rough billiards
Klaus M. Frahm, Dima L. Shepelyansky
TL;DR
This paper investigates how boundary roughness in billiards causes quantum localization and affects spectral statistics, with implications for optical resonator design.
Contribution
It introduces the study of quantum localization effects in rough billiards and links boundary roughness to spectral statistics transitions.
Findings
Localization of classical diffusion in angular momentum space due to quantum effects
Presence of Shnirelman peak in level spacing distribution at small s
Transition to Wigner-Dyson statistics in the ergodic regime as roughness varies
Abstract
We study the level spacing statistics p(s) and eigenfunction properties in a billiard with a rough boundary. Quantum effects lead to localization of classical diffusion in the angular momentum space and the Shnirelman peak in p(s) at small s. The ergodic regime with Wigner-Dyson statistics is identified as a function of roughness. Applications for the Q-spoiling in optical resonators are also discussed.
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