Wave chaos in quantum billiards with a small but finite-size scatterer

Abstract

We study the low-energy quantum spectra of two-dimensional rectangular billiards with a small but finite-size scatterer inside. We start by examining the spectral properties of billiards with a single pointlike scatterer. The problem is formulated in terms of the self-adjoint extension theory of functional analysis. The condition for the appearance of so-called wave chaos is clarified. We then relate the pointlike scatterer to a finite-size scatterer through an appropriate truncation of the basis. We show that the signature of wave chaos in low-energy states is most prominent when the scatterer is weakly attractive. As an illustration, numerical results of a rectangular billiard with a small rectangular scatterer inside are exhibited. \textcopyright{} 1996 The American Physical Society.

Locations

• Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics - View
• arXiv (Cornell University) - View - PDF
• PubMed - View
• DataCite API - View