Wave Chaos in Quantum Billiards with Small but Finite-Size Scatterer

Details Wave Chaos in Quantum Billiards with Small but Finite-Size Scatterer Wave Chaos in Quantum Billiards with Small but Finite-Size Scatterer

1996-01-17

arxiv.org/abs/chao-dyn/9601010v1

Phys. Rev. E54 (1996) 1321-1331

Physics

High Energy Physics

High Energy Physics - Theory

24 pages REVTeX file, 10 postscript figures, uuencoded

Scientific paper

10.1103/PhysRevE.54.1321

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 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 the appropriate truncation of 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.

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