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We study the low energy quantum spectra of two-dimensional rectangularbilliards with a small but finite-size scatterer inside. We start by examiningthe spectral properties of billiards with a single pointlike scatterer. Theproblem is formulated in terms of self-adjoint extension theory of functionalanalysis. The condition for the appearance of so-called wave chaos isclarified. We then relate the pointlike scatterer to a finite-size scattererthrough the appropriate truncation of basis. We show that the signature of wavechaos in low energy states is most prominent when the scatterer is weaklyattractive. As an illustration, numerical results of a rectangular billiardwith a small rectangular scatterer inside are exhibited.Comment: 24 pages REVTeX file, 10 postscript figures, uuencode

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