On the eigenvalue spacing distribution for a point scatterer on the flat torus

We study the level spacing distribution for the spectrum of a point scatterer on a flat torus. In the 2-dimensional case, we show that in the weak coupling regime the eigenvalue spacing distribution coincides with that of the spectrum of the Laplacian (ignoring multiplicties), by showing that the perturbed eigenvalues generically clump with the unperturbed ones on the scale of the mean level spacing. We also study the three dimensional case, where the situation is very different.Comment: 25 page

Flux String in Quantum Billiards with Two Particles

We examine the quantum motion of two particles interacting through a contact force which are confined in a rectangular domain in two and three dimensions. When there is a difference in the mass scale of two particles, adiabatic separation of the fast and slow variables can be performed. Appearance of the Berry phase and magnetic flux is pointed out. The system is reduced to a one-particle Aharonov-Bohm billiard in two-dimensional case. In three dimension, the problem effectively becomes the motion of a particle in the presence of closed flux string in a box billiard.Comment: 10 pages, REVTeX file, 3 postscript figures, uuencode

Resonance Tunneling in Double-Well Billiards with a Pointlike Scatterer

The coherent tunneling phenomenon is investigated in rectangular billiards divided into two domains by a classically unclimbable potential barrier. We show that by placing a pointlike scatterer inside the billiard, we can control the occurrence and the rate of the resonance tunneling. The key role of the avoided crossing is stressed. Keywords: chaotic tunneling, quantum billiard, delta potential, diabolical degeneracy PACS: 3.65.-w, 4.30.Nk, 5.45.+b, 73.40.GkComment: Five pages ReVTEX, two column format with epsf figure