Expanded boundary integral method and chaotic time-reversal doublets in quantum billiards

Details Expanded boundary integral method and chaotic time-reversal doublets in quantum billiards Expanded boundary integral method and chaotic time-reversal doublets in quantum billiards

2006-12-05

arxiv.org/abs/nlin/0612011v1

Nonlinear Sciences

Chaotic Dynamics

18 pages, 8 figures, with 3 additional GIF animations available at http://chaos.fiz.uni-lj.si/~veble/boundary/

Scientific paper

10.1088/1367-2630/9/1/015

We present the expanded boundary integral method for solving the planar Helmholtz problem, which combines the ideas of the boundary integral method and the scaling method and is applicable to arbitrary shapes. We apply the method to a chaotic billiard with unidirectional transport, where we demonstrate existence of doublets of chaotic eigenstates, which are quasi-degenerate due to time-reversal symmetry, and a very particular level spacing distribution that attains a chaotic Shnirelman peak at short energy ranges and exhibits GUE-like statistics for large energy ranges. We show that, as a consequence of such particular level statistics or algebraic tunneling between disjoint chaotic components connected by time-reversal operation, the system exhibits quantum current reversals.

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