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We present the expanded boundary integral method for solving the planarHelmholtz problem, which combines the ideas of the boundary integral method andthe scaling method and is applicable to arbitrary shapes. We apply the methodto a chaotic billiard with unidirectional transport, where we demonstrateexistence of doublets of chaotic eigenstates, which are quasi-degenerate due totime-reversal symmetry, and a very particular level spacing distribution thatattains a chaotic Shnirelman peak at short energy ranges and exhibits GUE-likestatistics for large energy ranges. We show that, as a consequence of suchparticular level statistics or algebraic tunneling between disjoint chaoticcomponents connected by time-reversal operation, the system exhibits quantumcurrent reversals.

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