  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.
