Semiclassical approximation for barrier billiards
Abstract
Barrier billiards are simple examples of pseudo-integrable models which form an appealing but poorly investigated subclass of dynamical systems. The paper examines the semiclassical limit of the exact quantum transfer operator for barrier billiards constructed in [J. Phys. A: Math. Theor. 55, 024001 (2022)]. The obtained asymptotic expressions are used to provide analytical arguments to support the conjecture that spectral statistical properties of barrier billiards are described by the semi-Poisson distribution and to derive the trace formulas for such billiards which in the transfer operator approach is not automatic.
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