Semiclassical approximation for barrier billiards

• URL: http://arxiv.org/abs/2504.18834v1
• Date: Sat, 26 Apr 2025 07:41:13 GMT
• Title: Semiclassical approximation for barrier billiards
• Authors: Eugene Bogomolny,
• Abstract summary: Barrier billiards are simple examples of pseudo-integrable models.<n>The paper examines the semi limit of the exact quantum transfer operator for barrier billiards constructed in [J. Phys. A: Math. Theortext 024bf55, 001 (2022)
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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. \textbf{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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