Barrier billiard and random matrices
arXiv:2107.03364 · doi:10.1088/1751-8121/ac3da6
Abstract
The barrier billiard is the simplest example of pseudo-integrable models with interesting and intricate classical and quantum properties. Using the Wiener-Hopf method it is demonstrated that quantum mechanics of a rectangular billiard with a barrier in the centre can be reduced to the investigation of a certain unitary matrix. Under heuristic assumptions this matrix is substituted by a special low-complexity random unitary matrix of independent interest. The main results of the paper are (i) spectral statistics of such billiards is insensitive to the barrier height and (ii) it is well described by the semi-Poisson distributions.
arXiv comment24 pages, 5 figures
References in corpus (11)
- Anderson Transitions
- Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
- Short-range plasma model for intermediate spectral statistics
- Weak Chaos in a Quantum Kepler Problem
- Random matrix ensembles associated with Lax matrices
- Spectral statistics of a quantum interval-exchange map
- Spectral properties of quantized barrier billiards
- Integrable random matrix ensembles
- Periodic orbits contribution to the 2-point correlation form factor for pseudo-integrable systems
- Generic spectral properties of right triangle billiards
- Statistical properties of structured random matrices