Singular statistics revised

Abstract

In the paper we analyze the "singular statistics" of pseudointegrable Seba billiards and show that taking into account growing number of resonances one observes the transition from "semi-Poissonian"-like statistics to Poissonian. This observation is in agreement with an argument that a classical particle does not feel a point perturbation. However, our findings contradict results reported earlier (P. Seba, Phys. Rev. Lett. 64, 1855 (1990)).

22 pages, 11 figures; submitted to New Journal of Physics

References in corpus (3)

• Quasi-periodic Green's functions of the Helmholtz and Laplace equations
• On the theory of cavities with point-like perturbations. Part I: General theory
• Diffractive orbits in the length spectrum of a 2D microwave cavity with a small scatterer

Cited by in corpus (11)

• Experimental investigation of the elastic enhancement factor in a transient region between regular and chaotic dynamics
• Long-range correlations in rectangular cavities containing point-like perturbations
• Quantum Chaos for point scatterers on flat tori
• Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards
• Microwave realisation of a periodically driven system
• On the eigenvalue spacing distribution for a point scatterer on the flat torus
• On the theory of cavities with point-like perturbations. Part II: Rectangular cavities
• Intermediate statistics for a system with symplectic symmetry: the Dirac rose graph
• Investigation of the enhancement factor in the regime of semi-Poisson statistics in a singular microwave cavity
• Eigenfrequencies of the randomly pinned drum and conductivity of graphene
• Morphology of wetting-layer states in a simple quantum-dot wetting-layer model