Singular statistics revised

TL;DR

This paper investigates the spectral statistics of pseudointegrable Seba billiards, revealing a transition from semi-Poissonian to Poissonian behavior as resonances grow, challenging earlier findings.

Contribution

It provides new insights into the spectral transition in Seba billiards by analyzing resonance effects, contradicting previous results.

Findings

Spectral statistics transition from semi-Poissonian to Poissonian with increasing resonances

Classical particles do not perceive point perturbations in this context

Results challenge earlier studies on Seba billiards

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)).