Spectral statistics of a pseudo-integrable map: the general case

TL;DR

This paper analytically derives the spectral statistics of a pseudo-integrable quantum map for all matrix dimensions, extending previous results limited to specific cases, and highlights its distinct spectral behavior from integrable and chaotic systems.

Contribution

It provides a comprehensive analytical characterization of spectral statistics for a pseudo-integrable map across all matrix sizes, not just special sequences.

Findings

Spectral statistics differ from integrable and chaotic systems.

Analytical results valid for all matrix dimensions.

Extends previous special-case analyses.

Abstract

It is well established numerically that spectral statistics of pseudo-integrable models differs considerably from the reference statistics of integrable and chaotic systems. In [PRL,93 (2004) 254102] statistical properties of a certain quantized pseudo-integrable map had been calculated analytically but only for a special sequence of matrix dimensions. The purpose of this paper is to obtain the spectral statistics of the same quantum map for all matrix dimensions.