Hikami boxes and the Sinai billiard

TL;DR

This paper computes the Hikami box diagram for the Sinai billiard, revealing its universality at low frequencies and suggesting non-universality in level statistics of generic chaotic systems due to diffraction effects.

Contribution

It introduces the calculation of the Hikami box for the Sinai billiard and links diffraction effects to non-universal level statistics in chaotic systems.

Findings

Hikami box computed for Sinai billiard

Universality at low frequencies due to particle conservation

Diffraction phase volume influences frequency range

Abstract

Diagram, known in theory of the Anderson localization as the Hikami box, is computed for the Sinai billiard. This interference effect is mostly important for trajectories tangent to the opening of the billiard. This diagram is universal at low frequencies, because of the particle number conservation law. An independent parameter, which we call phase volume of diffraction, determines the corresponding frequency range. This result suggests that level statistics of a generic chaotic system is not universal.