Spacings between phase shifts in a simple scattering problem

TL;DR

This paper proves that for most cylindrical surfaces of revolution, the distribution of quantum phase shifts at high energy levels follows a Poisson distribution, confirming a scattering theory version of the Berry-Tabor conjecture.

Contribution

It establishes a scattering theoretical proof of the Berry-Tabor conjecture for a broad class of cylindrical surfaces of revolution.

Findings

Large energy limit of pair correlation measure is Poisson for almost all surfaces.

Quantum phase shifts are uniformly distributed at high energies.

Confirms the conjecture in a scattering framework for specific geometries.

Abstract

We prove a scattering theoretical version of the Berry-Tabor conjecture: for an almost every surface in a class of cylindrical surfaces of revolution, the large energy limit of the pair correlation measure of the quantum phase shifts is Poisson, that is, it is given by the uniform measure.