Quantum mechanical calculation of spectral statistics of modified Kepler problem

TL;DR

This paper resolves discrepancies in spectral statistics of a modified Kepler problem using quantum mechanical calculations, improving agreement with numerical results by considering interference effects.

Contribution

It introduces a quantum mechanical approach that accounts for interference effects, enhancing the accuracy of spectral statistics predictions in modified Kepler and rectangular billiard systems.

Findings

Diagonal approximation fits numerical data well

Including coherent interference improves results further

Method applies to both Kepler problem and billiards

Abstract

Discrepancy between periodic orbit theory and numerical calculation of a modified Kepler problem is cleared by a quantum mechanical calculation. The diagonal approximation already gives a good fit for the numerical calculation. A better result yet is gained by considering the coherent interference between the classical periodic orbits and the Balian-Bloch term. This approach produces improved results for the rectangular billiards as well.