Application of the Trace Formula in Pseudointegrable Systems

TL;DR

This paper demonstrates that periodic-orbit theory can accurately compute the eigenvalues of pseudointegrable billiards, matching direct diagonalization results and enabling efficient eigenvalue estimation.

Contribution

It applies the trace formula to pseudointegrable systems, showing high accuracy in eigenvalue computation from periodic orbits.

Findings

Periodic-orbit calculations match direct diagonalization for first 100 eigenvalues.

The method provides a reliable way to estimate eigenvalues in pseudointegrable billiards.

High accuracy achieved with about 100 eigenvalues from periodic-orbit data.

Abstract

We apply periodic-orbit theory to calculate the integrated density of states $N(k)$ from the periodic orbits of pseudointegrable polygon and barrier billiards. We show that the results agree so well with the results obtained from direct diagonalization of the Schr\"odinger equation, that about the first 100 eigenvalues can be obtained directly from the periodic-orbit calculations in good accuracy.