Constrained quantum mechanics: chaos in non-planar billiards

TL;DR

This paper explores quantum chaos signatures in particles constrained to non-planar surfaces, analyzing systems like conical and Gaussian billiards to understand their chaotic behavior at the quantum level.

Contribution

It introduces techniques to identify chaos signatures in quantum systems constrained on non-planar surfaces, with specific analysis of cone and Gaussian billiards.

Findings

Chaos signatures are observable in quantum constrained systems.

Non-planar billiards exhibit distinct quantum chaos characteristics.

Techniques developed can be applied to other constrained quantum systems.

Abstract

We illustrate some of the techniques to identify chaos signatures at the quantum level using as a guiding examples some systems where a particle is constrained to move on a radial symmetric, but non planar, surface. In particular, two systems are studied: the case of a cone with an arbitrary contour or dunce hat billiard and the rectangular billiard with an inner Gaussian surface.