Relativistic Quantum Chaos in Neutrino Billiards

TL;DR

This paper reviews relativistic quantum chaos in neutrino billiards, exploring their properties, dynamics, and potential experimental realizations using graphene structures.

Contribution

It provides a comprehensive review of neutrino billiards, highlighting their relativistic quantum features and contrasting integrable and chaotic shapes, including experimental prospects.

Findings

Neutrino billiards model relativistic quantum chaos.

Chaotic neutrino billiards exhibit distinct spectral properties.

Graphene-based systems could realize relativistic quantum billiards.

Abstract

Neutrino billiards serve as a model system for the study of aspects of relativistic quantum chaos. These are relativistic quantum billiards consisting of a spin-1/2 particle which is confined to a planar domain by imposing boundary conditions on the spinor components which were proposed in [Berry and Mondragon 1987, {\it Proc. R. Soc.} A {\bf 412} 53) . We review their general features and the properties of neutrino billiards with shapes of billiards with integrable dynamics. Furthermore, we review the features of two neutrino billiards with the shapes of billiards generating a chaotic dynamics, whose nonrelativistic counterpart exhibits particular properties. Finally we briefly discuss possible experimental realizations of relativistic quantium billiards based on graphene billiards, that is, finite size sheets of graphene.