Anomalous Entanglement in Chaotic Dirac Billiards

TL;DR

This paper investigates the unique entanglement properties in Dirac Billiards, revealing anomalous behaviors and strong quantum interference effects that differ from non-relativistic systems, with implications for quantum dots made of graphene or topological insulators.

Contribution

It provides the first analytical and numerical analysis of entanglement behavior in Dirac Billiards, highlighting distinctive quantum interference and entanglement features.

Findings

Distinct entanglement distribution in Dirac Billiards compared to Schrödinger billiards

Presence of a plausible Bell state in Dirac Billiards

Sharp quantum interference amplitude observed in entangled electrons

Abstract

We present analytical and numerical results that demonstrate the presence of anomalous entanglement behavior on the Dirac Billiards. We investigate the statistical distribution of the characteristic entangled measures, focusing on the mean, on the variance and on the quantum interference terms. We show a quite distinct behavior of the Dirac Billiard compared with the non-relativist (Schrodinger) ones. Particularly, we show a very plausible Bell state and a sharp amplitude of quantum interference term on entangled electrons left from the Dirac Billiards. The results have remarkable relevance to the novel quantum dots build of materials like graphene or topological insulators.