Anomalous Entanglement in Chaotic Dirac Billiards

We present analytical and numerical results that demonstrate the presence of anomalous entan- glement behavior on the Dirac Billiards. We investigate the statistical distribution of the character- istic 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. PACS numbers: 73.23.-b,73.21.La,05.45.Mt The entanglement is one the most fundamental effect on quantum mechanics, with no classical analog 1 . Two or more particles are entangled if they support a nonlocal correlation which cannot be acquired by the dynamics of classical mechanics 2 . Because its non-classical character- istics, the control of entangled states has attracted the interest of numerous science communities 3 . The tech- nological applications of the effect has a broad range as quantum computation, teleportation, telecommunication and cryptography 2-4 .