Entanglement distribution statistic in Andreev billiards

We investigate statistical aspects of the entanglement production for open chaotic mesoscopic billiards in contact with superconducting parts, known as Andreev billiards. The complete distributions of concurrence and entanglement of formation are obtained by using the Altland–Zirnbauer symmetry clas...

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Bibliographic Details
Published in:The European physical journal. B, Condensed matter physics Condensed matter physics, 2017-11, Vol.90 (11), p.1-6, Article 232
Main Authors: Ramos, J. G. G. S., Macedo-Junior, A. F., Barbosa, A. L. R.
Format: Article
Language:English
Subjects:
Billiards
Complex Systems
Computer simulation
Condensed Matter Physics
Entanglement
Fluid- and Aerodynamics
Mathematical analysis
Matrix methods
Matrix theory
Monte Carlo methods
Monte Carlo simulation
Physics
Physics and Astronomy
Regular Article
Solid State Physics
Statistical analysis
Statistics
Superconductivity
Superconductors
Symmetry
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Summary:We investigate statistical aspects of the entanglement production for open chaotic mesoscopic billiards in contact with superconducting parts, known as Andreev billiards. The complete distributions of concurrence and entanglement of formation are obtained by using the Altland–Zirnbauer symmetry classes of circular ensembles of scattering matrices, which complements previous studies in chaotic universal billiards belonging to other classes of random matrix theory. Our results show a unique and very peculiar behavior: the realization of entanglement in a Andreev billiard always results in non-separable state, regardless of the time reversal symmetry. The analytical calculations are supported by a numerical Monte Carlo simulation.
ISSN:1434-6028
1434-6036
DOI:10.1140/epjb/e2017-80033-8