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Quantum-to-classical crossover for Andreev billiards in a magnetic field

M. C. Goorden·Ph. Jacquod·C. W. J. Beenakker
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Abstract

We extend the existing quasiclassical theory for the superconducting proximity effect in a chaotic quantum dot, to include a time-reversal-symmetry breaking magnetic field. Random-matrix theory (RMT) breaks down once the Ehrenfest time $τ_E$ becomes longer than the mean time $τ_D$ between Andreev reflections. As a consequence, the critical field at which the excitation gap closes drops below the RMT prediction as $τ_E/τ_D$ is increased. Our quasiclassical results are supported by comparison with a fully quantum mechanical simulation of a stroboscopic model (the Andreev kicked rotator).

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M. C. Goorden, Ph. Jacquod, C. W. J. Beenakker. 2005-09-19. Quantum-to-classical crossover for Andreev billiards in a magnetic field. https://doi.org/10.1103/physrevb.72.064526

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