Quantum-to-classical crossover for Andreev billiards in a magnetic field
M. C. Goorden, Ph. Jacquod, C. W. J. Beenakker
DOI 10.1103/PhysRevB.72.064526 · Physical Review B
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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 τE becomes longer than the mean time τD between Andreev reflections. As a consequence, the critical field at which the excitation gap closes drops below the RMT prediction as τE∕τD 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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