Adiabatic Quantization of Andreev Quantum Billiard Levels
P. G. Silvestrov, M. C. Goorden, C. W. J. Beenakker
DOI 10.1103/PhysRevLett.90.116801 · Physical Review Letters
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Abstract
We identify the time T between Andreev reflections as a classical adiabatic invariant in a ballistic chaotic cavity (Lyapunov exponent λ), coupled to a superconductor by an N-mode constriction. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods Tn, which in turn generate a ladder of excited states ϵnm=(m+1/2)πℏ/Tn. The largest quantized period is the Ehrenfest time T0=λ−1lnN. Projection of the invariant torus onto the coordinate plane shows that the wave functions inside the cavity are squeezed to a transverse dimension W/N, much below the width W of the constriction.
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