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Adiabatic quantization of Andreev levels

P. G. Silvestrov·M. C. Goorden·C. W. J. Beenakker
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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 point contact. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods $T_{n}$, which in turn generate a ladder of excited states $ε_{nm}=(m+1/2)π\hbar/T_{n}$. The largest quantized period is the Ehrenfest time $T_{0}=λ^{-1}\ln N$. Projection of the invariant torus onto the coordinate plane shows that the wave functions inside the cavity are squeezed to a transverse dimension $W/\sqrt{N}$, much below the width $W$ of the point contact.

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P. G. Silvestrov, M. C. Goorden, C. W. J. Beenakker. 2003-04-03. Adiabatic quantization of Andreev levels. https://doi.org/10.1103/physrevlett.90.116801

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