Quasiclassical fluctuations of the superconductor proximity gap in a chaotic system
Abstract
We calculate the sample-to-sample fluctuations in the excitation gap of a chaotic dynamical system coupled by a narrow lead to a superconductor. Quantum fluctuations on the order of magnitude of the level spacing, predicted by random-matrix theory, apply if
τ
E
≪ℏ/
E
T
(with
τ
E
the Ehrenfest time and
E
T
the Thouless energy). For $\tau_E\agt\hbar/ E_T$ the fluctuations are much greater than the level spacing. We demonstrate the quasiclassical nature of the gap fluctuations in the large-
τ
E
regime by correlating them to an integral over the classical dwell-time distribution.