Jacquod, Ph. and Schomerus, Henning and Beenakker, C. W. J. (2003) Quantum Andreev Map: A Paradigm of Quantum Chaos in Superconductivity. . Physical review letters, 90 (20). p. 207004. ISSN 1079-7114
Abstract
We introduce quantum maps with particle-hole conversion (Andreev reflection) and particle-hole symmetry, which exhibit the same excitation gap as quantum dots in the proximity to a superconductor. Computationally, the Andreev maps are much more efficient than billiard models of quantum dots. This makes it possible to test analytical predictions of random-matrix theory and semiclassical chaos that were previously out of reach of computer simulations. We have observed the universal distribution of the excitation gap for a large Lyapunov exponent and the logarithmic reduction of the gap when the Ehrenfest time becomes comparable to the quasiparticle dwell time.