title: Quantum Andreev map: a paradigm of quantum chaos in superconductivity.
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.
authors.affiliation: Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands.
authors.forename: Ph
authors.initials: P
authors.lastname: Jacquod
authors.forename: H
authors.initials: H
authors.lastname: Schomerus
authors.forename: C W J
authors.initials: CW
authors.lastname: Beenakker