2002/12/31 by Philippe Jacquod, Ph. Jacquod, Henning Schomerus +2 · 2 citations
Physics and Astronomy · #Quantum chaos and dynamical systems #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.mes-hall #nlin.CD
paper · pdf · doi:10.1103/physrevlett.90.207004
published as Phys. Rev. Lett. 90, 207004 (2003).
arxiv created 2003/03/24 · openalex publication_date 2003/05/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
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.