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 large Lyapunov exponent and the logarithmic reduction of the gap when the Ehrenfest time becomes comparable to the quasiparticle dwell time.

References in corpus (1)

• Adiabatic quantization of Andreev levels

Cited by in corpus (31)

• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Ehrenfest time dependent suppression of weak localization
• Quantum-to-classical correspondence in open chaotic systems
• Dynamical model for the quantum-to-classical crossover of shot noise
• Andreev billiards
• Ehrenfest-time dependence of weak localization in open quantum dots
• From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
• Quantum-to-classical crossover of mesoscopic conductance fluctuations
• Lifetime statistics in chaotic dielectric microresonators
• Dephasing in quantum chaotic transport: a semiclassical approach
• A model for chaotic dielectric microresonators
• Chaotic dynamics in superconducting nanocircuits
• On the mean density of complex eigenvalues for an ensemble of random matrices with prescribed singular values
• Classical limit of transport in quantum kicked maps
• Andreev magnetotransport in low-dimensional proximity structures: Spin-dependent conductance enhancement
• Weak localization of the open kicked rotator
• Quasiclassical fluctuations of the superconductor proximity gap in a chaotic system
• Effective Random Matrix Theory description of chaotic Andreev billiards
• Quantum-to-classical crossover for Andreev billiards in a magnetic field
• Nonmetallic thermal transport in low-dimensional proximity structures with partially preserved time-reversal symmetry in a magnetic field
• Semiclassical theory of a quantum pump
• Staggered repulsion of transmission eigenvalues in symmetric open mesoscopic systems
• Stroboscopic model of transport through a quantum dot with spin-orbit scattering
• Superconductivity-induced macroscopic resonant tunneling
• Quantum-classical correspondence in the wavefunctions of Andreev billiards
• Low-energy quasiparticle excitations in dirty d-wave superconductors and the Bogoliubov-de Gennes kicked rotator
• Macroscopic Resonant Tunneling through Andreev Interferometers
• Long-time signatures of short-time dynamics in decaying quantum-chaotic systems
• Effect of spin-orbit coupling on the excitation spectrum of Andreev billiards
• Degradation of electron-hole entanglement by spin-orbit coupling
• Non-universal suppression of the excitation gap in chaotic Andreev billiards: Superconducting terminals as sensitive probes for scarred states