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.

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Cited by in corpus (46)

• 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
• Geometrical enhancement of the proximity effect in quantum wires with extended superconducting tunnel contacts
• From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
• Semiclassical gaps in the density of states of chaotic Andreev billiards
• Quantum-to-classical crossover of mesoscopic conductance fluctuations
• Dephasing in quantum chaotic transport: a semiclassical approach
• Lifetime statistics in chaotic dielectric microresonators
• A model for chaotic dielectric microresonators
• The density of states of chaotic Andreev billiards
• Resonance eigenfunction hypothesis for chaotic systems
• Symmetry deduction from spectral fluctuations in complex quantum systems
• The Ehrenfest Oscillations in The Level Statistics of Chaotic Quantum Dots
• Chaotic dynamics in superconducting nanocircuits
• Semiclassical transport in nearly symmetric quantum dots I: symmetry-breaking in the dot
• On the mean density of complex eigenvalues for an ensemble of random matrices with prescribed singular values
• Universal spectral statistics in Wigner-Dyson, chiral and Andreev star graphs I: construction and numerical results
• 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
• 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
• Effective Random Matrix Theory description of chaotic Andreev billiards
• Quasiclassical fluctuations of the superconductor proximity gap in a chaotic system
• Ring--Shaped Andreev Billiards in Quantizing Magnetic Fields
• Fermionic Casimir Effect in Case of Andreev Reflection
• Super-sharp resonances in chaotic wave scattering
• Staggered repulsion of transmission eigenvalues in symmetric open mesoscopic systems
• Semiclassical theory of a quantum pump
• Stroboscopic model of transport through a quantum dot with spin-orbit scattering
• Superconductivity-induced macroscopic resonant tunneling
• Spectrum of the Andreev Billiard and Giant Fluctuations of the Ehrenfest Time
• Quantum-classical correspondence in the wavefunctions of Andreev billiards
• Resonance spectra for quantum maps of kicked scattering systems by complex scaling
• Low-energy quasiparticle excitations in dirty d-wave superconductors and the Bogoliubov-de Gennes kicked rotator
• Macroscopic Resonant Tunneling through Andreev Interferometers
• Effect of spin-orbit coupling on the excitation spectrum of Andreev billiards
• Long-time signatures of short-time dynamics in decaying quantum-chaotic systems
• Superconductor-proximity effect in hybrid structures: Fractality versus Chaos
• 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
• Breakdown of Universality in Quantum Chaotic Transport: the Two-Phase Dynamical Fluid Model