Effective Random Matrix Theory description of chaotic Andreev billiards

Abstract

An effective random matrix theory description is developed for the universal gap fluctuations and the ensemble averaged density of states of chaotic Andreev billiards for finite Ehrenfest time. It yields a very good agreement with the numerical calculation for Sinai-Andreev billiards. A systematic linear decrease of the mean field gap with increasing Ehrenfest time ${\tau }_E$ is observed but its derivative with respect to ${\tau }_E$ is in between two competing theoretical predictions and close to that of the recent numerical calculations for Andreev map. The exponential tail of the density of states is interpreted semi-classically.

arXiv comment4 pages, 4 figures

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Cited by in corpus (14)

• Quantum-to-classical correspondence in open chaotic systems
• Andreev billiards
• Semiclassical gaps in the density of states of chaotic Andreev billiards
• The density of states of chaotic Andreev billiards
• Quantum-to-classical crossover for Andreev billiards in a magnetic field
• Superconductivity-induced macroscopic resonant tunneling
• Effects of Andreev reflection on the conductance of quantum-chaotic dots
• Spectrum of the Andreev Billiard and Giant Fluctuations of the Ehrenfest Time
• Quantum-classical correspondence in the wavefunctions of Andreev billiards
• Bound states in Andreev billiards with soft walls
• Macroscopic Resonant Tunneling through Andreev Interferometers
• Effect of spin-orbit coupling on the excitation spectrum of Andreev billiards
• Non-universal suppression of the excitation gap in chaotic Andreev billiards: Superconducting terminals as sensitive probes for scarred states
• Quantized invariant tori in Andreev billiards of mixed phase space