Microscopic Theory for the Quantum to Classical Crossover in Chaotic Transport

Abstract

We present a semiclassical theory for the scattering matrix $\mathcal{S}$ of a chaotic ballistic cavity at finite Ehrenfest time. Using a phase-space representation coupled with a multi-bounce expansion, we show how the Liouville conservation of phase-space volume decomposes $\mathcal{S}$ as $\mathcal{S}={\mathcal{S}}^{\mathrm{cl}}\oplus {\mathcal{S}}^{\mathrm{qm}}$. The short-time, classical contribution ${\mathcal{S}}^{\mathrm{cl}}$ generates deterministic transmission eigenvalues T=0 or 1, while quantum ergodicity is recovered within the subspace corresponding to the long-time, stochastic contribution ${\mathcal{S}}^{\mathrm{qm}}$. This provides a microscopic foundation for the two-phase fluid model, in which the cavity acts like a classical and a quantum cavity in parallel, and explains recent numerical data showing the breakdown of universality in quantum chaotic transport in the deep semiclassical limit. We show that the Fano factor of the shot-noise power vanishes in this limit, while weak localization remains universal.

PRL version, added comment about 2 Ehrenfest times (4pages, 2figs)

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Cited by in corpus (20)

• Fundamental aspects of steady-state conversion of heat to work at the nanoscale
• Periodic-Orbit Theory of Universality in Quantum Chaos
• Shot noise in semiclassical chaotic cavities
• Semiclassical Theory of Quantum Chaotic Transport: Phase-Space Splitting, Coherent Backscattering and Weak Localization
• Fractal Weyl laws in discrete models of chaotic scattering
• Quantum-to-classical correspondence in open chaotic systems
• Suppression of weak-localization (and enhancement of noise) by tunnelling in semiclassical chaotic transport
• Many-Body Physics and Quantum Chaos
• Ehrenfest-time dependence of weak localization in open quantum dots
• Towards a semiclassical justification of the `effective random matrix theory' for transport through ballistic chaotic quantum dots
• Semiclassical gaps in the density of states of chaotic Andreev billiards
• Dephasing in quantum chaotic transport: a semiclassical approach
• Ehrenfest-time dependence of counting statistics for chaotic ballistic systems
• The density of states of chaotic Andreev billiards
• Conductance fluctuations in chaotic systems with tunnel barriers
• Classical limit of transport in quantum kicked maps
• Quantum-to-classical crossover for Andreev billiards in a magnetic field
• Pseudo-Path Semiclassical Approximation to Transport through Open Quantum Billiards: Dyson Equation for Diffractive Scattering
• How spin-orbit interaction can cause electronic shot noise
• Microscopic theory of the Andreev gap