Semiclassical Theory of Quantum Chaotic Transport: Phase-Space Splitting, Coherent Backscattering and Weak Localization

TL;DR

This paper develops a semiclassical phase-space theory for quantum chaotic transport, revealing how the Ehrenfest time influences conductance, shot-noise, and weak localization, including suppression effects and system splitting into classical and quantum cavities.

Contribution

It introduces a new semiclassical phase-space framework that accounts for Ehrenfest time effects on quantum transport and corrects previous assumptions about weak localization suppression.

Findings

Ehrenfest time causes block-diagonalization of the scattering matrix.

Suppression of shot-noise Fano factor with increasing Ehrenfest time.

Exponential decay of weak localization and coherent backscattering at finite Ehrenfest time.

Abstract

We investigate transport properties of quantized chaotic systems in the short wavelength limit. We focus on non-coherent quantities such as the Drude conductance, its sample-to-sample fluctuations, shot-noise and the transmission spectrum, as well as coherent effects such as weak localization. We show how these properties are influenced by the emergence of the Ehrenfest time scale $\tE$. Expressed in an optimal phase-space basis, the scattering matrix acquires a block-diagonal form as $\tE$ increases, reflecting the splitting of the system into two cavities in parallel, a classical deterministic cavity (with all transmission eigenvalues either 0 or 1) and a quantum mechanical stochastic cavity. This results in the suppression of the Fano factor for shot-noise and the deviation of sample-to-sample conductance fluctuations from their universal value. We further present a semiclassical theory for weak localization which captures non-ergodic phase-space structures and preserves the unitarity of the theory. Contrarily to our previous claim [Phys. Rev. Lett. 94, 116801 (2005)], we find that the leading off-diagonal contribution to the conductance leads to the exponential suppression of the coherent backscattering peak and of weak localization at finite $\tE$. This latter finding is substantiated by numerical magnetoconductance calculations.