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

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.