Dephasing in the semiclassical limit is system-dependent

TL;DR

This paper studies how dephasing effects in quantum chaotic systems depend on system-specific parameters, revealing different suppression behaviors of weak localization based on the dephasing mechanism and system details.

Contribution

It introduces a semiclassical approach to analyze dephasing in quantum dots, showing the system-dependent exponential suppression factor involving Ehrenfest time or correlation length.

Findings

Exponential suppression of weak localization depends on system-specific parameters.

Ehrenfest time governs dephasing when coupled to an external dot.

Correlation length influences dephasing when coupling occurs via an external dot.

Abstract

We investigate dephasing in open quantum chaotic systems in the limit of large system size to Fermi wavelength ratio, $L/\lambda_F >> 1$. We semiclassically calculate the weak localization correction $g^{wl}$ to the conductance for a quantum dot coupled to (i) an external closed dot and (ii) a dephasing voltage probe. In addition to the universal algebraic suppression $g^{wl} \propto (1+\tau_D/\tau_\phi)^{-1}$ with the dwell time $\tau_D$ through the cavity and the dephasing rate $\tau_\phi^{-1}$, we find an exponential suppression of weak localization by a factor $\propto \exp[-\tilde{\tau}/\tau_\phi]$, with a system-dependent $\tilde{\tau}$. In the dephasing probe model, $\tilde{\tau}$ coincides with the Ehrenfest time, $\tilde{\tau} \propto \ln [L/\lambda_F]$, for both perfectly and partially transparent dot-lead couplings. In contrast, when dephasing occurs due to the coupling to an external dot, $\tilde{\tau} \propto \ln [L/\xi]$ depends on the correlation length $\xi$ of the coupling potential instead of $\lambda_F$.