Dephasing in the semiclassical limit is system–dependent

We investigate dephasing in open quantum chaotic systems in the limit of large system size to Fermi wavelength ratio, $L/\lambda_\mathrm F\gg1$. We semiclassically calculate the weak localization correction $g^\mathrm{wl}$ 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 $g^\mathrm{wl}\propto (1+\tau_\mathrm{ D}/\tau_\phi)^{-1}$ with the dwell time $\tau_\mathrm D$ 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, $\tilde\tau\propto\ln [L/\lambda_\mathrm F]$, 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 $\lambda_\mathrm F$.