Dephasing in the semiclassical limit is system-dependent

Abstract

We investigate dephasing in open quantum chaotic systems in the limit of large system size to Fermi wavelength ratio, $L/λ_F >> 1$. 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 $g^{wl} \propto (1+τ_D/τ_ϕ)^{-1}$ with the dwell time $τ_D$ through the cavity and the dephasing rate $τ_ϕ^{-1}$, we find an exponential suppression of weak localization by a factor $\propto \exp[-\tildeτ/τ_ϕ]$, with a system-dependent $\tildeτ$. In the dephasing probe model, $\tildeτ$ coincides with the Ehrenfest time, $\tildeτ \propto \ln [L/λ_F]$, for both perfectly and partially transparent dot-lead couplings. In contrast, when dephasing occurs due to the coupling to an external dot, $\tildeτ \propto \ln [L/ξ]$ depends on the correlation length $ξ$ of the coupling potential instead of $λ_F$.