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, $L/{\lambda }_F>>1$. 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 $g^{wl}\propto (1+{\tau }_D/{\tau }_{\varphi }{)}^{-1}$ with the dwell time ${\tau }_D$ through the cavity and the dephasing rate ${\tau }_{\varphi }^{-1}$, we find an exponential suppression of weak localization by a factor $\propto \exp [-\tilde{\tau }/{\tau }_{\varphi }]$, 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 ${\lambda }_F$.

4 pages 3 figures (v2 contains numerous cosmetic changes)

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• Quantum coherent three-terminal thermoelectrics: maximum efficiency at given power output
• Semiclassical transport in nearly symmetric quantum dots I: symmetry-breaking in the dot
• Quantum corrections to transport in graphene: a trajectory-based semiclassical analysis
• Semiclassical theory of the interaction correction to the conductance of antidot arrays
• Transmission through a noisy network