Dephasing in quantum chaotic transport: A semiclassical approach

2007/10/31 by Robert S. Whitney, Philippe Jacquod, Cyril Petitjean
Physics and Astronomy · #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Quantum many-body systems #cond-mat.mes-hall #nlin.CD

paper · pdf · doi:10.1103/physrevb.77.045315

published as Phys. Rev. B 77, 045315 (2008) · 24 pages 10 figures (version2: references updated & minor typos fixed)

openalex publication_date 2008/01/15 · arxiv created 2008/02/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the effect of dephasing (decoherence) on quantum transport through open chaotic ballistic conductors in the semiclassical limit of small Fermi wavelength to system size ratio, \ensuremathλ_F∕L⪡1. We use the trajectory-based semiclassical theory to study a two-terminal chaotic dot with decoherence originating from (i) an external closed quantum chaotic environment, (ii) a classical source of noise, and (iii) a voltage probe, i.e., an additional current-conserving terminal. We focus on the pure dephasing regime, where the coupling to the external source of dephasing is so weak that it does not induce energy relaxation. In addition to the universal algebraic suppression of weak localization, we find an exponential suppression of weak localization \ensuremath∝exp[\ensuremath-\stackrel\ifmmode \else \~\fi\ensuremathτ∕\ensuremathτ_\ensuremathφ], with the dephasing rate \ensuremathτ_\ensuremathφ^\ensuremath-1. The parameter \stackrel\ifmmode \else \~\fi\ensuremathτ depends strongly on the source of dephasing. For a voltage probe, \stackrel\ifmmode \else \~\fi\ensuremathτ is of order the Ehrenfest time \ensuremath∝ln[L∕\ensuremathλ_F]. In contrast, for a chaotic environment or a classical source of noise, it has the correlation length \ensuremathξ of the coupling or noise potential replacing the Fermi wavelength \ensuremathλ_F. We explicitly show that the Fano factor for shot noise is unaffected by decoherence. We connect these results to earlier works on dephasing due to electron-electron interactions and numerically confirm our findings.

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