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arXiv · 2605.22701

Monitored quantum transport through a disordered one-dimensional conductor

J. Sánchez Fernán·J. Tworzydło·C. W. J. Beenakker
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Abstract

We formulate a quantum master equation for the many-particle density matrix of electrons propagating through a single-mode conductor, combining elastic scattering by disorder with time-resolved projective measurements that monitor the outcome of scattering events. The full counting statistics of transmitted electrons has a binomial distribution function, whose mean ${\cal T}$ and variance ${\cal T}(1-{\cal T})$ determine the conductance and shot noise power, respectively. Monitoring suppresses the phase coherence responsible for one-dimensional localization: The decay with conductor length $L$ of the typical transmission probability crosses over at $L\simeq \ell_ϕ$ from the exponential $e^{-L/ξ}$ (with localization length $ξ$) to the Ohmic $1/L$ decay. Numerical solution of the master equation gives, for weak monitoring, a logarithmic dependence $\ell_ϕ\simeq ξ\ln(v_{\rm F}τ_ϕ/ξ)$ of the coherence length $\ell_ϕ$ on the mean time $τ_ϕ$ between measurements.

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J. Sánchez Fernán, J. Tworzydło, C. W. J. Beenakker. 2026-05-21. Monitored quantum transport through a disordered one-dimensional conductor. https://arxiv.org/abs/2605.22701

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