Monitored quantum transport through a disordered one-dimensional conductor
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≃ ℓϕ 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 ℓϕ≃ ξln(vFτϕ/ξ) of the coherence length ℓϕ on the mean time τϕ between measurements.
Versions
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BibTeX
@misc{fernan2026monitored,
title = {{Monitored quantum transport through a disordered one-dimensional conductor}},
author = {J. Sánchez Fernán and J. Tworzydło and C. W. J. Beenakker},
howpublished = {arXiv},
year = {2026},
month = may,
doi = {10.48550/arxiv.2605.22701},
eprint = {2605.22701},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.22701},
}
RIS
TY - UNPB
TI - Monitored quantum transport through a disordered one-dimensional conductor
AU - J. Sánchez Fernán
AU - J. Tworzydło
AU - C. W. J. Beenakker
PY - 2026
DA - 2026/05/21
PB - arXiv
DO - 10.48550/arxiv.2605.22701
UR - https://arxiv.org/abs/2605.22701
AB - 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≃ ℓ_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 ℓ_ϕ≃ ξln(v_Fτ_ϕ/ξ) of the coherence length ℓ_ϕ on the mean time τ_ϕ between measurements.
ER -