Monitored quantum transport through a disordered one-dimensional conductor
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
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2026
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| _version_ | 1866913153179189248 |
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| author | Fernán, J. Sánchez Tworzydło, J. Beenakker, C. W. J. |
| author_facet | Fernán, J. Sánchez Tworzydło, J. Beenakker, C. W. J. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22701 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monitored quantum transport through a disordered one-dimensional conductor Fernán, J. Sánchez Tworzydło, J. Beenakker, C. W. J. Mesoscale and Nanoscale Physics 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. |
| title | Monitored quantum transport through a disordered one-dimensional conductor |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2605.22701 |