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arxiv: 2605.22701 · v1 · pith:FBL357JEnew · submitted 2026-05-21 · ❄️ cond-mat.mes-hall

Monitored quantum transport through a disordered one-dimensional conductor

J. S\'anchez Fern\'an , J. Tworzyd{\l}o , C. W. J. Beenakker This is my paper

Pith reviewed 2026-05-22 03:33 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords quantum transportAnderson localizationmonitored quantum systemsone-dimensional conductorsquantum master equationfull counting statisticsshot noise
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The pith

Continuous monitoring of electrons in a disordered one-dimensional conductor suppresses Anderson localization and replaces exponential transmission decay with Ohmic 1/L scaling.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a quantum master equation that includes both elastic scattering from disorder and time-resolved projective measurements on the electron density matrix. This allows calculation of the full counting statistics of transmitted electrons, which follows a binomial distribution. Monitoring destroys the phase coherence needed for localization, so that for conductor lengths exceeding a coherence length, the typical transmission probability decays as 1/L rather than exponentially. Numerical results show that for weak monitoring the coherence length grows logarithmically with the average time between measurements.

Core claim

By solving the quantum master equation for a single-mode conductor with disorder, the authors find that the typical transmission probability crosses over from exponential localization decay e^{-L/ξ} to Ohmic 1/L decay at length L approximately equal to the coherence length ℓ_φ, with ℓ_φ given by ξ ln(v_F τ_φ / ξ) for weak monitoring, where τ_φ is the mean time between measurements.

What carries the argument

A quantum master equation that combines elastic disorder scattering with time-resolved projective measurements on the many-particle density matrix, which determines the binomial full counting statistics of transmission.

If this is right

  • The mean transmission sets the conductance, which follows Ohmic 1/L scaling for lengths beyond the coherence length.
  • The variance of the binomial transmission distribution determines the shot noise power as T(1-T).
  • Phase coherence is lost due to the projective measurements, eliminating the interference responsible for one-dimensional localization.
  • For weak monitoring the coherence length scales as ξ ln(v_F τ_φ / ξ).

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The monitoring-induced crossover might be tunable in nanoscale devices by adjusting measurement frequency to control effective coherence.
  • The binomial counting statistics could apply to other monitored mesoscopic systems where localization competes with decoherence.
  • Extending the master equation to include interactions or multiple modes would test whether the Ohmic restoration generalizes beyond the single-mode case.

Load-bearing premise

The quantum master equation that combines elastic disorder scattering with time-resolved projective measurements on the many-particle density matrix accurately captures the monitored transport dynamics.

What would settle it

Experimental measurement of the typical transmission probability versus conductor length L in a controlled-monitoring setup, checking for a crossover from e^{-L/ξ} to 1/L at the predicted logarithmic ℓ_φ, would confirm or refute the central claim.

Figures

Figures reproduced from arXiv: 2605.22701 by C. W. J. Beenakker, J. S\'anchez Fern\'an, J. Tworzyd{\l}o.

Figure 1
Figure 1. Figure 1: FIG. 1. Representation on a 1+1 dimensional space-time lat [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Scattering phase shift [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Illustration of reciprocity breaking by monitoring [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Reciprocal of the typical transmission probability [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Coherence length [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Illustration of the voltage probe model of dephas [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Same as Fig. 2, comparing the result (6.6) from the [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
read the original 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 $L\simeq \ell_\phi$ from the exponential $e^{-L/\xi}$ (with localization length $\xi$) to the Ohmic $1/L$ decay. Numerical solution of the master equation gives, for weak monitoring, a logarithmic dependence $\ell_\phi\simeq \xi\ln(v_{\rm F}\tau_\phi/\xi)$ of the coherence length $\ell_\phi$ on the mean time $\tau_\phi$ between measurements.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript formulates a quantum master equation for the many-particle density matrix of electrons propagating through a single-mode disordered conductor. It combines elastic scattering by disorder with time-resolved projective measurements that monitor scattering outcomes. The full counting statistics of transmitted electrons is reported to be binomial, with mean transmission probability T determining the conductance and variance T(1-T) the shot noise. Monitoring is claimed to suppress phase coherence responsible for 1D localization, producing a crossover at L ≃ ℓ_φ from exponential decay e^{-L/ξ} of the typical transmission to Ohmic 1/L decay, with numerical solution of the master equation yielding the weak-monitoring scaling ℓ_φ ≃ ξ ln(v_F τ_φ / ξ).

Significance. If the master equation is shown to be accurate and the numerical results are robust, the work would provide a useful framework for how continuous monitoring affects Anderson localization and transport in mesoscopic 1D systems. The binomial statistics and the specific logarithmic form of the coherence length constitute concrete, potentially testable predictions that could connect to experiments on monitored quantum wires or quantum point contacts.

major comments (2)
  1. [Abstract] Abstract: The central claim that numerical solution of the master equation produces the logarithmic dependence ℓ_φ ≃ ξ ln(v_F τ_φ / ξ) is presented without any description of the discretization scheme, basis truncation, time-step convergence, system-size scaling, or validation against limiting cases (e.g., τ_φ → ∞ recovering full localization or the strong-monitoring limit). Because this numerical result is load-bearing for the reported crossover and scaling, the absence of these checks constitutes a major gap.
  2. [Master-equation formulation] Master-equation formulation (early sections): The specific Lindblad jump operators implementing the time-resolved projective measurements on the many-particle density matrix are not shown to suppress off-diagonal coherences responsible for 1D localization while preserving elastic disorder scattering without uncontrolled approximations in the weak-monitoring regime. An independent analytic check or limiting-case derivation confirming that this combination yields the claimed binomial statistics and logarithmic ℓ_φ is required to support the central physical picture.
minor comments (1)
  1. [Abstract] Abstract: The symbols ℓ_φ and τ_φ are introduced without an explicit sentence defining their physical meaning before they appear in the scaling relation; a brief parenthetical definition would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of the work's potential significance and for the detailed comments on the numerical implementation and master-equation justification. We have revised the manuscript to incorporate additional details and derivations addressing these points. Our responses to the major comments are given below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that numerical solution of the master equation produces the logarithmic dependence ℓ_φ ≃ ξ ln(v_F τ_φ / ξ) is presented without any description of the discretization scheme, basis truncation, time-step convergence, system-size scaling, or validation against limiting cases (e.g., τ_φ → ∞ recovering full localization or the strong-monitoring limit). Because this numerical result is load-bearing for the reported crossover and scaling, the absence of these checks constitutes a major gap.

    Authors: We agree that the numerical methods require explicit documentation to substantiate the central scaling result. In the revised manuscript we have added a dedicated appendix describing the spatial discretization via a finite-difference grid with Δx ≪ λ_F, the truncation of the many-body basis to a fixed maximum particle number chosen to exceed the mean transmitted charge, convergence with respect to time step Δt ≪ τ_φ and conductor length L up to several times ξ, and explicit validation runs: in the τ_φ → ∞ limit the typical transmission recovers the expected exponential Anderson localization, while in the strong-monitoring limit it crosses over to 1/L decay. These checks confirm the robustness of the reported logarithmic dependence of ℓ_φ. revision: yes

  2. Referee: [Master-equation formulation] Master-equation formulation (early sections): The specific Lindblad jump operators implementing the time-resolved projective measurements on the many-particle density matrix are not shown to suppress off-diagonal coherences responsible for 1D localization while preserving elastic disorder scattering without uncontrolled approximations in the weak-monitoring regime. An independent analytic check or limiting-case derivation confirming that this combination yields the claimed binomial statistics and logarithmic ℓ_φ is required to support the central physical picture.

    Authors: We acknowledge the need for a clearer analytic underpinning. The Lindblad operators are defined to implement instantaneous projective measurements of the scattering outcome (transmission or reflection) at each monitoring time; between measurements the evolution remains unitary under the disordered single-particle Hamiltonian, thereby preserving elastic scattering. In the revised manuscript we have inserted a new subsection that derives, in the weak-monitoring limit, the dephasing of off-diagonal coherences in the scattering-state basis and shows that the resulting coherence length scales as ξ ln(v_F τ_φ / ξ). We further demonstrate that the full counting statistics remains exactly binomial by construction, since each electron’s transmission probability is independently sampled by the measurement process. This analytic argument is corroborated by exact diagonalization on small systems. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained via numerical solution of master equation

full rationale

The paper formulates a quantum master equation that combines elastic disorder scattering with projective measurements on the many-particle density matrix, then numerically integrates this equation to extract the binomial full-counting statistics, the length-dependent typical transmission probability, and the logarithmic coherence length scaling. All reported results (crossover at L ≃ ℓ_φ, ℓ_φ ≃ ξ ln(v_F τ_φ / ξ)) follow directly from this integration under the stated model assumptions. No load-bearing self-citations, self-definitional relations, fitted parameters renamed as predictions, or ansatzes imported via prior work are present; the chain remains independent and externally falsifiable through the numerical outputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model rests on the binomial form of full counting statistics and the standard definition of localization length ξ; the monitoring interval τ_φ is introduced as an external control parameter.

free parameters (1)
  • τ_φ
    Mean time between projective measurements; enters the logarithmic expression for ℓ_φ.
axioms (1)
  • domain assumption Full counting statistics of transmitted electrons is binomial with mean T and variance T(1-T)
    Stated directly in the abstract as the basis for conductance and shot noise.

pith-pipeline@v0.9.0 · 5721 in / 1158 out tokens · 46777 ms · 2026-05-22T03:33:02.083543+00:00 · methodology

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Reference graph

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