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arxiv: 2504.06989 · v3 · pith:JC6NRJQAnew · submitted 2025-04-09 · ❄️ cond-mat.stat-mech · cond-mat.quant-gas· math-ph· math.MP· quant-ph

Exact Current Fluctuations in a Tight-Binding Chain with Dephasing Noise

Taiki Ishiyama , Kazuya Fujimoto , Tomohiro Sasamoto This is my paper

Pith reviewed 2026-05-22 20:10 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.quant-gasmath-phmath.MPquant-ph
keywords full counting statisticscurrent fluctuationstight-binding chaindephasing noiseFredholm determinantdiffusive scalingHubbard modelquantum many-body dynamics
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The pith

The moment generating function of time-integrated current in a dephasing tight-binding chain is given exactly by a Fredholm determinant obtained via mapping to the Hubbard model.

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

This paper establishes the first exact solution for the full counting statistics of current in a diffusive quantum many-body system. It starts from a tight-binding chain subject to dephasing noise and uses the model's SU(2) symmetry to map the dynamics onto the one-dimensional Hubbard model. From that mapping the authors obtain a closed Fredholm determinant expression for the generating function of the integrated current. Long-time asymptotics of this expression show that all cumulants scale diffusively whenever dephasing is present. A sympathetic reader would care because the result supplies a precise benchmark for fluctuation phenomena in open quantum systems where only approximate or numerical methods had been available before.

Core claim

By leveraging the system's SU(2) symmetry and a mapping to the one-dimensional Hubbard model, we derive an exact Fredholm determinant representation for the moment generating function of the time-integrated current. Our long-time asymptotic analysis shows that the cumulant generating function, and hence the corresponding large-deviation function, exhibit diffusive scaling for any nonzero dephasing.

What carries the argument

The SU(2) symmetry of the tight-binding chain with dephasing noise, which permits an exact mapping to the one-dimensional Hubbard model and thereby produces the Fredholm determinant for the current moment generating function.

If this is right

  • The cumulant generating function and large-deviation function both display diffusive scaling for any nonzero dephasing strength.
  • Higher-order cumulants of the current can be extracted systematically from the Fredholm determinant.
  • The exact variance matches the diffusive scaling observed in experimental measurements of current fluctuations.
  • The large-deviation function for current fluctuations becomes available in closed form rather than through approximation.

Where Pith is reading between the lines

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

  • The same symmetry-mapping technique might be tested on other noisy integrable chains to obtain exact fluctuation formulas.
  • Cold-atom or superconducting-circuit experiments could measure higher cumulants to check the predicted diffusive scaling beyond the variance.
  • The Fredholm determinant may supply universal benchmarks for comparing quantum and classical diffusive transport fluctuations.
  • Small-system exact diagonalization could be used to verify the determinant expression before taking the thermodynamic limit.

Load-bearing premise

The dephasing noise preserves an SU(2) symmetry that allows an exact mapping of the tight-binding chain to the one-dimensional Hubbard model.

What would settle it

A direct numerical computation of the time-integrated current distribution in a finite tight-binding chain with dephasing that deviates from the predictions of the Fredholm determinant formula would falsify the exact representation.

Figures

Figures reproduced from arXiv: 2504.06989 by Kazuya Fujimoto, Taiki Ishiyama, Tomohiro Sasamoto.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of the step initial condition for [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Numerical verification for the asymptotic form in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of the cumulant generating function [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

The full counting statistics (FCS) of current has long provided fundamental insights into nonequilibrium systems. Recently, the FCS in quantum many-body systems has attracted growing attention, driven by rapid experimental progress in measuring current fluctuations. Nevertheless, for diffusive quantum many-body dynamics, the FCS of current has yet to be obtained exactly. In this Letter, we present the first exact solution for the FCS of current in a diffusive quantum many-body system, specifically a tight-binding chain with dephasing noise. By leveraging the system's SU(2) symmetry and a mapping to the one-dimensional Hubbard model, we derive an exact Fredholm determinant representation for the moment generating function of the time-integrated current. Our long-time asymptotic analysis shows that the cumulant generating function, and hence the corresponding large-deviation function, exhibit diffusive scaling for any nonzero dephasing. We compare our theoretical predictions with experimentally measured current variance and find consistent diffusive scaling.

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

1 major / 0 minor

Summary. The manuscript claims the first exact solution for the full counting statistics (FCS) of current in a diffusive quantum many-body system, specifically a tight-binding chain subject to dephasing noise. It invokes an SU(2) symmetry to map the Lindblad dynamics onto the one-dimensional Hubbard model, yielding an exact Fredholm determinant representation for the moment generating function of the time-integrated current. Long-time analysis is said to establish diffusive scaling of the cumulant generating function (and thus the large-deviation function) for any nonzero dephasing strength, with consistency checks against experimental current-variance data.

Significance. If the symmetry mapping is rigorously justified, the result would supply the first exact, non-perturbative benchmark for current fluctuations in an open diffusive quantum chain, enabling direct computation of all cumulants via the Fredholm determinant and providing a concrete test of diffusive large-deviation principles in many-body open systems.

major comments (1)
  1. [Abstract and mapping discussion] The central claim rests on an exact SU(2) isomorphism that converts the FCS generating function into a known Hubbard-model Fredholm determinant while preserving both the integrated current operator and the dephasing Lindblad operators. The abstract asserts the mapping exists, yet the manuscript must supply an explicit verification that the counting field couples correctly to the symmetry generators and that the dephasing jump operators are invariant under the full SU(2) action (rather than only U(1)); any mismatch would invalidate the determinant representation for the original model.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We appreciate the positive evaluation of the significance of our results and address the major comment below.

read point-by-point responses

  1. Referee: [Abstract and mapping discussion] The central claim rests on an exact SU(2) isomorphism that converts the FCS generating function into a known Hubbard-model Fredholm determinant while preserving both the integrated current operator and the dephasing Lindblad operators. The abstract asserts the mapping exists, yet the manuscript must supply an explicit verification that the counting field couples correctly to the symmetry generators and that the dephasing jump operators are invariant under the full SU(2) action (rather than only U(1)); any mismatch would invalidate the determinant representation for the original model.

    Authors: We agree that an explicit verification strengthens the rigor of the central mapping. Although the manuscript derives the isomorphism from the SU(2) symmetry of the Lindblad equation and shows that the integrated current is preserved, we will revise the text to include a dedicated subsection (or appendix) that explicitly verifies the required properties. We will demonstrate that the dephasing jump operators are invariant under the full SU(2) action (beyond the U(1) charge conservation) by direct computation of their commutation with the symmetry generators, and we will confirm that the counting field, introduced through the modified current operators, couples consistently to these generators without breaking the isomorphism. This addition will make the applicability of the Hubbard-model Fredholm determinant fully transparent for the original model. revision: yes

Circularity Check

0 steps flagged

Symmetry mapping to Hubbard model provides independent exact representation

full rationale

The paper's central derivation identifies an SU(2) symmetry in the dephasing Lindblad dynamics of the tight-binding chain and uses it to map the system to the one-dimensional Hubbard model, from which the Fredholm determinant for the moment generating function of the time-integrated current follows directly. This mapping is presented as a structural property of the model rather than a fitted ansatz or self-referential definition, and the subsequent long-time asymptotic analysis yielding diffusive scaling is performed on the resulting representation. No load-bearing step reduces by construction to a prior fit, a self-citation chain, or an imported uniqueness theorem; the result is self-contained against the external benchmark of known Hubbard-model solutions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The derivation rests on symmetry properties of the model and a mapping to an established integrable system rather than new fitted parameters or postulated entities.

axioms (2)
  • domain assumption The dephasing tight-binding chain possesses SU(2) symmetry
    Invoked to enable mapping to the one-dimensional Hubbard model
  • domain assumption The mapping to the one-dimensional Hubbard model yields an exact Fredholm determinant for the current generating function
    Central step asserted in the abstract

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