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Universal classical and quantum fluctuations in the large deviations of current of noisy quantum systems: Quantum symmetric simple exclusion and inclusion processes
Statistical Mechanics · Submitted 23 Jan 2026 · Published version
abstract compiled · 2026-09-28 · no language-model review
The authors' main claim To leading order in system size and for each noise realization, it converges to that of the corresponding classical process, establishing a classical typicality of current fluctuations in these noisy quantum systems.
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The abstract, sentence by sentence
We study the fluctuation statistics of integrated currents in noisy quantum diffusive systems, focusing on the Quantum Symmetric Simple Exclusion and Inclusion Processes (QSSEP/QSSIP). These one-dimensional fermionic (QSSEP) and bosonic (QSSIP) models feature stochastic nearest-neighbor hopping driven by Brownian noise, together with boundary injection and removal processes. They provide solvable microscopic settings in which quantum coherence coexists with diffusion. Upon noise averaging, their dynamics reduce to those of the classical SSEP/SSIP. We show that the cumulant-generating function of the integrated current, at large scales, obeys a large deviation principle. To leading order in system size and for each noise realization, it converges to that of the corresponding classical process, establishing a classical typicality of current fluctuations in these noisy quantum systems. We further demonstrate a direct connection with Macroscopic Fluctuation Theory (MFT), showing that the large-scale equations satisfied by biased quantum densities coincide with the steady-state Hamilton equations of MFT, thereby providing a microscopic quantum justification of the MFT framework in these models. Finally, we identify the leading finite-size corrections to the current statistics. We show the existence of subleading contributions of purely quantum origin, which are absent in the corresponding classical setting, and provide their explicit expressions for the second and third current cumulants. These quantum corrections are amenable to direct experimental or numerical verification, provided sufficient control over the noise realizations can be achieved. Their presence points toward the necessity of a quantum extension of MFT.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the fluctuation statistics of integrated currents in noisy quantum diffusive systems, focusing on the Quantum Symmetric Simple Exclusion and Inclusion Processes (QSSEP/QSSIP). | contribution 0.91 | 0.89 | 0.05 | asserted 0.90 |
| s1 | These one-dimensional fermionic (QSSEP) and bosonic (QSSIP) models feature stochastic nearest-neighbor hopping driven by Brownian noise, together with boundary injection and removal processes. | background 0.52 | 0.13 | 0.03 | asserted 1.00 |
| s2 | They provide solvable microscopic settings in which quantum coherence coexists with diffusion. | background 0.81 | 0.18 | 0.03 | asserted 1.00 |
| s3 | Upon noise averaging, their dynamics reduce to those of the classical SSEP/SSIP. | background 0.77 | 0.22 | 0.06 | asserted 1.00 |
| s4 | We show that the cumulant-generating function of the integrated current, at large scales, obeys a large deviation principle. | result 0.97 | 0.94 | 0.22 | asserted 1.00 |
| s5 | To leading order in system size and for each noise realization, it converges to that of the corresponding classical process, establishing a classical typicality of current fluctuations in these noisy quantum systems. | result 0.96 | 0.94 | 0.57 | asserted 1.00 |
| s6 | We further demonstrate a direct connection with Macroscopic Fluctuation Theory (MFT), showing that the large-scale equations satisfied by biased quantum densities coincide with the steady-state Hamilton equations of MFT, thereby providing a microscopic quantum justification of the MFT framework in these models. | result 0.72 | 0.94 | 0.25 | asserted 1.00 |
| s7 | Finally, we identify the leading finite-size corrections to the current statistics. | result 0.56 | 0.95 | 0.05 | asserted 1.00 |
| s8 | We show the existence of subleading contributions of purely quantum origin, which are absent in the corresponding classical setting, and provide their explicit expressions for the second and third current cumulants. | result 0.96 | 0.95 | 0.15 | asserted 1.00 |
| s9 | These quantum corrections are amenable to direct experimental or numerical verification, provided sufficient control over the noise realizations can be achieved. | limitation 0.44 | 0.32 | 0.05 | hedged possibility 0.76 |
| s10 | Their presence points toward the necessity of a quantum extension of MFT. | interpretation 0.94 | 0.62 | 0.20 | hedged possibility 0.77 |
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Original abstract
We study the fluctuation statistics of integrated currents in noisy quantum diffusive systems, focusing on the Quantum Symmetric Simple Exclusion and Inclusion Processes (QSSEP/QSSIP). These one-dimensional fermionic (QSSEP) and bosonic (QSSIP) models feature stochastic nearest-neighbor hopping driven by Brownian noise, together with boundary injection and removal processes. They provide solvable microscopic settings in which quantum coherence coexists with diffusion. Upon noise averaging, their dynamics reduce to those of the classical SSEP/SSIP. We show that the cumulant-generating function of the integrated current, at large scales, obeys a large deviation principle. To leading order in system size and for each noise realization, it converges to that of the corresponding classical process, establishing a classical typicality of current fluctuations in these noisy quantum systems. We further demonstrate a direct connection with Macroscopic Fluctuation Theory (MFT), showing that the large-scale equations satisfied by biased quantum densities coincide with the steady-state Hamilton equations of MFT, thereby providing a microscopic quantum justification of the MFT framework in these models. Finally, we identify the leading finite-size corrections to the current statistics. We show the existence of subleading contributions of purely quantum origin, which are absent in the corresponding classical setting, and provide their explicit expressions for the second and third current cumulants. These quantum corrections are amenable to direct experimental or numerical verification, provided sufficient control over the noise realizations can be achieved. Their presence points toward the necessity of a quantum extension of MFT.
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9 arXiv papers cite this in 12 sentences
Papers citing it · 2 sentences without a confident label
Compares with it 2 papers
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To our knowledge, such a comparison was previously only available in the QSSEP for late-time stationary states [ref] , with no finite-time result available.
Domain-wall melting in all-to-all QSSEP from random-matrix theory · Outlook · 0.91
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The late time limit we have considered above applies to the lattice model itself and is very different from continuum scaling limits that have been considered for the QSSEP and similar models [ref] .
Interacting hydrodynamic modes in spinless fermions with dephasing noise · Diffusive continuum scaling limit · 0.91
Cites it as support 1 paper
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Interestingly, these coherence loops fully encode the MFT fluctuation statistics of densities and currents [ref] , but also additional quantum effects that are absent at the classical level [ref] .
Interacting Quantum Symmetric Exclusion Process · Introduction · 0.97
Cites it as background 6 papers
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For quantum mechanical systems, the same depth of understanding is still lacking (but see e.g. [ref] for recent developments).
The Quantum Mechanics of Rare Events: From Quantum Walks to Stochastic Inflation · Introduction · 0.85
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Recently, quantum versions of simple exclusion processes have attracted significant interest [ref] .
Nonequilibrium phases and quantum correlations in synthetic transport models · Introduction · 0.90
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On timescales beyond this rapid initial equilibration, the dynamics of local operators can be captured by hydrodynamics [ref] .
Long-lived local quantum coherences from hydrodynamic large deviations · Introduction · 0.90
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