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arxiv: 2605.16494 · v1 · pith:QZCX5E6Nnew · submitted 2026-05-15 · ❄️ cond-mat.quant-gas · cond-mat.stat-mech· quant-ph

Universal dynamics from a single-particle dark state

Ruben Daraban , Arghavan Safavi-Naini , Johannes Schachenmayer , Mohammad Maghrebi This is my paper

Pith reviewed 2026-05-19 21:29 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.stat-mechquant-ph
keywords dark statesopen quantum systemsdissipative spin chainsuniversal scalingmany-body dynamicssubradiant statescorrelated dissipationlong-time decay
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0 comments X

The pith

A single-particle dark state at zero momentum in a dissipative spin chain leads to universal many-body scaling dynamics at long times.

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

A spin chain with correlated dissipation on neighboring sites has a dark state for a single particle at zero momentum. This state remains protected at the few-body level but gets dressed by other modes at the many-body level through an effective nonlinearity created by the dissipation. The dressing causes the zero-momentum mode to decay slowly, resulting in a momentum distribution that scales universally with the variable k times the square root of time. The total density then falls off as one over the square root of t multiplied by the log of t. This picture matters because it reveals how seemingly protected states can still shape the collective long-time behavior in open quantum systems and clarifies earlier conflicting observations.

Core claim

While the zero-momentum mode is dark at the single-particle level, it decays slowly as 1/log t as it becomes dressed by other modes through a dissipation-induced nonlinearity. The momentum distribution takes a universal scaling form in k sqrt(t), and the total density decays as 1/sqrt(t) log t. The same universal behavior persists for soft-core interactions.

What carries the argument

The dissipation-induced nonlinearity that dresses the single-particle dark state at zero momentum and generates the universal scaling in the many-body dynamics.

If this is right

  • The momentum distribution adopts a universal scaling form when expressed in terms of k sqrt(t).
  • The total particle density decays asymptotically according to 1/(sqrt(t) log t).
  • The universal dynamics remain unchanged even when soft-core interactions replace hard-core ones.
  • This framework accounts for the conflicting results reported in recent studies of similar dissipative systems.

Where Pith is reading between the lines

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

  • Similar dressing mechanisms could appear in other open quantum platforms, such as arrays of Rydberg atoms or circuit QED systems, producing analogous scaling laws.
  • Experiments with ultracold atoms could measure the predicted slow decay to confirm the role of the dark state.
  • Extending the model to include driving fields might allow control over the effective nonlinearity and the resulting decay rates.

Load-bearing premise

The long-time behavior is controlled by the slow dressing of the zero-momentum dark state through the dissipation-induced nonlinearity rather than by other processes such as finite-size effects or initial condition details.

What would settle it

Numerical simulation or experimental measurement showing that the momentum distribution fails to collapse onto a single curve when scaled by k sqrt(t) at sufficiently long times would falsify the universal dynamics claim.

Figures

Figures reproduced from arXiv: 2605.16494 by Arghavan Safavi-Naini, Johannes Schachenmayer, Mohammad Maghrebi, Ruben Daraban.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic representation of a spin chain (al [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Long-time dynamics of fermionic densities start [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Universal dynamics for the dissipative Bose [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

Open quantum systems can host dark or subradiant states whose decay is highly suppressed. While these states have been extensively studied in the few-excitation regime, their impact on the many-body dynamics remains largely unexplored. Here, we study a spin chain subject to correlated dissipation on neighboring sites, which admits a single-particle dark state at zero momentum. We show that the single-particle dark state qualitatively alters the many-body dynamics at long times, and identify its distinct universal behavior. While the zero-momentum mode is dark at the single-particle level, it decays slowly as $1/\log t$ as it becomes dressed by other modes through a dissipation-induced nonlinearity. We demonstrate that the momentum distribution takes a universal scaling form in $k\sqrt{t}$, and the total density decays as $1/\sqrt{t}\log t$. Our results further elucidate the origin of the conflicting results in recent works. Finally, we corroborate the analytics with matrix product state simulations and show that the same universal behavior persists for soft-core interactions, underscoring the universality of the emergent dynamics.

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 / 2 minor

Summary. The manuscript studies a spin chain with correlated dissipation on neighboring sites that supports a single-particle dark state at zero momentum. It claims that this dark state is dressed at long times by other modes through a dissipation-induced nonlinearity arising from the Lindblad structure, producing a slow decay of the zero-momentum occupation as 1/log t. The momentum distribution is shown to collapse onto a universal scaling function of k sqrt(t), while the total density decays as 1/sqrt(t) log t. Analytical arguments are corroborated by matrix-product-state simulations, and the same scaling is reported to persist under soft-core interactions. The work also addresses the origin of conflicting results in earlier studies.

Significance. If the central scaling relations hold, the paper makes a useful contribution to open quantum many-body physics by demonstrating how a single-particle dark state can generate universal long-time dynamics through an effective nonlinearity. The explicit forms 1/log t, k sqrt(t), and 1/sqrt(t) log t, together with the numerical confirmation and the extension to soft-core interactions, provide concrete, testable predictions that could guide future experiments in dissipative spin systems.

major comments (2)
  1. The central claim that the dissipation-induced nonlinearity dominates the late-time dressing of the k=0 mode (producing the 1/log t decay and the k sqrt(t) scaling) rests on the assumption that higher-order or multi-particle processes remain subleading. The manuscript should supply a clearer scaling argument or bound showing why this effective term controls the asymptotics, rather than relying primarily on the existing MPS runs whose finite-time and finite-size reach may not yet probe the true t→∞ regime.
  2. The abstract states that the results elucidate conflicting findings in recent works, yet the manuscript does not appear to contain a direct, quantitative comparison (e.g., a table or figure overlay) that maps the present model onto those earlier setups. Without such a comparison, it remains unclear whether the reported universality resolves the discrepancies or merely reproduces them under different parameters.
minor comments (2)
  1. The scaling variable k sqrt(t) should be defined explicitly in the main text, including the precise normalization of the momentum k and any prefactors that may depend on the dissipation strength.
  2. A short paragraph summarizing the precise form of the neighboring-site jump operators and the single-particle dark-state wave function would help readers assess the generality of the nonlinearity without consulting the supplemental material.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and outline the revisions we will make to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: The central claim that the dissipation-induced nonlinearity dominates the late-time dressing of the k=0 mode (producing the 1/log t decay and the k sqrt(t) scaling) rests on the assumption that higher-order or multi-particle processes remain subleading. The manuscript should supply a clearer scaling argument or bound showing why this effective term controls the asymptotics, rather than relying primarily on the existing MPS runs whose finite-time and finite-size reach may not yet probe the true t→∞ regime.

    Authors: We agree that an explicit scaling argument would make the dominance of the effective nonlinearity more transparent. In the revised manuscript we will add a dedicated paragraph deriving the scaling of higher-order multi-particle contributions relative to the leading dissipation-induced term, showing that they remain subleading for t ≫ 1 in the regime of interest. This analytical bound will be presented alongside the existing MPS data, which we maintain already capture the onset of the asymptotic regime but which we acknowledge are limited by finite simulation times. revision: yes

  2. Referee: The abstract states that the results elucidate conflicting findings in recent works, yet the manuscript does not appear to contain a direct, quantitative comparison (e.g., a table or figure overlay) that maps the present model onto those earlier setups. Without such a comparison, it remains unclear whether the reported universality resolves the discrepancies or merely reproduces them under different parameters.

    Authors: We thank the referee for highlighting this point. The manuscript discusses the origin of the conflicting results in the introduction and in the concluding section by contrasting the dissipation structure and initial conditions with those of prior studies. However, we agree that a direct, quantitative mapping would improve clarity. In the revision we will add a new figure that overlays the parameter regimes of the earlier works with our model and explicitly shows how the presence or absence of the single-particle dark state accounts for the differing long-time scalings. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper starts from the Lindblad master equation for a spin chain with neighboring-site correlated dissipation, identifies the single-particle zero-momentum dark state by direct inspection of the jump operators, then constructs an effective nonlinear dressing term whose consequences (1/log t decay, k sqrt(t) scaling of the momentum distribution, and 1/sqrt(t) log t density decay) are derived analytically and cross-checked against independent matrix-product-state simulations. No equation reduces to a fitted parameter renamed as a prediction, no load-bearing premise rests solely on a self-citation, and no ansatz is imported without independent justification; the claimed universality follows from the structure of the dissipation operators and the long-time asymptotics of the resulting effective dynamics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence of the zero-momentum dark state under the chosen dissipation and on the emergence of a dissipation-induced nonlinearity that dresses this mode at long times.

axioms (1)
  • domain assumption Correlated dissipation on neighboring sites admits a single-particle dark state at zero momentum.
    This is the foundational premise that allows the many-body analysis to proceed from the single-particle level.

pith-pipeline@v0.9.0 · 5726 in / 1284 out tokens · 48290 ms · 2026-05-19T21:29:38.351929+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    While the zero-momentum mode is dark at the single-particle level, it decays slowly as 1/log t as it becomes dressed by other modes through a dissipation-induced nonlinearity. ... momentum distribution takes a universal scaling form in k √t, and the total density decays as 1/√t log t

  • IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    1/Γ dρ_k/dt = −F_k({ρ_p}) with F_k containing the nonlocal integral terms |δ_p ρ_p / (δ_p − k)|^2 and 2m ∫ (ρ_k − ρ_p)/|δ_p − k|^2

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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    We start with Eq

    Analytical solution at long times In this and the next subsection, we set Γ = 1 for convenience. We start with Eq. (6) of the main text at long wavelengths (1/|eip −1| 2 ≈p 2): d dt ρ0(t) =− 1 π2 Z dλρλ(t) 2 − 2m π Z ρ0(t)−ρ λ(t) λ2 ,(S.53) together with the scaling solutionρ k(t) =ρ 0(t)f(k √ t) [(Eq. (7) of the main text)] to obtain an analytical soluti...

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    (10) of the main text and expand it aroundz= 1

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    (S.67) to vanish, which then yields A1 → √π 4 ⇒f 1(x) = π 2 e−x2 .(S.68) We thus obtain the universal coefficient as expected

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    We first consider a fully excited initial state

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    Universality at long times Here, we show that the asymptotic behavior is independent of the initial state. In Fig. S.4, we find that the inverseρ 0(t) exhibits the same logarithmic scaling down to the same coefficient, i.e., with the same slope in the log-linear plot. FIG. S.4. Universality of the late-time decay of the zero mode. Inverse zero-mode densit...

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    The spin correlation function is given byC(j)≡ ⟨σ + j+lσ− l ⟩which can be written in terms of fermions as C(j)≡ * ˆc† j j−1Y l=1 (−1)ˆc† l ˆclˆc0 + .(S.78) 19 (a) (b) (c) FIG

    Bosonic momentum distribution The fermionic correlation function is given by ⟨ˆc† jc0⟩= Z π −π dk 2π ρk cos(kj) = ( a0, j= 0 1 2 a|j|, j̸= 0 (S.77) where we have usedρ k =ρ −k. The spin correlation function is given byC(j)≡ ⟨σ + j+lσ− l ⟩which can be written in terms of fermions as C(j)≡ * ˆc† j j−1Y l=1 (−1)ˆc† l ˆclˆc0 + .(S.78) 19 (a) (b) (c) FIG. S.5....

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    The long-time dynamics appear independent of the specific initial conditions and loss rate, and the curves show the same trend at late times

    Total density and trajectory-averaged entanglement entropy Figure S.6(a) shows the unscaled total density for several system sizes, initial filling fractions and loss rates. The long-time dynamics appear independent of the specific initial conditions and loss rate, and the curves show the same trend at late times. For a bipartition into subsystemsAandB, t...

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    (7,12), on a finite open spin chain of lengthL= 110

    Fermionic momentum space observables Figure S.7 tests the analytical predictions for the fermionic observables (after JW), Eqs. (7,12), on a finite open spin chain of lengthL= 110. The rescaled total density (n √ Γt)−1 is shown in Fig. S.7(a), where the straight line gives the logarithmic decay predicted by Eq. (12) of the main text vian= R dk 2π ρk. The ...

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    S.7(b,c) for the hard-core boson (spin) observables, i.e

    Hard-core boson momentum observables Figure S.8 shows the analog of Fig. S.7(b,c) for the hard-core boson (spin) observables, i.e. without the Jordan-Wigner string. The trends mirror the fermionic case with similar fitted coefficients. The bosonic MPS data may also be compared with the GGE results of Fig. S.5; we again find agreement within at most a factor of 2

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    Fishman, S

    Comparison with the GGE at short times Figure S.9 compares the momentum distributionρ k from MPS against the GGE solution with the initial fillingn(0) = 0.8. Panel (a) shows that both methods reproduce theρ 0 ∼1/Γt→1/log(Γt) crossover around Γτ∼1, and panel (b) shows good quantitative agreement of the fullρ k at short times. This agreement is remarkable g...

    work page arXiv 2017