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arxiv: 2502.18246 · v2 · submitted 2025-02-25 · ❄️ cond-mat.stat-mech · cond-mat.quant-gas

Reaction-diffusion dynamics of the weakly dissipative Fermi gas

Hannah Lehr , Igor Lesanovsky , Gabriele Perfetto This is my paper

Pith reviewed 2026-05-23 02:42 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.quant-gas
keywords reaction-diffusionFermi gasdissipative systemsalgebraic decayabsorbing-state transitiondirected percolationquantum master equationcontinuum space
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The pith

Weakly dissipative continuum Fermi gas exhibits algebraic density decay and mean-field directed percolation transition like lattice systems.

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

The paper investigates whether critical behaviors seen in lattice fermionic reaction-diffusion systems appear in a continuum Fermi gas under weak dissipation. Using the time-dependent generalized Gibbs ensemble method, it demonstrates that for annihilation and coagulation processes, the particle density decays algebraically in time, matching lattice results. Temperature affects the decay speed but not the exponents. It also identifies a phase transition in the directed percolation class when branching competes with decay. This suggests that such emergent phenomena are not limited to discrete lattices but can occur in continuous space, potentially observable in ultra-cold atoms.

Core claim

For the one-dimensional Fermi gas with dissipative reactions in the weakly dissipative regime, the density shows asymptotic algebraic decay for 2A→∅, 3A→∅, and A+A→A processes, similar to lattice problems, with exponents unaffected by initial temperature. A second-order absorbing-state phase transition in the mean-field directed percolation universality class emerges from competition between branching A→A+A and decay processes.

What carries the argument

The time-dependent generalized Gibbs ensemble method applied to the quantum master equation for the continuum Fermi gas, capturing the reaction-limited regime of weak dissipation.

If this is right

  • The density decay accelerates with higher initial temperature but retains the same algebraic exponents.
  • Emergent critical behavior from lattice systems is present in continuum space.
  • The phase transition belongs to the mean-field directed percolation class.
  • Such features may be probed using ultra-cold atomic physics.

Where Pith is reading between the lines

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

  • This could imply that continuum models are sufficient for studying reaction-diffusion criticality without needing lattice discreteness.
  • Experiments with ultra-cold fermions might directly test these predictions by tuning dissipation strength.
  • The universality suggests similar behavior in higher dimensions or other particle statistics.

Load-bearing premise

The time-dependent generalized Gibbs ensemble method accurately derives the dynamics of the continuum Fermi gas in the weakly dissipative regime.

What would settle it

An experiment measuring the long-time density decay exponent in a one-dimensional ultra-cold Fermi gas under controlled two-body annihilation and finding it differs from the lattice-predicted algebraic form.

Figures

Figures reproduced from arXiv: 2502.18246 by Gabriele Perfetto, Hannah Lehr, Igor Lesanovsky.

Figure 1
Figure 1. Figure 1: Time dependent generalised Gibbs ensemble (tGGE). [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Momentum occupation function at various times [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Reaction-limited binary annihilation in the continuum limit. [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Reaction-limited binary annihilation on the lattice [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Momentum occupation function for various values of time [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Reaction-limited three-body annihilation in the continuum limit. [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Reaction-limited dynamics of coagulation in the continuum limit. [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Momentum occupation function for various values of time [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Reaction-limited coagulation dynamics in the continuum for various [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Stationary momentum occupation function in the active phase of the [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Reaction-limited phase diagram of the fermionic contact process in [PITH_FULL_IMAGE:figures/full_fig_p027_11.png] view at source ↗
read the original abstract

We study the one-dimensional Fermi gas subject to dissipative reactions. The dynamics is governed by the quantum master equation, where the Hamiltonian describes coherent motion of the particles, while dissipation accounts for irreversible reactions. For lattice one-dimensional fermionic systems, emergent critical behavior has been found in the dynamics in the reaction-limited regime of weak dissipation. Here, we address the question whether such features are present also in a gas in continuum space. We do this in the weakly dissipative regime by applying the time-dependent generalized Gibbs ensemble method. We show that for two body $2A\to \emptyset$ and three $3A\to \emptyset$ body annihilation, as well as for coagulation $A+A\to A$, the density features an asymptotic algebraic decay in time akin to the lattice problem. In all the cases, we find that upon increasing the temperature of the initial state the density decay accelerates, but the asymptotic algebraic decay exponents are not affected. We eventually consider the competition between branching $A\to A+A$ and the decay processes $A\to \emptyset$ and $2A\to \emptyset$. We find a second-order absorbing-state phase transition in the mean-field directed percolation universality class. This analysis shows that emergent behavior observed in lattice quantum reaction-diffusion systems is present also in continuum space, where it may be probed using ultra-cold atomic physics.

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 applies the time-dependent generalized Gibbs ensemble (tGGE) method to the one-dimensional continuum Fermi gas in the weak-dissipation regime governed by a quantum master equation. For the reactions 2A→∅, 3A→∅ and A+A→A it reports algebraic long-time density decay with the same exponents as the corresponding lattice problems; initial temperature only rescales the prefactor. For the branching-decay competition A→A+A versus A→∅ and 2A→∅ it identifies a second-order absorbing-state transition belonging to the mean-field directed-percolation universality class.

Significance. If the tGGE mapping is justified, the work establishes that the emergent algebraic decays and mean-field DP transition previously seen on lattices survive in continuum space, thereby strengthening the case for experimental probes with ultra-cold atoms. The temperature independence of the exponents is a clear, falsifiable prediction.

major comments (2)
  1. [Method and tGGE application] The central claim rests on the validity of the tGGE reduction for the continuum dispersion; the manuscript does not supply an explicit derivation showing that the continuous kinetic term does not generate additional relevant operators beyond those retained in the lattice tGGE (see the paragraph following Eq. (3) and the rate-equation section).
  2. [Branching-decay competition] The assertion that the branching-decay transition lies in the mean-field DP class is stated without a supporting calculation of the critical exponents or the scaling function; a direct comparison to the mean-field rate equations or a finite-size scaling analysis is required to substantiate the universality-class assignment.
minor comments (2)
  1. [Abstract] The abstract states that the algebraic exponents are 'akin to the lattice problem' but does not quote the numerical values obtained for the continuum case, making immediate comparison difficult.
  2. [Model definition] Notation for the reaction rates (e.g., the symbols used for the two-body and three-body annihilation strengths) is introduced without a consolidated table; a short table would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and positive assessment of the work. We address each major comment below and will revise the manuscript to incorporate the requested clarifications.

read point-by-point responses

  1. Referee: [Method and tGGE application] The central claim rests on the validity of the tGGE reduction for the continuum dispersion; the manuscript does not supply an explicit derivation showing that the continuous kinetic term does not generate additional relevant operators beyond those retained in the lattice tGGE (see the paragraph following Eq. (3) and the rate-equation section).

    Authors: We acknowledge the need for a more explicit justification. In the revised manuscript we will expand the discussion immediately after Eq. (3) to derive that the quadratic continuum dispersion, when integrated against the local reaction kernels in the weak-dissipation limit, produces no additional relevant operators beyond those already retained in the lattice tGGE. The resulting effective rate equations therefore retain the same structure, with the continuous kinetic term only renormalizing the diffusion constant without altering the scaling of the reaction terms. revision: yes

  2. Referee: [Branching-decay competition] The assertion that the branching-decay transition lies in the mean-field DP class is stated without a supporting calculation of the critical exponents or the scaling function; a direct comparison to the mean-field rate equations or a finite-size scaling analysis is required to substantiate the universality-class assignment.

    Authors: We agree that an explicit comparison is required. In the revision we will add a direct comparison of the tGGE steady-state and relaxation data to the mean-field rate equations for the branching-decay process. This will demonstrate that the order-parameter exponent, the density decay exponent at criticality, and the scaling function near the transition coincide with the known mean-field directed-percolation values, thereby substantiating the universality-class assignment without invoking finite-size scaling. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation applies the established time-dependent generalized Gibbs ensemble (tGGE) method to the weakly dissipative continuum Fermi gas, yielding algebraic decay for 2A→∅, 3A→∅, A+A→A and a mean-field DP transition for branching-decay competition. These outcomes follow from the method's application to the new continuum setting rather than from self-definition, fitted inputs renamed as predictions, or load-bearing self-citations. The abstract and description indicate the approach is restricted to the weak-dissipation regime where tGGE is designed to operate, with temperature only rescaling prefactors; no equation reduces to its input by construction and the central claims retain independent content from the lattice comparisons.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the validity of the T-GGE method for this system, which is a domain assumption from the field of open quantum systems.

axioms (1)
  • domain assumption The time-dependent generalized Gibbs ensemble method applies to the weakly dissipative regime of the continuum one-dimensional Fermi gas.
    The paper uses this method to obtain the density dynamics and phase transition.

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