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arxiv: 2604.21553 · v1 · submitted 2026-04-23 · ❄️ cond-mat.stat-mech

Dean-Kawasaki fluctuating hydrodynamics for backscattering hard rods

Mrinal Jyoti Powdel This is my paper

Pith reviewed 2026-05-08 13:36 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords backscattering hard rodsDean-Kawasaki hydrodynamicsfluctuating hydrodynamicsintegrability breakingdensity-density correlationsballistic to diffusive crossoverone-dimensional transport
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The pith

Backscattering hard rods switch from ballistic to diffusive spreading in their two-time density correlations after the velocity flip timescale.

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

This paper examines one-dimensional hard rods whose velocities reverse sign at rate gamma, which halves the number of conserved quantities by breaking integrability. It employs a Dean-Kawasaki fluctuating hydrodynamic description of the density field to track how the two-time density-density correlation evolves. The calculation establishes ballistic spreading of the correlation for times much shorter than one over gamma and diffusive spreading for times much longer than one over gamma. A reader would care because the result shows how a minimal integrability-breaking perturbation alters transport behavior in an exactly solvable interacting particle model.

Core claim

We show using a Dean-Kawasaki fluctuating hydrodynamic formulation that for t ≫ 1/γ, the two-time density density correlation spreads in a diffusive manner, and for t ≪ 1/γ, the correlation spreads ballistically.

What carries the argument

The Dean-Kawasaki fluctuating hydrodynamic formulation for the density field, which incorporates the stochastic effects of velocity sign flips at rate gamma.

Load-bearing premise

The Dean-Kawasaki fluctuating hydrodynamics remains a valid description of the density fluctuations even after the integrability-breaking velocity-flipping perturbation is introduced.

What would settle it

Numerical simulation or experiment on backscattering hard rods that measures the two-time density-density correlation and checks whether spreading changes from ballistic to diffusive around t equal to one over gamma.

Figures

Figures reproduced from arXiv: 2604.21553 by Mrinal Jyoti Powdel.

Figure 1
Figure 1. Figure 1: Mass density, q0(x, t), momentum density, q1(x, t) and energy density, q2(x, t)/2 of a system of backscattering hard rods of length a = 1 at different times. The solid lines represents theory and the circles represent the results from molecular dynamics. Here, the initial positions and velocities are drawn from a gaussian distribution (6) with σx = 5 and T = 1. The numerical results have been obtained afte… view at source ↗
Figure 2
Figure 2. Figure 2: Unequal space-time correlation of mass densities for a hard rod system consisting of view at source ↗
read the original abstract

We study a system of backscattering hard rods in one dimension. Contrary to the usual ballistic hard rods, these hard rods flip the sign of their velocities with a rate $\gamma$. This leads to the decay of the odd moments of velocity while preserving the even moments: the number of conserved quantities in the system becomes half. The introduction of the flipping rate, $\gamma$, is a kind of integrability-breaking perturbation. One expects a change in the transport properties in the system due to the integrability breaking. We show using a Dean-Kawasaki fluctuating hydrodynamic formulation that for $t \gg 1/\gamma$, the two-time density density correlation spreads in a diffusive manner, and for $t \ll 1/\gamma$, the correlation spreads ballistically.

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 studies a one-dimensional system of hard rods that flip the sign of their velocities at a Poisson rate γ, which breaks integrability by halving the number of conserved quantities. Using a Dean-Kawasaki fluctuating hydrodynamic formulation for the density field, the authors claim that the two-time density-density correlation spreads ballistically for t ≪ 1/γ and diffusively for t ≫ 1/γ.

Significance. If the fluctuating hydrodynamics is justified for the perturbed microscopic dynamics, the result supplies a hydrodynamic account of the ballistic-to-diffusive crossover induced by integrability breaking, which is of interest for transport in one-dimensional systems with weak perturbations. The approach may generalize to other models where velocity flips or similar scattering mechanisms are added to integrable dynamics.

major comments (2)
  1. [Abstract and the section introducing the fluctuating hydrodynamic equations] The central claim (abstract) that the standard Dean-Kawasaki stochastic continuity equation governs the density fluctuations after the velocity-flip perturbation is introduced lacks an explicit microscopic derivation. The original DK construction projects Brownian Langevin dynamics onto the density; here the unperturbed rules are deterministic hard-rod collisions plus independent Poisson flips, so the noise correlator may acquire a memory kernel decaying on timescale 1/γ or require auxiliary right- and left-mover fields to recover finite propagation speed at short times. This assumption is load-bearing for the stated crossover.
  2. [The derivation or application of the Dean-Kawasaki equations] No re-derivation of the drift and multiplicative noise terms from the perturbed Liouville/master operator is provided. Without this step, it is not shown that the white-noise structure and hydrodynamic closure remain valid once the flipping rate γ is nonzero, which directly affects the validity of the long-time diffusive and short-time ballistic regimes.
minor comments (1)
  1. [Abstract] The abstract would be clearer if it specified the initial condition (e.g., whether the correlation is computed from a local density perturbation or equilibrium fluctuations) and the precise definition of the two-time density-density correlation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for their thorough evaluation of our manuscript on backscattering hard rods using Dean-Kawasaki fluctuating hydrodynamics. The comments raise valid questions about the justification of the stochastic hydrodynamic equations under the integrability-breaking perturbation. We respond to each major comment below, indicating the revisions we plan to implement.

read point-by-point responses

  1. Referee: [Abstract and the section introducing the fluctuating hydrodynamic equations] The central claim (abstract) that the standard Dean-Kawasaki stochastic continuity equation governs the density fluctuations after the velocity-flip perturbation is introduced lacks an explicit microscopic derivation. The original DK construction projects Brownian Langevin dynamics onto the density; here the unperturbed rules are deterministic hard-rod collisions plus independent Poisson flips, so the noise correlator may acquire a memory kernel decaying on timescale 1/γ or require auxiliary right- and left-mover fields to recover finite propagation speed at short times. This assumption is load-bearing for the stated crossover.

    Authors: We acknowledge that the manuscript applies the standard Dean-Kawasaki form without a full microscopic derivation from the perturbed dynamics. The justification is that the density remains the sole hydrodynamic field, the Poisson flips relax odd velocity moments while preserving the continuity equation structure, and memory effects in the noise are negligible beyond the microscopic scale. Finite propagation speed at short times is recovered because, for t ≪ 1/γ, flips are rare and the deterministic hard-rod collisions (equivalent to free streaming after mapping) produce ballistic spreading. In the revised manuscript we will add a dedicated paragraph (or short appendix) clarifying these points and the validity ranges of the white-noise approximation. revision: partial

  2. Referee: [The derivation or application of the Dean-Kawasaki equations] No re-derivation of the drift and multiplicative noise terms from the perturbed Liouville/master operator is provided. Without this step, it is not shown that the white-noise structure and hydrodynamic closure remain valid once the flipping rate γ is nonzero, which directly affects the validity of the long-time diffusive and short-time ballistic regimes.

    Authors: We agree that an explicit re-derivation from the perturbed Liouville or master operator is absent. The drift follows from the deterministic hard-rod collisions (which conserve even velocity moments), while the multiplicative noise is inherited from the standard density-fluctuation construction; the flips enter only by relaxing the velocity distribution, inducing effective diffusion at long times without altering the local noise structure at hydrodynamic scales. We will revise the theory section to include a concise justification of why the white-noise form and closure remain applicable for γ > 0, explicitly linking the long-time diffusive regime to flip-induced scattering and the short-time ballistic regime to the unperturbed deterministic dynamics. revision: partial

Circularity Check

0 steps flagged

No circularity: crossover derived from assumed hydrodynamic equations

full rationale

The manuscript introduces the velocity-flip rate γ as an explicit parameter that breaks integrability and then applies the standard Dean-Kawasaki stochastic continuity equation to the density field. The two-time correlation is obtained by solving these equations, yielding ballistic spreading on timescales t ≪ 1/γ (where flips are rare) and diffusive spreading on t ≫ 1/γ (where flips dominate). No quantity is fitted to data and then relabeled as a prediction, no self-citation supplies a load-bearing uniqueness theorem, and the crossover timescale is not defined in terms of itself. The derivation is therefore self-contained once the hydrodynamic ansatz is granted; any doubt concerns the validity of that ansatz after the perturbation, not circularity within the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the Dean-Kawasaki fluctuating hydrodynamics to the velocity-flipping model; no free parameters, invented entities, or additional axioms are identifiable from the abstract alone.

axioms (1)
  • domain assumption Dean-Kawasaki fluctuating hydrodynamics accurately captures the density fluctuations of the backscattering hard-rod system.
    Invoked to obtain the time-dependent spreading of the two-time density correlation.

pith-pipeline@v0.9.0 · 5421 in / 1345 out tokens · 53236 ms · 2026-05-08T13:36:58.368821+00:00 · methodology

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Reference graph

Works this paper leans on

29 extracted references · 29 canonical work pages

  1. [1]

    O. A. Castro-Alvaredo, B. Doyon, and T. Yoshimura, Phys. Rev. X6, 041065 (2016)

    work page 2016

  2. [2]

    Bertini, M

    B. Bertini, M. Collura, J. De Nardis, and M. Fagotti, Phys. Rev. Lett.117, 207201 (2016)

    work page 2016

  3. [3]

    Doyon, S

    B. Doyon, S. Gopalakrishnan, F. Møller, J. Schmied- mayer, and R. Vasseur, Phys. Rev. X15, 010501 (2025)

    work page 2025

  4. [4]

    Malvania, Y

    N. Malvania, Y. Zhang, Y. Le, J. Dubail, M. Rigol, and D. S. Weiss, Science373, 1129 (2021), https://www.science.org/doi/pdf/10.1126/science.abf0147

    work page doi:10.1126/science.abf0147 2021

  5. [5]

    V. Alba, B. Bertini, M. Fagotti, L. Piroli, and P. Rug- giero, Journal of Statistical Mechanics: Theory and Ex- periment2021, 114004 (2021)

    work page 2021

  6. [6]

    Doyon, Journal of Mathematical Physics60, 073302 (2019)

    B. Doyon, Journal of Mathematical Physics60, 073302 (2019)

    work page 2019

  7. [7]

    Kinoshita, T

    T. Kinoshita, T. Wenger, and D. S. Weiss, Nature440, 900 (2006). 6

    work page 2006

  8. [8]

    J.-S. Caux, B. Doyon, J. Dubail, R. Konik, and T. Yoshimura, SciPost Phys.6, 070 (2019)

    work page 2019

  9. [9]

    Bastianello, A

    A. Bastianello, A. De Luca, and R. Vasseur, Journal of Statistical Mechanics: Theory and Experiment2021, 114003 (2021)

    work page 2021

  10. [10]

    Y. Tang, W. Kao, K.-Y. Li, S. Seo, K. Mallayya, M. Rigol, S. Gopalakrishnan, and B. L. Lev, Physical Review X8, 021030 (2018)

    work page 2018

  11. [11]

    Jung and A

    P. Jung and A. Rosch, Physical Review B76, 245108 (2007)

    work page 2007

  12. [12]

    ˇZnidariˇ c, Physical Review Letters110, 070602 (2013)

    M. ˇZnidariˇ c, Physical Review Letters110, 070602 (2013)

    work page 2013

  13. [13]

    Karrasch, D

    C. Karrasch, D. M. Kennes, and F. Heidrich-Meisner, Physical Review B91, 115130 (2015)

    work page 2015

  14. [14]

    Biella, A

    A. Biella, A. De Luca, J. Viti, D. Rossini, L. Mazza, and R. Fazio, Physical Review B93, 205121 (2016)

    work page 2016

  15. [15]

    Steinigeweg, F

    R. Steinigeweg, F. Heidrich-Meisner, J. Gemmer, K. Michielsen, and H. De Raedt, Physical Review B90, 094417 (2014)

    work page 2014

  16. [16]

    F. M. Surace and O. Motrunich, Physical Review Re- search5, 043019 (2023)

    work page 2023

  17. [17]

    Akemann, F

    G. Akemann, F. Balducci, A. Chenu, P. P¨ aßler, F. Roc- cati, and R. Shir, Physical Review Research7, 013098 (2025)

    work page 2025

  18. [18]

    V. B. Bulchandani, D. A. Huse, and S. Gopalakrishnan, Physical Review B105, 214308 (2022)

    work page 2022

  19. [19]

    Tonks, Phys

    L. Tonks, Phys. Rev.50, 955 (1936)

    work page 1936

  20. [20]

    X. Cao, V. B. Bulchandani, and J. E. Moore, Phys. Rev. Lett.120, 164101 (2018)

    work page 2018

  21. [21]

    Lopez-Piqueres and R

    J. Lopez-Piqueres and R. Vasseur, Phys. Rev. Lett.130, 247101 (2023)

    work page 2023

  22. [22]

    M. J. Powdel and A. Kundu, Journal of Statistical Me- chanics: Theory and Experiment2024, 123205 (2024)

    work page 2024

  23. [23]

    D. S. Dean, Journal of Physics A: Mathematical and Gen- eral29, L613 (1996)

    work page 1996

  24. [24]

    Illien, Reports on Progress in Physics88, 086601 (2025)

    P. Illien, Reports on Progress in Physics88, 086601 (2025)

    work page 2025

  25. [25]

    Doyon, SciPost Phys

    B. Doyon, SciPost Phys. Lect. Notes , 18 (2020)

    work page 2020

  26. [26]

    J. L. Lebowitz, J. K. Percus, and J. Sykes, Phys. Rev. 171, 224 (1968)

    work page 1968

  27. [27]

    J. K. Percus, Physics of Fluids12, 1560 (1969)

    work page 1969

  28. [28]

    Malakar, V

    K. Malakar, V. Jemseena, A. Kundu, K. V. Ku- mar, S. Sabhapandit, S. N. Majumdar, S. Redner, and A. Dhar, Journal of Statistical Mechanics: Theory and Experiment2018, 043215 (2018)

    work page 2018

  29. [29]

    Mukherjee, S

    I. Mukherjee, S. Chahal, and A. Kundu, Microscopic and hydrodynamic correlation in 1d hard rod gas (2026), arXiv:2601.04951 [cond-mat.stat-mech]. Appendix A: Solution of the Fokker-Planck equation for RTPs within hard walls In this section, we solve the Fokker-Planck equation (Eq. (4)) for RTPs in a box with fully reflecting walls. We define the total PSD...

    work page arXiv 2026