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Chapman-Enskog theory for nearly integrable quantum gases
by Maciej Łebek, Miłosz Panfil
Submission summary
| Authors (as registered SciPost users): | Milosz Panfil · Maciej Łebek |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2410.23209v1 (pdf) |
| Date submitted: | 2024-10-31 12:34 |
| Submitted by: | Łebek, Maciej |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Integrable systems feature an infinite number of conserved charges and on hydrodynamic scales are described by generalised hydrodynamics (GHD). This description breaks down when the integrability is weakly broken and sufficiently large space-time-scales are probed. The emergent hydrodynamics depends then on the charges conserved by the perturbation. We focus on nearly-integrable Galilean-invariant systems with conserved particle number, momentum and energy. Basing on the Boltzmann collision approach to integrability breaking we describe dynamics of the system with GHD equation supplemented with collision term. The limit of large space-time-scales is addressed using Chapman-Enskog expansion adapted to the GHD equation. We recover Navier-Stokes equations and find transport coefficients: viscosity and thermal conductivity, which are given by generalizations of Chapman-Enskog integral equations. We also observe that the diffusion of quasiparticles introduces an additional small parameter enriching the structure of the expansion as compared to the standard Boltzmann equation.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report
The authors develop a Chapman-Enskog theory for perturbed integrable systems. The Chapman-Enskog expansion is a textbook method for deriving the Navier-Stokes equations of fluid dynamics from the Boltzmann equation. However, the Chapman-Enskog theory is not a rigorous or controlled theory of hydrodynamics, does not yield exact results in practice and to my mind offers mostly qualitative insight into how perturbing a free (and thus trivially integrable) system gives rise to irreversible, diffusive behaviour.
In fact I believe that the authors’ results are invalid, because the broadening of sound modes in one dimension momentum-conserving systems is not diffusive, as the authors’ analysis would predict, but is instead well-known to exhibit z=3/2 KPZ-type scaling, as discussed e.g. in Ref. 79 and references therein. The heat mode would presumably also exhibit anomalous broadening. Thus I expect that all the dissipative transport coefficients obtained by the authors are in fact infinite! Only when the integrability-breaking perturbation is exactly zero, and there is no nonlinear mode coupling (which turns out to be guaranteed by the linear degeneracy property of GHD) is it possible to escape anomalous broadening.
I do not believe that the authors’ remarks in the conclusion adequately address this point, which is specific to the one-dimensional setting in which interacting integrable systems are known to occur. (It does not occur in three dimensions, which is why Chapman-Enskog theory is successful there.) Since the authors make no attempt to test the quantitative accuracy of their predictions, e.g. by numerically simulating a specific (presumably classical) model, I am skeptical that they are applicable in any spacetime regime, as the transport coefficients would all have to diverge as a function of time to be consistent with nonlinear fluctuating hydrodynamics.
Given this, I am afraid that I cannot recommend the current version of this paper for publication.
Recommendation
Reject
Strengths
1. The problem considered in the paper is timely, given current research in the field.
2. The theoretical background is outlined clearly, and the computations are explained in detail.
3. The authors present a partial discussion of the potential limitations of the approach.
Weaknesses
1. The authors give no explicit example of applying the formalism developed in the paper, which also means that the possible complications and issues arising in an application are not explored.
2. Connected to the previous point, application to at least one system would be necessary to demonstrate the approach's range of validity.
Report
It is hard to assess whether the acceptance criteria are met due to the weaknesses of the paper. The derivation presented in the paper is a more or less straightforward application of Chapman-Enskog theory in the GHD framework. Whether this is a significant step forward depends on its applicability, which is hard to gauge given that the authors present no application of the formalism to any concrete system, and there is no comparison to some other approach, such as, e.g., a numerical simulation. This prevents assessing whether the journal expectations claimed by the authors are satisfied.
Additionally, without a concrete example, the potential complications of applying the formalism are left unclear.
Due to these weaknesses, I suggest transferring the paper to Scipost Physics Core, where it meets the application criteria and can be published without significant revision.
Requested changes
See the report.
Recommendation
Accept in alternative Journal (see Report)