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Identifying diffusive length scales in one-dimensional Bose gases

by Frederik Møller, Federica Cataldini, Jörg Schmiedmayer

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Submission summary

Authors (as registered SciPost users): Frederik Skovbo Møller · Jörg Schmiedmayer
Submission information
Preprint Link:  (pdf)
Date accepted: 2024-04-12
Date submitted: 2024-03-13 14:24
Submitted by: Møller, Frederik Skovbo
Submitted to: SciPost Physics Core
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Experiment
  • Atomic, Molecular and Optical Physics - Theory
  • Fluid Dynamics
Approaches: Theoretical, Experimental


In the hydrodynamics of integrable models, diffusion is a subleading correction to ballistic propagation. Here we quantify the diffusive contribution for one-dimensional Bose gases and find it most influential in the crossover between the main thermodynamic regimes of the gas. Analysing the experimentally measured dynamics of a single density mode, we find diffusion to be relevant only for high wavelength excitations. Instead, the observed relaxation is solely caused by a ballistically driven dephasing process, whose time scale is related to the phonon lifetime of the system and is thus useful to evaluate the applicability of the phonon bases typically used in quantum field simulators.

List of changes

- Restructured section of the manuscript. The former section 3 is now section 2.2, while former sections 2.2 and 2.3 are now sections 3.2.1 and part of 3.2.4, respectively.

- Added paragraph in start of section 2.2 to motivate the measure \Gamma.

- In section 3.1, added sentence to specify how temperature and coupling strength of the experimental system are obtained.

- Moved discussions of phonons previously featured in the end of section 2.2 to middle of section 3.2.3.

Published as SciPost Phys. Core 7, 025 (2024)

Reports on this Submission

Anonymous Report 1 on 2024-4-5 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2312.14007v3, delivered 2024-04-05, doi: 10.21468/SciPost.Report.8831


The authors took some of my suggestions into account and made small improvements to the manuscript. The paper can be published as it is, as I had already said in my first report.

Nevertheless, let me point out that my main concern (the fact that the choice of the quantifier $\Gamma$ is arbitrary) has not been addressed satisfactorily. In their answer to my point 2, the authors simply rephrased what was already in the manuscript. In particular, their argument "An exchange in the numerator and denominator in the definition of $\Gamma$ would produce an equivalent measure" sounds very naive and possibly very wrong. Indeed, this is equivalent to the claim that the integral $\int \frac{\rho(\theta) d\theta}{ f(\theta)} $ is necessarily of the same order as $1/\left( \int f(\theta) \rho(\theta) d\theta \right)$, which is obviously wrong in general. Perhaps it is true here, for the specific function $f(\theta)$ and the rapidity distribution $\rho(\theta)$ considered by the authors; it would have been nice to check this. But fine, I guess such refinements can be kept for future work. The paper contains enough new results and insights to be published as it is.

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Author:  Frederik Skovbo Møller  on 2024-04-08  [id 4397]

(in reply to Report 1 on 2024-04-05)

We thank the Referee for their comments and their continued support of our manuscript. We are sorry that our previous response regarding the measure $\Gamma$ was not satisfactory; in the following we will try to rectify this.

The choice of $\Gamma$ is not arbitrary in the sense that it is physically motivated; as previously specified in the main text, and now explicitly written in formula, it describes a weighted average of the ballistically traveled distance of a quasi-particle relative to the diffusively broadened width of its trajectory.
However, we agree that the exact construction of the measure indeed does appear a bit arbitrary: In our previous response, we stated that defining a measure $\tilde \Gamma = \frac{1}{n} \int_{-\infty}^{\infty} \mathrm{d}\theta \: \rho_{\mathrm{p}}(\theta) \frac{\delta \bar z^2 (\theta)}{\bar z (\theta)}$, i.e. with the ratio of ballistic distance to diffusive width inverted, would "produce an equivalent measure" to $\Gamma$. This formulation was rather poor: Of course, $\tilde\Gamma$ is not equal to $\Gamma$, however, from analysing either function one will arrive at similar conclusions regarding which regimes diffusive the most/least, as the location of their extrema in the $(\gamma, \mathcal{T})$-phase-space coincide. To verify this, we have calculated $\tilde\Gamma$ for thermal states at various $\mathcal{T}$ and $\gamma$ (for $c =1$, see attachment). Note, that we omitted calculating the measure deep in the quasi-condensate regime, as high rapidity resolution (and thus large numerical computation time) is needed for proper convergence of the thermal state. Comparing the attached plot of $\tilde\Gamma$ to the plot of $\Gamma$ found in the manuscript, we indeed observe the same qualitative features, namely that the most diffusive thermal states are found around $\mathcal{T} \sim 1$ and $\gamma \sim 1-10$, that diffusive contributions become vanishingly small in the asymptotic regimes, and that for higher temperatures diffusion is most prominent near the transition between the quasi-condensate and ideal Bose gas regimes.


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