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Out-of-equilibrium dynamical properties of Bose-Einstein condensates in a ramped up weak disorder
by Rodrigo P. A. Lima, Milan Radonjić, Axel Pelster
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Rodrigo Lima |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00017v1 (pdf) |
| Date submitted: | July 5, 2025, 10:10 p.m. |
| Submitted by: | Rodrigo Lima |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We theoretically study how the superfluid and condensate deformation of a weakly interacting ultracold Bose gas evolve during the ramp-up of an external weak disorder potential. Both resulting deformations turn out to consist of two distinct contributions, namely a reversible equilibrium one, already predicted by Huang and Meng in 1992, and a nonequilibrium dynamical one, whose magnitude depends on the details of the ramping protocol. For the specific case of the exponential ramp-up protocol, we are able to derive analytical time-dependent expressions for the above quantities. After a sufficiently long time, a steady state emerges that is generically out of equilibrium. We take the first step in investigating its properties by studying its relaxation dynamics. In addition, we analyze the two-time correlation function and elucidate its relation to the equilibrium and the dynamical part of the condensate deformation.
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- 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
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We thank the Referee for their careful review of the manuscript and the supporting remarks for improvement. In the revised manuscript, we made a number of modifications marked in blue, which address the questions and comments of the Referee. In the following, we give a summary of changes and a point-by-point reply to the Referee. We hope that our work will be suitable for publication.
Below you will find:
i) List of changes in the amended version of manuscript No. 2501.01513v1.
ii) Reply to the comments and criticisms raised by the Referee.
Sincerely yours,
On behalf of all author
List of changes
1) A new paragraph at the end of Section 4 has been added.
2) Two new panels, (c) and (d), have been added to Fig.~1.
3) Panel (a) of Fig.~1 has been updated with the points showing the maximums.
4) A sentence has been added at the end of Section 5.
5) Improvements in formulation have been made.
6) The omission in the caption of Fig.~3 has been corrected.
7) The last paragraph of the Introduction has been improved.
Current status:
Reports on this Submission
Report
The authors study the response of a three-dimensional Bose-Einstein condensate to a weak disordered external potential, which is switched on following a certain time-dependent protocol (the main focus of the paper is on the exponential ramp). The problem is treated perturbatively in the first order in the disorder strength. This is to say that starting from a homogeneous Bose-Einstein condensate the authors derive the first-order response of each Bogoliubov mode, and then integrate over momenta to calculate various correlation functions. An important technical contribution of the paper is the analytical calculation of these momentum integrals. Analytical results are obtained for the exponential ramp protocol and uncorrelated disorder. One can thus address the limiting behaviors (fast and slow ramp, short-time and long-time limits, etc.), which would be difficult to consider numerically.
The paper is very clear and the results are new (in particular, consideration of finite condensate momentum and discussion of the superfluid deformation tensor). I recommend publication. Let me just mention a few points which popped up when reading the manuscript.
1) Could the authors denote the disorder correlation function Eq.(3) and its Fourier transform in Eq.(4) by different letters?
2) After Eq.(28) it would be nice to explain what means small or large tau. The characteristic time scale tau_MF, to which tau should (apparently?) be compared, shows up only in Eq.(35).
3) After Eq.(33), where the authors say that "for... any dynamical disorder switch-on protocol" the dynamically induced part "can be at most as large as the equilibrium part". I think they mean "any tau" rather than "any protocol" since all this discussion refers to the exponential ramp Eq.(28).
4) According to Eqs.(43) and (49) there is an interesting dynamical threshold for tau/tau_MF=1. It can be seen mathematically (the pole c_gamma is either on the branch cut or not), but the authors give no physical interpretation of this phenomenon. Is this behavior related to the maximum of the ramping rate (short-time property) or to its long-time tail? Is it associated with the phononic spectrum and finite sound velocity (similar to the Landau criterium)? Could the authors have another look at this? I do not insist, but it would be a shame to miss something physically interesting.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Rodrigo Lima on 2025-07-11 [id 5633]
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Reply to the report of Referee 1 on the manuscript No. 2501.01513v1
We thank Referee 1 for their favorable opinion and for providing useful remarks for improvement. We address each of the points raised by the Referee below.
Referee 1:
Our response:
We agree that the overshooting deserves more attention. We performed the first step towards its understanding by adding new panels (c) and (d) to Fig. 1 and a new paragraph at the end of Section 4. Panel (c) shows the maximal values of the condensate and superfluid deformations, while panel (d) displays the positions of those maximums as functions of $τ$. We updated panel (a) by including the points corresponding to the maximums. They appear within the intermediate time window $1 \lesssim t_\text{max} \lesssim 10$, as shown in (d). As we state in the text, alongside with the analysis of the new plots, one plausible physical mechanism behind the overshooting is the excitation of high-energy Bogoliubov modes when the ramp-up protocol is rapid enough. We verified that overshooting is still present in the linear ramp-up protocol. Consequently, this qualitative feature appears to be protocol-independent. More detailed understanding of the underlying mechanisms would certainly provide valuable insight into the corresponding intermediate dynamics. However, the latter is outside the scope of this work.
Currently, we do not see an obvious connection between the overshooting and the correlation hole in the spectral form factor of chaotic systems mentioned by the Referee. Additionally, the equal-space correlation function relates to the stationary state and is therefore not directly related to the aforementioned intermediate dynamical window.
Referee 1:
Our response:
Referee 1:
Our response:
Referee 1:
Our response: