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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
Submission summary
| Authors (as registered SciPost users): | Rodrigo Lima |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00017v2 (pdf) |
| Date submitted: | Dec. 3, 2025, 11:21 a.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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Reply to the report of Referee 2 on the manuscript No. 2501.01513v1
We thank Referee 2 for their favorable opinion and useful comments, as well as their recommendation for publication. We address each of the points mentioned by the Referee below. To make navigation easier, we marked the changes corresponding to Referee 2's criticism in magenta within the manuscript. Please note that the changes made in response to Referee 1 are still shown in blue.
Referee 2:
- Could the authors denote the disorder correlation function Eq. (3) and its Fourier transform in Eq. (4) by different letters?
Our response:
- We agree with the Referee. We changed the notation of all spatially Fourier-transformed quantities to use tildes.
Referee 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).
Our response:
- Well spotted. We introduced $\tau_{\text{MF}}$ after Eq. (2) and made some clarifications accordingly after Eq. (28).
Referee 2:
- 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).
Our response:
- We agree with the Referee. We made the necessary improvements to the text following Eq. (33).
Referee 2:
- 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.
Our response:
- This is a valuable suggestion from the Referee. Following Eq. (44) and Eq. (50), we provide a physical explanation of how the asymptotic behavior of the quantities under consideration is related to the two timescales involved: the mean field-related timescale and the switch-on protocol-induced timescale. Additionally, we briefly discuss the mathematical origin due to the role of the pole $c_\gamma$ position at the end of Appendix A.
List of changes
To make navigation easier, we marked the changes corresponding to Referee 2's criticism in magenta within the manuscript.
Please note that the changes made in response to Referee 1 are still shown in blue.