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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 | |
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| Preprint Link: | https://arxiv.org/abs/2501.01513v1 (pdf) |
| Date submitted: | Jan. 8, 2025, 2:10 p.m. |
| Submitted by: | Lima, Rodrigo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| 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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Current status:
Reports on this Submission
Strengths
1- Analytic expressions for the superfluid and condensation deformation for a driven non-equilibirum system.
2- limits clearly explained and related to previous works.
3- Connections of the deformation quantities to relevant correlation functions.
Weaknesses
1- Dense presentation of the analytic results lacking some physical insight in parts.
Report
The authors derive analytic expressions for the superfluid and condensate deformation of a BEC after an expontential ramp of a disordered potential. They find both equilibrium and non-equilibrium contributions, the former predicted previously in the literature. These quantities are studied for different driving times of the ramp, from sudden quench to adiabatic driving, exploring the entire range of dynamical response. Furthermore, two-time correlation functions are calculated and related to the condensate transformation in different limits (spatial and time), showing that the quench induces long-range spatial correlations.
I find the paper well written and explained. I cannot comment on the validity of all the analytic expressions presented in the manuscript, but have no grounds to thing they are incorrect, as the results shown intuitively appear correct. The work is a fine treatise on the non-equilibrium dynamics of quenched disordered, but I think it could benefit from more interpretation of the results that are presented and any extra insights that could be gained from them. I have a couple of comments below and suggestions that I would like to see answered by the authors.
Comments:
1- What physical insight can be inferred from the maximum of the superfluid and condensate deformations in Fig.1(a) that appears for fast driving (tau_I and tau_II)? It seems that the system is driven to a "far" out of equilibrium state before relaxing to the infinite time average. I know it is mentioned in the authors previous work, but again there is a lack of discussion. This overshoot reminds me of the appearance of the correlation hole in the spectral form factor in chaotic systems (https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.013181) before the system relaxes to the infinite time average. Maybe in this case the overshoot is related to the complex phase in the equal-space correlation function?
2- Can the adiabaticity of the dynamics be inferred from the phase of the correlation function in Fig.3b? For instance for driving times larger than tau_3 the phase contribution vanishes, while the below this, if integrating over T there will always be some contribution, saturating at the sudden quench limit. The time average of this dynamical phase could then be related to the degree of non-equilibrium excitations created by the ramp?
3- Related to the last point, just out of interest, can the non-equilibrium part of the deformations be related to non-equilibrium work statistics? What comes to mind is this work (https://doi.org/10.1103/PhysRevA.107.012209) which does not consider disorder, but rather driving through the critical point in the Ising model. In essence the degree of deformation should be related to the amount of irreversible excitations created during the ramp, maybe finding a relation would be an interesting future work.
Requested changes
1- Address the comments 1 and 2 from the report.
2- "Initially, i.e., at t = 0, the superfluid deformation vanishes." - This sentence implies, at least to me, that some dynamical process is making it vanish, when in fact the initial state is just a superfluid. Maybe can be rewritten as "Initially, i.e., at t = 0, the system is a condensate and therefore superfluid deformation is zero."
3- In Fig.3 when referring to the plots of the correlation function for different \tau it is said in the caption that "while in the right panels we have 103τ0 = τ1 = τ3/3 = 1." Shouldn't this be the top panels?
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