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Variational truncated Wigner approximation for weakly interacting Bose fields: Dynamics of coupled condensates
by Christopher D. Mink, Axel Pelster, Jens Benary, Herwig Ott, Michael Fleischhauer
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Christopher Mink |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2106.05354v2 (pdf) |
| Date accepted: | 2021-12-08 |
| Date submitted: | 2021-11-29 12:55 |
| Submitted by: | Mink, Christopher |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Experimental, Computational |
Abstract
The truncated Wigner approximation is an established approach that describes the dynamics of weakly interacting Bose gases beyond the mean-field level. Although it allows a quantum field to be expressed by a stochastic c-number field, the simulation of the time evolution is still very demanding for most applications. Here, we develop a numerically inexpensive scheme by approximating the c-number field with a variational ansatz. The dynamics of the ansatz function is described by a tractable set of coupled ordinary stochastic differential equations for the respective variational parameters. We investigate the non-equilibrium dynamics of a three-dimensional Bose gas in a one-dimensional optical lattice with a transverse isotropic harmonic confinement. The accuracy and computational inexpensiveness of our method are demonstrated by comparing its predictions to experimental data.
Author comments upon resubmission
List of changes
-The first mention of the residual (non-macroscopic) field has been moved to the introduction
-the caption of figure 1 now includes all relevant parameters.
-The change of variables in the functional Fokker-Planck equation and subsequent neglection of the residual field on p. 8-9 (most importantly eq. 22) have been overhauled to make the decoupling of the fields $\psi_0$ and $\psi_1$ more clear.
-a newly added paragraph at the end of section 5.1 motivates the experimental data and stresses that it is - in fact - newly obtained data.
-Section 5.2.2 has been reworked to explain why the overestimation of the number fluctuations is a generic artifact of few-mode approximations such as our variational ansatz.
-The new section 5.2.3 introduces local incoherent gains and losses to the optical lattice. We derive the positive-semidefinite diffusion matrix within the variational scheme and derive a set of stochastic differential equations. The incoherent contribution to the dynamics for a coupled and a single trap is shown in the new figure 6.
Published as SciPost Phys. 12, 051 (2022)
Reports on this Submission
Report #2 by Anonymous (Referee 4) on 2021-12-1 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2106.05354v2, delivered 2021-12-01, doi: 10.21468/SciPost.Report.3981
Report
In the revised version of the paper and in their reply, the authors address most of the point that I raised in my previous report. In particular, a whole new section demonstrating the simulation of a dissipative system has been added, which nicely illustrates the generality of the described method. Overall, I am satisfied with the reply by the authors and the changes in revisions in the manuscript. Since the method seems to be very powerful and applicable for a broad range of problems, I recommend to publish the current version of the paper in SciPost Physics.