SciPost Submission Page
Adaptive Numerical Solution of Kadanoff-Baym Equations
by Francisco Meirinhos, Michael Kajan, Johann Kroha, Tim Bode
This Submission thread is now published as
|Authors (as registered SciPost users):||Tim Bode · Johann Kroha · Francisco Meirinhos|
|Preprint Link:||https://arxiv.org/abs/2110.04793v2 (pdf)|
|Date submitted:||2022-04-05 08:32|
|Submitted by:||Meirinhos, Francisco|
|Submitted to:||SciPost Physics|
A time-stepping scheme with adaptivity in both the step size and the integration order is presented in the context of non-equilibrium dynamics described via Kadanoff-Baym equations. The accuracy and effectiveness of the algorithm are analysed by obtaining numerical solutions of exactly solvable models. We find a significant reduction in the number of time-steps compared to fixed-step methods. Due to the at least quadratic scaling of Kadanoff-Baym equations, reducing the amount of steps can dramatically increase the accessible integration time, opening the door for the study of long-time dynamics in interacting systems. A selection of illustrative examples is provided, among them interacting and open quantum systems as well as classical stochastic processes. An open-source implementation of our algorithm in the scientific-computing language Julia is made available.
Published as SciPost Phys. Core 5, 030 (2022)
Author comments upon resubmission
List of changes
See "Author comments".
Submission & Refereeing History
You are currently on this page
- Report 3 submitted on 2022-04-19 16:18 by Anonymous
- Report 2 submitted on 2022-04-06 23:23 by Anonymous
- Report 1 submitted on 2022-04-05 10:20 by Anonymous
Reports on this Submission
I have read the Authors reply to my previous report and the new manuscript. I think the Authors have successfully addressed the points I previously raised and improved their manuscript accordingly. I think this work is now suitable for publication. Given the acceptance criteria of Scipost I think Scipost Physics Core would be more appropriate in this case.
- Cite as: Anonymous, Report on arXiv:2110.04793v2, delivered 2022-04-06, doi: 10.21468/SciPost.Report.4880
The authors have substantially improved the paper in the aspects I had commented on. The code has now been published. However, in its current form it will be of little use to the community because it is not enough documented, in particular the examples are not usable in its current form. It would probably increase the reach of this code, the number of people using it and therefore citing this paper, if the authors improved on the documentation.
The central novelty of this paper is the application of adaptive time stepping to KBE, which is a purely algorithmic/numerical progress and no new results on physical phenomena is presented. Therefore, I would still recommend rather publishing this paper in either Codebase or Core.