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On the difference between thermalization in open and isolated quantum systems: a case study
by Archak Purkayastha, Giacomo Guarnieri, Janet Anders, Marco Merkli
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Archak Purkayastha |
| Submission information | |
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| Preprint Link: | scipost_202507_00062v1 (pdf) |
| Date submitted: | July 23, 2025, 10:27 a.m. |
| Submitted by: | Archak Purkayastha |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Thermalization of isolated and open quantum systems has been studied extensively. However, being the subject of investigation by different scientific communities and being analysed using different mathematical tools, the connection between the isolated (IQS) and open (OQS) approaches to thermalization has remained opaque. Here we demonstrate that the fundamental difference between the two paradigms is the order in which the long time and the thermodynamic limits are taken. This difference implies that they describe physics on widely different time and length scales. Our analysis is carried out numerically for the case of a double quantum dot (DQD) coupled to a fermionic lead. We show how both OQS and IQS thermalization can be explored in this model on equal footing, allowing a fair comparison between the two. We find that while the quadratically coupled (free) DQD experiences no isolated thermalization, it of course does experience open thermalization. For the non-linearly interacting DQD coupled to a fermionic lead, the many-body interaction in the DQD breaks the integrability of the whole system. We find that this system shows strong evidence of both OQS and IQS thermalization in the same dynamics, but at widely different time scales, consistent with reversing the order of the long time and the thermodynamic limits.
Author indications on fulfilling journal expectations
- 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
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We are grateful to you and the two Referees for their careful reading and their comments. We have majorly revised the paper, adding more plots, clarifying various aspects, and restructuring the text. With these edits, we are confident that the Referees will now find the manuscript suitable for SciPost Physics.
Response to specific comments of the Referees and the list of main changes are given at the specified places in SciPost.
Thank you for handling our manuscript.
The authors:
Archak Purkayastha
Giacomo Guarnieri
Janet Anders
Marco Merkli
List of changes
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Based on comments by Prof. Joachen Gemmer (JG), one of the Referees, we have added a new figure, the Fig.2 of the revised manuscript, and a Section, Sec. 3.2, discussing the figure. This figure and the section clearly highlight the crossover from thermalization in open quantum system (OQS) sense to thermalization in isolated quantum system (IQS) sense, in the same dynamics, which is our main result. We have correspondingly changed our “Summary of results” in Sec. 1, along with the table in Fig 1. Small changes are made throughout the manuscript to make it coherent with this new section.
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Based on comments by JG, we have now removed the emphasis on partially integrable systems, moving most of the discussion to a new Appendix. In the main text, we only discuss this shortly in Sec 3.4.1, titled “Integrability breaking in the interacting DQD”. Nevertheless, based on comments by the second Referee (anonymous), in the Appendix we have now provided more data for integrability breaking, showing system-size scaling, and plot of mean ratio of adjacent gaps.
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Based on comments from the second Referee, we have modified statements about chemical potential in our setting, removing previously made ambiguous statements. We have added Eq. (33) and a few sentences below it to precisely state what we mean and why that is important for a fair comparison between thermalization in open and isolated quantum systems.
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Based on a comment by JG, we have now mentioned in Sec 4, “Summary and Outlook”, that our numerical results are for a case where the system (double-quantum-dot) and the bath (fermionic lead) have different parameters. But, our method can also be used to make a fair comparison between thermalization in open and isolated approaches, even in cases where there is no distinction between system and bath parameters, which is an interesting avenue for future work.
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Various typos, many pointed out by the second Referee, have been corrected.