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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
Submission summary
| Authors (as registered SciPost users): | Archak Purkayastha |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2409.11932v3 (pdf) |
| Date accepted: | Oct. 30, 2025 |
| Date submitted: | Oct. 21, 2025, 11:46 a.m. |
| Submitted by: | Archak Purkayastha |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| 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, also known as the interacting resonant level model in quantum impurity physics. 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
List of changes
b. Equation (34) has been added to explicitly state how the thermal expectation values are calculated.
c. Following suggestion from the editor, we have added a few sentences at the end of section 2.2, as well as after equation (36), to explicitly state that in numerical simulation, OQS thermalization effectively occurs even with finite bath sizes.
d. Following suggestion from the editor, we have now added a sentence Sec 3.4.2 (fourth line),
“Note that, all the physics discussed here are for timescales much less than the timescale of Poincare recurrences [84,85], which is expected to scale super-exponentially with $L_B$, and is impossible to reach in any practical numerical or experimental investigation for chain lengths of our interest.”
References [84,85] are newly added citation for recent works on Poincare recurrences in quantum many-body systems.
e. In response to comment from the editor, we have changed the following line:
"To our knowledge, such convergence has not numerically been shown for any system with many-body interactions."
to
"To our knowledge, convergence to the mean force Gibbs state, $\hat{\rho}_\MGS$, has also not been numerically shown for any system with many-body interactions (i.e, non-Gaussian systems)."
Published as SciPost Phys. 19, 136 (2025)