SciPost Submission Page
Scaling of free cumulants in closed system-bath setups
by Merlin Füllgraf, Jochen Gemmer, Jiaozi Wang
Submission summary
| Authors (as registered SciPost users): | Merlin Füllgraf |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202512_00012v1 (pdf) |
| Date submitted: | Dec. 4, 2025, 10:24 a.m. |
| Submitted by: | Merlin Füllgraf |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The Eigenstate Thermalization Hypothesis (ETH) has been established as a cornerstone for understanding thermalization in quantum many-body systems. Recently, there has been growing interest in the full ETH, which extends the framework of the conventional ETH and postulates a smooth function to describe the multi-point correlations among matrix elements. Within this framework, free cumulants play a central role, and most previous studies have primarily focused on closed systems. In this paper, we extend the analysis to a system–bath setup, considering both an idealized case with a random- matrix bath and a more realistic scenario where the bath is modeled as a defect Ising chain. In both cases, we uncover a universal scaling of microcanonical free cumulants of system observables with respect to the interaction strength. Furthermore we estab- lish a connection between this scaling behavior and the thermalization dynamics of the thermal free cumulants of corresponding observables.
Current status:
Reports on this Submission
Strengths
- The paper addresses an interesting problem by extending ETH-related concepts to a setting involving open quantum systems, in the framework of free probability.
- The analysis is focused and well-structured, and the presentation is clear and concise, making the results accessible to readers already familiar with the topic.
- The authors avoid unnecessary technical detours and present the essential ingredients needed to support their findings.
Weaknesses
- The paper has a very short discussion which lacks of a broader picture about limitations, validity and physical interpretation of the presented results.
Report
General remarks: - The paper addresses a timely and relevant topic at the intersection of ETH and open quantum systems. - The paper presents well-executed results: the numerical analysis is carefully performed. This advances the current knowledge and understanding of the field. - The analysis in terms of free cumulants is interesting and original. - The paper is written in a clear way, free of unnecessary jargon, ambiguities and misrepresentations, at the same time presenting all the details for reproducing derivations and following the discussion (for qualified experts).
Given so, most of this Journal’s acceptance criteria are met. However, my general impression is that the paper lacks of a broader picture: the overall impact is somewhat limited by the brevity of the physical discussion in the conclusion. Even if the summary is clear with objective statements, at present, the discussion section is brief and does not fully explore the physical implications, the validity and the limitations of the reported scaling laws. There are also no concrete perspectives for future work.
Therefore, in my opinion SciPost Core is the right Journal and the paper could be accepted after minor revision; some more detailed changes are suggested below.
Requested changes
As said above, the major suggestions for changes regard the discussion and conclusions section. Here some questions in this direction: 1. How do the authors compare their results with related works in closed quantum systems? In particular, are there explanations on why the scalings are different and there are no differences in the energy scale for different orders of the correlations? Indeed the conceptual framework relies on applying ETH to the total (system + bath) Hamiltonian and studying local observables. This approach is standard in the ETH literature, and the manuscript would benefit from a clearer discussion of which aspects are specific to the open system setting, and which are expected to hold more generally for local observables in large closed chaotic systems. 2. Why the observed universal scaling of higher-order free cumulants emerges, and how should it be interpreted physically? 3. Which is the physical meaning for the independence of this energy scale on the system size of the bath? 4. Which are concrete perspectives for future works?
Other questions: 5. The authors say that in chaotic systems the free cumulants usually thermalize after a characteristic time scale $T^n_{eq}$ that they call thermalization time and define as the inverse of the defined energy scale. Which is the physical meaning of this timescale, and how is it related to the thermalization of the system? Is this comparable with freeness timescales defined for closed quantum systems? 6. Why do the authors study the specific thermal free cumulants which appear in the 2n-OTOC and not others? 7. It would be important to clarify the role of operator choice: in the appendix results for a different observable are shown, but again a more careful discussion on the physical meaning is missing: why the results are different from the ones for the observable in the main text?
Minor comments: 8. The authors say “It should be noted that, although $\kappa_n^{ETH}$ and $C_n^{\beta}$ appear closely related, there is generally no one-to-one correspondence between them” What do they mean with this statement? And in which point of the paper is this relevant? 9. Why different free cumulants have similar magnitude? I would expect that the higher the order the smaller is the cumulant in absolute value…
Recommendation
Ask for minor revision