SciPost Submission Page
Non-adiabatic linear response in open quantum systems
by Xiaotian Nie, Wei Zheng
Submission summary
| Authors (as registered SciPost users): | Xiaotian Nie |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202509_00021v1 (pdf) |
| Date accepted: | Dec. 2, 2025 |
| Date submitted: | Sept. 9, 2025, 12:37 p.m. |
| Submitted by: | Xiaotian Nie |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
The author(s) disclose that the following generative AI tools have been used in the preparation of this submission:
ChatGPT (GPT-4o) was used solely for language polishing of the Abstract and Introduction (grammar, clarity, and tone, not for generating text from scratch). All text was reviewed by the authors, who take full responsibility for the content.
Abstract
Adiabatic theorem and non-adiabatic corrections have been widely applied in modern quantum technology. Recently, non-adiabatic linear response theory has been developed to probe the many-body correlations in closed systems. In this work, we generalize the non-adiabatic linear response theory to open quantum many-body systems. We show that, similar to the closed case, the first-order deviation from the instantaneous steady state is memoryless—it depends only on the final parameters and not on the initial state or ramping path. When ramping the Hamiltonian, the linear response of observables is governed by the derivative of the retarded Green's function, as in closed systems. In contrast, ramping the dissipation gives rise to a different response, characterized by a high-order correlation function defined in the steady state. Our results offer a compact and physically transparent formulation of non-adiabatic response in open systems, and demonstrate that ramping dynamics can serve as a versatile tool for probing many-body correlations beyond equilibrium.
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
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Reports on this Submission
Report
1. What are the minimal Lindbladian spectral conditions required for the linear approximation to remain controlled during the ramp?
2. In the numerical tests, how close do you approach the EP?
3. Does the proposed response formula handle cases with multiple steady states?
4. Add a discussion of physical observables most sensitive to EP crossings and how experimental noise/dissipation might affect the continuity claims.
5. Define all abbreviations and symbols at first use (e.g., EP, PXP).
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report
Overall, I believe the work is of high quality. It presents a clear and versatile framework for probing many-body correlations in open systems through controlled parameter ramps. The manuscript is well written and accessible to a broad audience, with direct experimental relevance. Therefore, I am pleased to recommend its publication in SciPost Physics.
Here are some minor questions:
The authors focus on the response of observables. How about entropic quantities? For example, does a first-order contribution appear in the system’s purity?
What happens if the ramp crosses a phase transition, such as spontaneous weak symmetry breaking (SWSSB)?
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Author: Xiaotian Nie on 2025-11-25 [id 6070]
(in reply to Report 1 on 2025-11-13)The comment author discloses that the following generative AI tools have been used in the preparation of this comment:
We use ChatGPT 5.1 (OpenAI) for grammar correction and tone polishing.
Response to Referee 1
We thank Referee 1 for their very positive and encouraging report, for recommending publication in SciPost Physics, and for the careful reading of our manuscript. We are grateful in particular for the two insightful questions, which help clarify the generality and limitations of our results. Below we address these points in order.
The referee writes:
The authors focus on the response of observables. How about entropic quantities? For example, does a first-order contribution appear in the system’s purity?
Our response:
We thank Referee 1 for raising this insightful question. Let us discuss the purity, which is directly related to the Rényi-2 entropy. Starting from Eq. (23) of the manuscript, we write the final state after the ramp as
Expanding the purity to first order in $v$, we obtain
The referee writes:
What happens if the ramp crosses a phase transition, such as spontaneous weak symmetry breaking (SWSSB)?
Our response:
We thank Referee 1 for this fundamental question. Our derivation explicitly relies on the condition stated in Footnote [57] of the manuscript: the ramp velocity $v$ must be much smaller than the Lindbladian gap around the steady state along the ramp protocol. This separation of scales is crucial for controlling the non-adiabatic corrections and for showing that the leading-order response depends only on the final parameter value.
At a phase transition, such as one involving spontaneous weak symmetry breaking, the Lindbladian gap closes in the thermodynamic limit. In this regime, the basic assumption underlying our expansion breaks down, and one expects qualitatively different, non-perturbative behavior. Therefore, our linear-response formula in its present form is not applicable to ramps that cross such phase transitions. A proper treatment would require a separate analysis that explicitly takes into account the critical closing of the gap, which lies beyond the scope of the current work.
Author: Xiaotian Nie on 2025-11-25 [id 6071]
(in reply to Report 2 on 2025-11-17)The comment author discloses that the following generative AI tools have been used in the preparation of this comment:
We use ChatGPT 5.1 (OpenAI) for grammar correction and tone polishing.
Response to Referee 2
We thank Referee 2 for their careful reading of our manuscript and for the very positive assessment, including the recommendation for publication in SciPost Physics. We are also grateful for the clear questions and helpful suggestions. Below we address these points in order.
The referee writes:
Our response:
We thank Referee 2 for this fundamental question. In our paper, we provide a necessary condition in Footnote [57], which gives an upper bound on the ramp velocity in terms of the spectral gap between the zero eigenvalue (corresponding to the steady state) and the rest of the spectrum. However, we are not able to provide a simple sufficient condition that guarantees that the linear-response regime always holds. As we emphasize in Appendix B, although we cannot specify the precise boundary of validity, once a linear regime is identified in the slow-ramping limit, the first-order result provides the correct slope.
The referee writes:
Our response:
We thank Referee 2 for this detailed question. In Appendix A, we discuss numerical ramps that cross, end at, or approach an exceptional point (EP). Ramp 2 in Fig. 4 corresponds to a protocol whose final parameter is tuned exactly to an EP, while Ramp 3 ends very close to the EP (with a deviation of order (0.01) in units of the relevant energy scale). In both cases, the results are consistent with our non-adiabatic linear-response prediction.
The referee writes:
Our response:
We thank Referee 2 for this important question. As mentioned in the Introduction, our analysis is explicitly aimed at the case of a unique steady state, which is precisely what allows us to arrive at a simple and universal formula for the first-order response. In the presence of multiple steady states, our derivation does not apply: the final state is then in general not memoryless, because information about the ramping history can be encoded in the steady-state subspace. This regime has been studied in detail in Ref. [31] (Victor V. Albert, Barry Bradlyn, Martin Fraas, and Liang Jiang, Phys. Rev. X 6, 041031), where multiple steady states lead to rich geometric phenomena such as holonomy. A full treatment of this scenario lies beyond the scope of our work.
The referee writes:
Our response:
We thank Referee 2 for this comment. We have added discussion in the main text like, “Since there is a no-go theorem that EP will not happen on the steady state of a Lindbladian and our paper is talking about physics near the steady state [PHYSICAL REVIEW A 98, 042118 (2018)], so the physics is not sensitive to EP” and “Experimental noise may shift the exact position of EPs but the continuity claims will still hold”.
The referee writes:
Our response:
We thank Referee 2 for this useful reminder. We have gone through the manuscript to check all abbreviations and symbols and have ensured that they are now defined at their first occurrence (including EP, PXP, and other acronyms).
Anonymous on 2025-11-26 [id 6074]
(in reply to Xiaotian Nie on 2025-11-25 [id 6071])I think the authors have addressed my questions in a scientific way. Now I would like to recommend the publication.