SciPost Submission Page
Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies
by Patrik Penc, Fabian H. L. Essler
Submission summary
| Authors (as registered SciPost users): | Patrik Penc |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202509_00037v1 (pdf) |
| Date submitted: | Sept. 19, 2025, 5:20 p.m. |
| Submitted by: | Patrik Penc |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We consider a class of spinless-fermion Lindblad equations that exhibit decoupled BBGKY hier- archies. In the cases where particle number is conserved, their late time behaviour is characterized by diffusive dynamics, leading to an infinite temperature steady state. Some of these models are Yang-Baxter integrable, others are not. The simple structure of the BBGKY hierarchy makes it pos- sible to map the dynamics of Heisenberg-picture operators on few-body imaginary-time Schr¨odinger equations with non-Hermitian Hamiltonians. We use this formulation to obtain exact hydrody- namic projections of operators quadratic in fermions, and to determine linear response functions in Lindbladian non-equilibrium dynamics.
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:
Reports on this Submission
Strengths
1- Very. through and detailed 2- Authors go beyond hydrodynamic projection and study linear response
Weaknesses
Report
I find this paper insightful and well written. It will certainly contribute to the literature on Lindbladian hydrodynamics. I strongly recommend publication in SciPost Physics.
Requested changes
I only would like to ask the authors to consider the following suggested optional changes and questions:
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In the introduction (p.2, lhs column): "The presence of a conservation law then implies that certain observables will exhibit hydrodynamic power-law tails at late times, which are related to the existence of diffusive eigenmodes of the Lindbladian" - Is this obvious? Maybe one would need to have add certain caveats?
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"In contrast to unitary quench dynamics [50] integrability in LEs does not imply the existence of conservation laws. This is immediately obvious from the fact that many integrable LEs have unique steady states that are completely mixed, i.e. correspond to infinite temperature density matrices." - one should cite the relevant papers e.g. in [21-31]. For instance, in [26] the unique steady state is all down (up to certain boundary bound states and the formation of domain walls in the thermodynamic limit).
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p. 7, lhs column: In Fig 3 why are there (two) gaps? Is there a physical reason? In fact Fig. 3 does not seem to be referenced in the text.
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p. 10, rhs column: "B. Spatially local operators" - why spatially local? It seems to me to be more like "Spatially local without well defined momentum"? Maybe renaming this would make things clearer.
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In Sec. VI dealing with quadratic operators in model V, it would be possibly interesting to see how the operators exponentially decay? Or is it not interesting?
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p. 17, lhs column: "It would be interesting to pursue a more precise description by treating the ”particles” as interacting and following the logic of Ref. [64]." - This claim I find interesting and would ask that the authors elaborate slightly.
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Is the relevance of momentum $\pi$ for the eigenvalues closing to 0 related to a possible $\eta$-pairing operator (at momentum $\pi$) that appears from "spin up and down" vectorized fermions? Can the authors comment?
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)