SciPost Submission Page
A perturbation theory for multi-time correlation functions in open quantum systems
by Piotr Szańkowski
Submission summary
| Authors (as registered SciPost users): | Piotr Szańkowski |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2502.19137v3 (pdf) |
| Date accepted: | Aug. 14, 2025 |
| Date submitted: | Aug. 5, 2025, 10:18 a.m. |
| Submitted by: | Piotr Szańkowski |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
Dynamical maps are the principal subject of the open system theory. Formally, the dynamical map of a given open quantum system is a density matrix transformation that takes any initial state and sends it to the state at a later time. Physically, it encapsulates the system's evolution due to coupling with its environment. Hence, the theory provides a flexible and accurate framework for computing expectation values of open system observables. However, expectation values---or more generally, single-time correlation functions---capture only the simplest aspects of a quantum system's dynamics. A complete characterization of the dynamics requires access to multi-time correlation functions as well: phenomena like detailed balance, linear and non-linear response, non-equilibrium transport in general, or even sequential measurements of system observables are all described in terms of multi-time correlations. For closed systems, such correlations are well-defined, even though knowledge of the system's state alone is insufficient to determine them fully. In contrast, the standard dynamical map formalism for open systems does not account for multi-time correlations, as it is fundamentally limited to describing state evolution. Here, we extend the scope of open quantum system theory by developing a systematic perturbation theory for computing multi-time correlation functions.
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
Aside the changes to the manuscript asked for by the Reviewers, I have corrected certain issues with Sec.1 (Introduction). First, some formulas in the original version were given in a simplified form that assumed in advance quantum regression formula; I have reverted them to their general, non-simplified form, see Eqs. (1.6), (1.7), (1.8), (1.10), (1.11), (1.12), and (1.16).
Second, I have made a mistake where I wrote that the Davies map, Eq.(1.6), will thermalize *any* initial state of the qubit $q$; this is untrue. In reality, $\hat\sigma_x$ is an eigenvector of the generator $\mathcal L^q$ corresponding to zero eigenvalue. Therefore, the dynamical map $\exp(t\mathcal L^q)$ will thermalize the initial state provided that $\operatorname{tr}(\hat\sigma_x\hat\rho_0^q) = 0$. In response, I have elected to set the initial condition in the example to a specific pure state $\hat\rho_0^q = |{1_z}\rangle\langle{1_z}|$. This mistake–and the subsequent fix–did not affected in any meaningful way the validity of the example.
List of changes
- Added a sentence to the abstract:
A complete characterization of the dynamics requires access to multi-time correlation functions as well: phenomena like detailed balance, linear and non-linear response, non-equilibrium transport in general, or even sequential measurements of system observables are all described in terms of multi-time correlations.
-
In Sec.1, several equations have been modified, see Eqs. (1.6), (1.7), (1.8), (1.10), (1.11), (1.12), and (1.16). For explanation, see the Author resubmission comment.
-
Added the paper outline at the end of Sec.1.
-
The notation for multi-time correlations has been slightly modified: $\langle A^+(t_2)B^-(t_1)\rangle_\rho \to \langle A(t_2^+)B(t_1^-)\rangle$.
-
The first paragraph of Sec.2.2: added a passage referring to process tensor formalism.
-
Changed the name of function $\Delta$: discrete-time comb -> discrete-time filter function.
-
Sec.3, Eq.(3.5): added a footnote explaining the difference between Markovianity and finite range of cumulants.
-
Sec.5, Eq.(5.12): added the clarification of the used notation for super-operator identity.
-
Sec.6, Eq.(6.4): fixed a slight error.
-
Sec.8: added a three paragraphs at the end of the section.
Published as SciPost Phys. 19, 066 (2025)
Reports on this Submission
Report
In conclusion, I am happy to recommend the manuscript for publication in Sci-Post in its current form.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)