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Self-consistent dynamical maps for open quantum systems
by Orazio Scarlatella, Marco Schirò
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Submission summary
| Authors (as registered SciPost users): | Orazio Scarlatella · Marco Schirò |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2107.05553v6 (pdf) |
| Date accepted: | 2024-01-02 |
| Date submitted: | 2023-11-14 10:56 |
| Submitted by: | Scarlatella, Orazio |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In several cases, open quantum systems can be successfully described using master equations relying on Born-Markov approximations, but going beyond these approaches has become often necessary. In this work, we introduce the NCA and NCA-Markov dynamical maps for open quantum systems, which go beyond these master equations replacing the Born approximation with a self-consistent approximation, known as non-crossing approximation (NCA). These maps are formally similar to master equations, but allow to capture non-perturbative effects of the environment at a moderate extra numerical cost. To demonstrate their capabilities, we apply them to the spin-boson model at zero temperature for both a Ohmic and a sub-Ohmic environment, showing that they can both qualitatively capture its strong-coupling behaviour, and be quantitatively correct beyond standard master equations.
List of changes
- We clarified the assumptions and generality of our approach, in response to Report 1, at the beginning of Sec. 2 and at the end of Sec. 2.2.
- We commented and clarified on the non-Markovian effects captured by our approach, below Eqs. (4), (5) and mainly below Eq. (6), in response to Report 2.
- We moved the discussion of the quantum regression theorem (and the steady-state equation) from the Appendix into the main text in Sec. 2.1, to give it more emphasis as suggested by Report 1. We also added a comment on the numerical cost of correlation functions calculations.
- We commented on the feasibility of going beyond NCA in Sec. 2.2, in response to Report 1.
- We added a comment on the computational cost of OCA in Sec. 2.3, in response to Report 2.
- We changed the wording that our approach sees a “very little increase” in numerical cost compared to standard master equation, with “moderate increase”, throughout the manuscript, in response to Report 2.
- We commented in Sec. 2.3 and in the Conclusions about the possibility of compressing our maps with matrix product operators, in response to Report 2.
- We improved the graphics of Fig. 2 in the main text and Fig. 8 in the supplemental in response to Report 2.
- We added 2 panels in Fig.3 showing the process fidelity of the various maps, as compared to the most accurate OCA approximation, as a quantitative benchmark of accuracy, in response to Report 1. We also rephrased Sec. 3.2 accordingly.
- We clarified the statement with references [119,146] in App. E.1 as suggested by Report 2.
Published as SciPost Phys. 16, 026 (2024)
Reports on this Submission
Report
I thank the authors for taking my comments very seriously , and for making the changes/adaptations in the paper to clarify better the points I raised. All my questions are properly discussed and clarified. I think the paper is of high quality and the method for solving non-Markovian quantum system is quite original, so it can be a very valuable contribution to the community. I recommend publication of this paper in SciPost as is.