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Introduction to the theory of open quantum systems
by Piotr Szańkowski
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Piotr Szankowski |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2209.10928v4 (pdf) |
| Date accepted: | 2023-02-13 |
| Date submitted: | 2022-12-29 13:37 |
| Submitted by: | Szankowski, Piotr |
| Submitted to: | SciPost Physics Lecture Notes |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
This manuscript is an edited and refined version of the lecture script for a one-semester graduate course given originally at the PhD school in the Institute of Physics of Polish Academy of Sciences in the Spring/Summer semester of 2022. The course expects from the student only a basic knowledge on graduate-level quantum mechanics. The script itself is largely self-contained and could be used as a textbook on the topic of open quantum systems. The program of this course is based on a novel approach to the description of the open system dynamics: It is showed how the environmental degrees of freedom coupled to the system can be represented by a multi-component quasi-stochastic process. Using this representation one constructs the super-quasi-cumulant (or super-qumulant) expansion for the system's dynamical map -- a parametrization that naturally lends itself for the development of a robust and practical perturbation theory. Thus, even an experienced researcher might find this manuscript of some interest.
Author comments upon resubmission
List of changes
- The solutions to assignments has been moved to dedicated appendix; the system of hyperlinks has been setup to ease the navigation in the pdf format of the manuscript.
- The abstract has been modified to include more explicit information how the approach of this script is novel.
- In Sec.2.5, the discussion on the decomposition of density matrix into a mixture of projectors has been augmented to make it more clear.
- In Sec.2.6.1, the explanation how density matrix is a member of a vector space has be rewritten to make it more clear.
- In Sec.3.1.2, the explanation has been added why moments of stochastic process are completely symmetric functions of their time arguments.
- The definition of the coherence function W(t) in Sec.3.4.3 has been changed make it consistent with the conventional definition of the characteristic functional (i.e., i was replaced with -i).
- In Sec.3.2 a comment has been added to immediately point out that, in general, stochastic maps are no longer unitary.
- In Sec.3.6.3 an additional comment has been added before Eq.(154) to make it cleared that the equation is an implicit definition of super-cumulants \mathcal{C}^{(k)}.
- Various typos has been fixed thought the manuscript.
Published as SciPost Phys. Lect. Notes 68 (2023)
Reports on this Submission
Report
Having read the reply of the author, I do believe that the manuscript has been substantially improved compared to the first version. In particular, I do like the decision to collect the solutions in an appendix. All errors have been fixed. The author did disagree with some of my suggestions. In each case, the reasons have been explained in details and I do understand the different point of view.
The subject "open systems" is of current ongoing interest. The presentation of the material is original, correct, and may serve as a reference for students and researchers entering the field. As a result, I do believe that the manuscript should be published as a Scipost lecture note.