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Introduction to the theory of open quantum systems

by Piotr Szańkowski

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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:
  • Quantum Physics
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

I would like to thank the Reviewer for careful evaluation of this, admittedly voluminous, manuscript. Many of the comments and critiques raised by the Reviewer have inspired me to reconsider some of the choices I have made composing this script. The one with the most impact was the criticism of the approach to the presentation of the assignments and their solutions: as the Reviewer has correctly pointed out, some of the solutions take too much space and because of that they quite severely disrupt the natural flow the text. To remedy this issue I have decided to move all of the solutions to the dedicated appendix at the end of the manuscript—this is the largest change I have made but the resultant improvements cannot be overstated.

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 #1 by Anonymous (Referee 1) on 2023-1-14 (Invited Report)

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.

  • validity: top
  • significance: high
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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