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Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation
by Berislav Buca, Cameron Booker, Dieter Jaksch
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Cameron Booker · Berislav Buca · Dieter Jaksch |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2103.01808v5 (pdf) |
| Date accepted: | 2022-02-16 |
| Date submitted: | 2022-01-12 16:53 |
| Submitted by: | Buca, Berislav |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessary and sufficient algebraic criteria for persistently oscillating eigenmodes (limit cycles) of time-independent quantum master equations. We show these eigenmodes must be quantum coherent and give an exact analytical solution for all such dynamics in terms of a dynamical symmetry algebra. Using our theory, we study both stable synchronization and metastable/transient synchronization. We use our theory to fully characterise spontaneous synchronization of autonomous systems. Moreover, we give compact algebraic criteria that may be used to prove absence of synchronization. We demonstrate synchronization in several systems relevant for various fermionic cold atom experiments.
Author comments upon resubmission
We would like to thank you and the referees again for carefully assessing our responses and the revised manuscript, and for recommending publication in SciPost Physics subject to minor amendments. We have now made further revisions to our work according to the referees' suggestions, and we have attached a list of changes together with responses to each of the referees' individual comments.
We hope they find our minor amendments acceptable.
Yours sincerely,
Berislav Buca, Cameron Booker and Dieter Jaksch
List of changes
1. In Sec. 2.1 we have explicitly pointed out to the reader that our definitions are stricter that the Pearson correlation indicator.
2. We have added a new subsection 3.4 to discuss in more detail adaptations of our results to weaker notions of synchronization.
3. A footnote has been added to Theorem 4 defining the commutant of a set.
4. References have been added to appendix K as suggested by referee 1.
Published as SciPost Phys. 12, 097 (2022)