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Quantum pure noise-induced transitions: Truly nonclassical limit cycles sensitive to number parity
by A. Chia, W. -K. Mok, C. Noh, L. C. Kwek
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Submission summary
| Authors (as registered SciPost users): | Dariel Mok · Changsuk Noh |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202302_00010v1 (pdf) |
| Date submitted: | 2023-02-07 05:53 |
| Submitted by: | Noh, Changsuk |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
It is universally accepted that noise may bring order to complex nonequilibrium systems. Most strikingly, entirely new states not seen in the noiseless system can be induced purely by including multiplicative noise - an effect known as pure noise-induced transitions. It was first observed in superfluids in the 1980s. Recent results in complex nonequilibrium systems have also shown how new collective states emerge from such pure noise-induced transitions, such as the foraging behavior of insect colonies, and schooling in fish. Here we report such effects of noise in a quantum-mechanical system. We find that multiplicative quantum noise can induce a classically forbidden transition. We use a minimal model of a nonlinearly damped oscillator in a fluctuating environment that is analytically tractable, and whose microscopic physics can be understood. When environmental noise is included, the system is seen to transition to a limit-cycle state. The noise-induced quantum limit cycle exhibits genuine nonclassical traits such as Wigner negativity and number-parity sensitive circulation in phase space. Such quantum limit cycles are also conservative. These properties are in stark contrast to those of a widely used limit cycle in the literature, which is dissipative and loses all Wigner negativity. Our results establish the existence of a pure noise-induced transition that is nonclassical and unique to open quantum systems. They illustrate a fundamental difference between quantum and classical noise.
Author comments upon resubmission
Thank you for handling our manuscript. We also thank the referees for reviewing our work. In order to answer the referee’s comments, we have extensively revised our manuscript, which can be found in arXiv:2204.03267v5. We are also submitting a separate colored text (which includes the supplementary material) to ease the reviewing process. Due to the lengths of our detailed replies, we chose to attach separate files in ‘Reply to the above Report’ section in the server. We hope that the referees find our revised version acceptable for publication in Scipost Physics.
Sincerely,
Andy Chia, Wai Keong Mok, Changsuk Noh, and Leong Chuan Kwek.
List of changes
1. We have modified the title to “Quantum pure noise-induced transitions: Truly nonclassical limit cycles sensitive to number parity”.
2. We have modified a part of the introduction and Section III B.1, and added a footnote 2 to improve the manuscript. The changes are colored green in the submitted colored text.
3. To incorporate referee 1’s suggestions, we have extensively revised the manuscript, including new figures 1 and 2, a new subsections III.B.2 and III.C. The changes are colored red.
4. To incorporate referee 2’s suggestions, we have parts of sections I and II and the supplementary material (p13, below eq (113)). The changes are colored blue.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 4) on 2023-5-30 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202302_00010v1, delivered 2023-05-30, doi: 10.21468/SciPost.Report.7275
Report
The authors have provided a complete answer to the main questions raised in my first report and also significantly changed the manuscript (including illustrations, definitions, and clarifications). The nature of the process and the novelty of the reported limit cycle is now clear. Also, the connection with the classical process has been better justified.
The analysis of this problem is non-trivial and the results are original. The added material does improve the readability of this work making it accessible to a broader audience. Furthermore, the detailed author's answers will be useful.
After considering the author's answer, I better appreciate the novelty of the work. Even if the research community interested in quantum dynamics of complex systems is not the broadest, this pure noise-induced limit cycle is actually a nice quantum effect and in my opinion, this work deserves publication in SciPost.
Report
The authors have revised the paper and addressed most of my concerns. The presentation has substantially improved.
The comparison with the “classical” model remains artificial. The absence of a rigorous classical limit of the model the authors analyse is not clearly emphasized. The corresponding claims in the paper keep on being confusing and shall be revised (see “We find that multiplicative quantum noise can induce a classically forbidden transition” in the abstract, and similar claims across the paper).