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Quantum pure noise-induced transitions: A truly nonclassical limit cycle sensitive to number parity
by A. Chia, W. -K. Mok, C. Noh, L. C. Kwek
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Dariel Mok · Changsuk Noh |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2204.03267v6 (pdf) |
| Date accepted: | 2023-07-24 |
| Date submitted: | 2023-06-12 04:14 |
| Submitted by: | Noh, Changsuk |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| 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 without a classical limit. 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 multiplicative environmental noise is included, the system is seen to transition to a limit-cycle state. The noise-induced quantum limit cycle also exhibits other genuinely 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
We would like to thank the editor for handling our manuscript and the referees for their comments. Please find below our replies to the comments.
Anonymous report 1: 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).
Our reply: We thank the referee for his/her report. It is unclear to us why the referee is emphasizing the lack of a classical limit in our quantum model as this is in fact a highly novel feature. We have now incorporated the referee’s comments in the new edition of our paper. There are now three locations in the manuscript where we state that our quantum model has no classical limit:
We would like to point out that, on the previous version of our paper, we had already explained explicitly the absence of a classical limit as defined by the system-size expansion where the classical model was first introduced (see the first paragraph on the right hand column on page 5).
We have now stated the absence of a classical limit in the paper abstract by adding a sentence "without a classical limit".
Finally, the lack of a classical limit is brought up again in the conclusion of our paper (the last paragraph), where we have also reminded the reader why our quantum-classical comparison is worthwhile even though the quantum system has no classical limit.
On a separate point, we have voluntarily included a new reference as part of our literature review (Ref. [87] in the new bibliography).
Anonymous report 2 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.
Our reply: We thank the reviewer for taking the time to examine our previous reply. We have nothing to add except for including Ref. [87] in our literature review (the results of which are actually classical, see red text on page 2).
List of changes
1. Added a sentence "...without a classical limit" in the abstract.
2. Added a sentence "The effect of multiplicative noise on a bistable..." on p3 to add a new reference [87].
3. Added a paragraph to the conclusion.
Published as SciPost Phys. 15, 121 (2023)