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Thermalization of the Quantum Planar Rotor with external potential
by Birthe Schrinski, Yoon Jun Chan, Björn Schrinski
Submission summary
| Authors (as registered SciPost users): | Björn Schrinski |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2207.04810v2 (pdf) |
| Date submitted: | 2024-09-20 13:03 |
| Submitted by: | Schrinski, Björn |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study decoherence, diffusion, friction, and how they thermalize a planar rotor in the presence of an external potential. Representing the quantum master equation in terms of auxiliary Wigner functions in periodic phase space not only illustrates the thermalization process in a concise way, but also allows for an efficient numerical evaluation of the open quantum dynamics and its approximate analytical description. In particular, we analytically and numerically verify the existence of a steady state that, in the high-temperature regime, closely approximates a Gibbs state. We also derive the proper classical limit of the planar rotor time evolution and present exemplary numerical studies to verify our results.
Current status:
Reports on this Submission
Strengths
1 important problem addressed
2 novel & timely
3 clearly written
Weaknesses
1
Report
The manuscript by Schrinski et al. studies the thermalization dynamics of a planar quantum rotor in the presence of an external potential. The authors present a Wigner-Weyl formalism suitable for periodic degrees of freedom, which is then used to numerically show that the system relaxes into a steady state. These numerical calculations are supplemented by analytical results, discussing how the corresponding steady state approaches the Gibbs state for high temperatures.
The manuscript addresses the important open problem of how non-linear but periodic degrees of freedom thermalize. The manuscript is novel and timely, and well written. I thus recommend publication of the work in SciPost Physics Core after the authors considered the following minor comments on the presentation of their work.
1. Though the main focus on the work is on thermalization of planar rotors, the corresponding dissipator is not introduced before Eq. (16) on page 4. I do acknowledge that the Wigner Weyl formalism for the planar rotor is non-trivial and central to this work, but it has been published before. I am thus wondering if Sec. II (apart from a few definitions) could be moved to the Appendix to streamline the manuscript on what is novel.
2. At the beginning of Sec. V the authors introduce the dimensionless time, temperature, and Planck constant. While this might be suitable for the numerical implementation, the readability of the subsequent discussion would profit from explicitly writing out the expressions. For instance in and around Eq. (3), or in Figs. 3 and 4.
3. It would be great if the authors could briefly comment in the conclusion on how their methods could be extended to 3D rotors and what challenges they expect there.
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Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)