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Stochastic Representation of the Quantum Quartic Oscillator
by Gennaro Tucci, Stefano De Nicola, Sascha Wald, Andrea Gambassi
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Submission summary
| Authors (as registered SciPost users): | Gennaro Tucci |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2211.01923v1 (pdf) |
| Date accepted: | 2023-02-09 |
| Date submitted: | 2022-11-28 10:49 |
| Submitted by: | Tucci, Gennaro |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic processes has been proposed. Here we provide first steps towards the extension of this stochastic approach to bosonic systems by considering the one-dimensional quantum quartic oscillator. We show how to exactly parameterize the time evolution of this prototypical model via the dynamics of a set of classical variables. We interpret these variables as stochastic processes, which allows us to propose a novel way to numerically simulate the time evolution of the system. We benchmark our findings by considering analytically solvable limits and providing alternative derivations of known results.
Published as SciPost Phys. Core 6, 029 (2023)
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2023-1-6 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2211.01923v1, delivered 2023-01-06, doi: 10.21468/SciPost.Report.6466
Report
This is a very detailed and comprehensive paper (for the brave reader)
on the time evolution of the quartic harmonic oscillator studied in terms of
classical stochastic variables.
A first section introduces the stochastic representation via the introduction
of a ''disentanglement transformation" allowing for the definition of stochastic variables. The dynamics of a Gaussian wave packet is then analyzed and exactly solved limits are considered.
The central part of the paper is probably the stochastic interpretation of section IV and then a perturbative expansion of the time evolution operator is proposed.
According to the authors, the method allow for a ''simple'' and intuitive numerical approach, in spite of possible divergences due to the non-unitarity of the effective evolution operator.
The paper is very well written, with many details of calculations, and very likely useful for readers in the community of open quantum systems. This is nevertheless hard to follow for non experts, but this is due to the technical difficulty of the technique itself.
I recommend publication in the present form. In my opinion, it meets criteria for SciPost Physics but since I am not an expert in the field of open quantum systems, I cannot decide whether it is appropriate for SciPost Physics Core.