SciPost Submission Page
Population Dynamics of Schrödinger Cats
by Foster Thompson, Alex Kamenev
Submission summary
| Authors (as registered SciPost users): | Foster Thompson |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2409.07047v2 (pdf) |
| Date submitted: | 2024-09-27 05:43 |
| Submitted by: | Thompson, Foster |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We demonstrate an exact equivalence between classical population dynamics and Lindbladian evolution admitting a dark state and obeying a set of certain local symmetries. We then introduce {\em quantum population dynamics} as models in which this local symmetry condition is relaxed. This allows for non-classical processes in which animals behave like Schr\"odinger's cat and enter superpositions of live and dead states, thus resulting in coherent superpositions of different population numbers. We develop a field theory treatment of quantum population models as a synthesis of Keldysh and third quantization techniques and draw comparisons to the stochastic Doi-Peliti field theory description of classical population models. We apply this formalism to study a prototypical ``Schr\"odigner cat'' population model on a $d$-dimensional lattice, which exhibits a phase transition between a dark extinct phase and an active phase that supports a stable quantum population. Using a perturbative renormalization group approach, we find a critical scaling of the Schr\"odinger cat population distinct from that observed in both classical population dynamics and usual quantum phase transitions.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1. interesting results relating quantum and classical population dynamics
2. pedagogical presentation of the results
Weaknesses
no weakness
Report
The work “Population Dynamics of Schrodinger Cats” is devoted to study of a specific bosonic Keldysh field theory corresponding to extension of classical population dynamics to include non-classical processes. The paper is interesting and timely. The manuscript provide a novel and synergetic link between Linbladian dynamics of bosonic quantum systems (described in terms of Keldysh part integral) and classical population dynamics - an area well-studied previously. The paper is written in pedagogical style with many details simplifying the understanding of the matter. I strongly recommend publication of the manuscript in SciPost. Before publication I suggests for authors to consider the following comments:
i) The absence of some qubic terms, e.g. \bar\chi \chi \phi in Eq. (40) is discussed in the footnote on page 17. In particular, there is a claim that such terms are not generated by RG procedure. In my opinion, a bit more detailed discussion of this point would be beneficial for a reader. Is some symmetry that forbids emergence of such terms in the course of RG?
ii) The one-loop diagrams, responsible for renormalization of vertices \beta_1 and \beta_2 are shown In Fig. 5. It would be useful to connect these diagrams with diagrams (processes) in terms of reaction processes. It could make physics behind renormalization of the Keldysh action more transparent.
iii) As we know in \phi^4 field theory we can consider a complex field \phi to become a N-dimensional vector. It will affect the theory, in general, and RG equation in particular. Do such extensions are possible and meaningful for the Keldysh action (40)? If yes, is it possible to develop a kind of 1/N expansion? I understand that, perhaps, a detailed answer needs to do a separate work, but, in my opinion, a brief discussion of this issue would be useful for a reader.
Requested changes
some optional amendments are possible, see the report's items (i)-(iii)
Recommendation
Ask for minor revision