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Markovian to non-Markovian phase transition in the operator dynamics of a mobile impurity
by Dominic Gribben, Jamir Marino, Shane P. Kelly
Submission summary
| Authors (as registered SciPost users): | Dominic Gribben · Shane Kelly |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2401.17066v2 (pdf) |
| Date accepted: | 2024-08-20 |
| Date submitted: | 2024-07-01 09:17 |
| Submitted by: | Gribben, Dominic |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We study a random unitary circuit model of an impurity moving through a chaotic medium. The exchange of information between the medium and impurity is controlled by varying the velocity of the impurity, $v_d$, relative to the speed of information propagation within the medium, $v_B$. Above supersonic velocities, $v_d> v_B$, information cannot flow back to the impurity after it has moved into the medium, and the resulting dynamics are Markovian. Below supersonic velocities, $v_d< v_B$, the dynamics of the impurity and medium are non-Markovian, and information is able to flow back onto the impurity. We show the two regimes are separated by a continuous phase transition with exponents directly related to the diffusive spreading of operators in the medium. This is demonstrated by monitoring an out-of-time-order correlator (OTOC) in a scenario where the impurity is substituted at an intermediate time. During the Markovian phase, information from the medium cannot transfer onto the replaced impurity, manifesting in no significant operator development. Conversely, in the non-Markovian phase, we observe that operators acquire support on the newly introduced impurity. We also characterize the dynamics using the coherent information and provide two decoders which can efficiently probe the transition between Markovian and non-Markovian information flow. Our work demonstrates that Markovian and non-Markovian dynamics can be separated by a phase transition, and we propose an efficient protocol for observing this transition.
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For Journal SciPost Physics Core: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
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I thank the authors for considering the referees' concerns, which are adequately addressed by the revised manuscript. I support its publication in SciPost Physics Core.
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In my previous report, I addressed two main concerns: i) the preexisting literature was not properly referenced, and ii) while the study and result are interesting, I think they do not meet the high standard of SciPost Physics and I recommended SciPost Physics Core as a more proper venue.
Both issues have been resolved by the authors, and therefore I can recommend the manuscript for publication in SciPost Physics Core.
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