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Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics

by Michel Bauer, Denis Bernard, Tony Jin

Submission summary

As Contributors: Denis Bernard · Tony Jin
Arxiv Link: http://arxiv.org/abs/1706.03984v4 (pdf)
Date accepted: 2017-10-18
Date submitted: 2017-10-13 02:00
Submitted by: Bernard, Denis
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Mathematical Physics
Approach: Theoretical

Abstract

Motivated by the search for a quantum analogue of the macroscopic fluctuation theory, we study quantum spin chains dissipatively coupled to quantum noise. The dynamical processes are encoded in quantum stochastic differential equations. They induce dissipative friction on the spin chain currents. We show that, as the friction becomes stronger, the noise induced dissipative effects localize the spin chain states on a slow mode manifold, and we determine the effective stochastic quantum dynamics of these slow modes. We illustrate this approach by studying the quantum stochastic Heisenberg spin chain.

Ontology / Topics

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Dissipation Friction Heisenberg spin chains Hydrodynamics Localization Quantum noise Quantum spin chains Stochastic differential equations Stochastic dynamics

Published as SciPost Phys. 3, 033 (2017)



Author comments upon resubmission

1) Following the referee’s suggestion, we have rewritten the general discussion of quantum stochastic processes, using a more intuitive and physical approach.

2) Indeed, the author of ref. PRL 112, 040602 (2014) computed large deviation functions. These refer to quantum randomness encoded into a system quantum state (time evolving according to a Lindblad equation). As we said in our previous answer, there are two origins of randomness in stochastic quantum theory : that due to the noise and that due to the probabilistic nature of quantum mechanics. Ref. PRL 112, 040602 (2014) deals with those due to the probabilistic nature of quantum mechanics. In presence of external noise, as in the models we discussed in this paper, there are also randomness due to that noise. Those are not encoded into the mean system quantum state and hence not in the (mean) Lindblad equation, but in stochastic extensions of it which we describe in the paper.

Submission & Refereeing History

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Resubmission 1706.03984v4 on 13 October 2017

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