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Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics
by Michel Bauer, Denis Bernard, Tony Jin
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Denis Bernard · Tony Jin |
| Submission information | |
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| Preprint 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 |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| 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.
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.
Published as SciPost Phys. 3, 033 (2017)