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Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics
by Michel Bauer, Denis Bernard, Tony Jin
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Denis Bernard · Tony Jin |
| Submission information | |
|---|---|
| Preprint Link: | http://arxiv.org/abs/1706.03984v2 (pdf) |
| Date submitted: | June 23, 2017, 2 a.m. |
| Submitted by: | Denis Bernard |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| 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.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2017-8-10 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1706.03984v2, delivered 2017-08-10, doi: 10.21468/SciPost.Report.207
Strengths
- Interesting and timely topic
- Novel aspects on dissipative dynamics of XXZ chain
Weaknesses
- Introduction poorly written and hard to understand
- Better comparison to standard Lindblad formalism should be provided
Report
using the methods of quantum stochastic calculus.
In particular, they are interested in the limit of large friction,
i.e. when the coefficient of the dissipative coupling to an environment
is much larger in magnitude then the couplings generating the
coherent part of the time evolution. After introducing the
general formalism of stochastic calculus, they study the slow-modes
of the dynamics in a perturbative expansion w.r.t. the inverse friction
coefficient. The concrete example of an XXZ chain with a dephasing
noise is considered afterwards, where the slow-mode observables
are explicitly constructed and the evolution equations for the
density matrix and observables are presented.
In my opinion, although the paper is rather technical and thus somewhat
difficult to read, it contains some interesting novel results which
are worth publishing. There are, however, certain amendments that
should be considered in order to improve the quality of the
manuscript.
Requested changes
1) The introduction is not well written. In particular, I do not understand why the various evolution equations are presented here. On one hand, these are impossible to comprehend without any clue about the notation and the underlying methods. On the other hand, this only makes the manuscript repetitive, the introduction lengthy, without providing a better insight to the reader. Some more detailed general introduction to quantum stochastic differential equations (e.g. what are the main assumptions to their applicability? where are they used?) would be much more instructive at this point than quoting the results for the XXZ chain. I would suggest the authors to extensively revise their introductory chapter.
2) I found the notion of “stochastic Lindblad equation” rather confusing. The Lindblad master equation describes the evolution of a system density matrix interacting with its environment in a Markovian approximation, after integrating out the bath degrees of freedom. The Lindblad dynamics describes coherent as well as stochastic processes, resulting in a $non$-$unitary$ time-evolution of the density matrix. In contrast, the stochastic differential equations the authors consider describe a $unitary$ time evolution of the density matrix. After an averaging over the noise terms they indeed yield the Lindblad equation. However, this difference should be made clear from the very beginning, or one should rather stick to “stochastic differential equation” when referring to the noisy dynamics.
3) It did not become completely clear to me what the advantage of working with the stochastic differential equation formalism really is? If I understood it correctly, the Lindblad generators completely fix the form of the noise term. On the other hand, when considering expectation values, the noise has to be averaged over anyway. What extra information can one expect to have on the dynamics of the density operator and physical observables which is not there when working with a Lindblad master equation? I believe this issue deserves some more clarification.
4) The word “hopping” is misspelled throughout the text.