# Infinite Range Correlations in Non-Equilibrium Quantum Systems and Their Possible Experimental Realizations

### Submission summary

 As Contributors: Zohar Nussinov Arxiv Link: https://arxiv.org/abs/1710.06710v4 Date submitted: 2017-11-28 Submitted by: Nussinov, Zohar Submitted to: SciPost Physics Domain(s): Theoretical Subject area: Quantum Physics

### Abstract

We consider systems that start from and/or end in thermodynamic equilibrium while experiencing a finite rate of change of their energy density or of other intensive quantities $q$ at intermediate times. We demonstrate that at these times, during which the global intensive quantities $q$ vary, the size of the associated covariance, the connected pair correlator $|G_{ij}| = |\langle q_{i} q_{j} \rangle - \langle q_{i} \rangle \langle q_{j} \rangle|$, between any two (arbitrarily far separated) sites $i$ and $j$ is, on average, finite. This non-vanishing character of the connected correlations for asymptotically distant sites also applies to theories with purely local interactions. In simple models, these correlations may be traced to the generic volume law entanglement of finite temperature states. Once the global mean of $q$ no longer changes, the average of $|G_{ij}|$ over all spatial separations $|i-j|$ may tend to zero. However, when the equilibration times are significant (e.g., as in a glass that is not in true thermodynamic equilibrium yet in which the energy density (or temperature) reaches a final steady state value), these long range correlations may persist also long after $q$ ceases to change. We briefly discuss possible experimental implications of our findings and speculate on their potential realization in glasses (where a prediction of a theory based on the effect that we describe here suggests a universal collapse of the viscosity that agrees with all published viscosity measurements) and non-Fermi liquids.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission 1710.06710v9 (3 October 2018)
Resubmission 1710.06710v7 (24 May 2018)
Submission 1710.06710v4 (28 November 2017)

## Invited Reports on this Submission

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### Strengths

1 The manuscript adresses a fundamentally relevant question
2 A number of relevant examples are discussed in detail

### Weaknesses

1 Not easy to follow in parts
2 Not putting the manuscript into context with recent and relevant literature on quantum thermalization

### Report

In this work, the author investigates correlations in non-equilibrium quantum systems for which he argues that the connected pair correlator is on average finite. This observation is linked to the volume law entanglement. Moreover, experimental realizations are discussed.

The presented work is on a timely topic and considers important fundamental questions. While I can follow the general discussion in the paper, I would suggest to make the context more clear:

(1) In arXiv:1708.09349 it is shown that thermofield double states (TDS) obey an area law and can be efficiently represented using a matrix-product form. This implies that that the correlations decay exponentially at any finite temperature. It would be useful to relate this finding to the claim of the paper. I assume that an adiabatic cooling can be done without building up long range correlations?

(2) There is an extensive literature on quantum thermalization including a more detailed understanding of operator scrambling and entanglement growth. It would be useful to include a brief discussion of those results and put it into context with the results obtained in the manuscript.

(3) Regarding the experimental realization, I would assume that the coupling to a bath (e.g., photons) will destroy the long-range correlations. Is that correct?

To conclude, if the author can improve the clarity and address the above points, I recommend the manuscript for publication on SciPost.

### Requested changes

1 Improve the introduction
2 Put the findings into context with recent literature

• validity: good
• significance: high
• originality: high
• clarity: ok
• formatting: good
• grammar: excellent