Out-of-time ordered correlators, complexity, and entropy in bipartite systems

Pablo D Bergamasco,Alejandro M F Rivas,Gabriel G Carlo

doi:10.1103/physrevresearch.1.033044

Pablo D Bergamasco, Alejandro M F Rivas + Show 1 more

Open Access

https://doi.org/10.1103/physrevresearch.1.033044

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Abstract

There is a remarkable interest in the study of Out-of-time ordered correlators (OTOCs) that goes from many body theory and high energy physics to quantum chaos. In this latter case there is a special focus on the comparison with the traditional measures of quantum complexity such as the spectral statistics, for example. The exponential growth has been verified for many paradigmatic maps and systems. But less is known for multi-partite cases. On the other hand the recently introduced Wigner separability entropy (WSE) and its classical counterpart (CSE) provide with a complexity measure that treats equally quantum and classical distributions in phase space. We have compared the behavior of these measures in a system consisting of two coupled and perturbed cat maps with different dynamics: double hyperbolic (HH), double elliptic (EE) and mixed (HE). In all cases, we have found that the OTOCs and the WSE have essentially the same behavior, providing with a complete characterization in generic bi-partite systems and at the same time revealing them as very good measures of quantum complexity for phase space distributions. Moreover, we establish a relation between both quantities by means of a recently proven theorem linking the second Renyi entropy and OTOCs.

Highlights

There is a huge interest in out-of-time ordered correlators (OTOCs) within the quantum chaos community, where they have been related to traditional measures as spectral statistics and the like [1]
In order to reach our twofold objective we have investigated the evolution of OTOCs much in the same way we have done in Ref. [17], that is, we have evaluated their behavior for three different dynamics
A third component comes from information theory which has established a precise connection between OTOCs and the second Rényi entropy via the OTOC-RE theorem

Summary

INTRODUCTION

There is a huge interest in out-of-time ordered correlators (OTOCs) within the quantum chaos community, where they have been related to traditional measures as spectral statistics and the like [1]. These correlators were first introduced in superconductivity studies [2], where their exponential growth over time was associated with chaotic behavior. It is worth mentioning that there are previous studies linking entanglement and chaos but They do not consider all possible dynamical scenarios or make reference to OTOC measures (see, for example, [18]). Beyond the existing relation with different entropies and our conjecture on how to demonstrate it, one of the main points of this paper is that OTOCs behave differently according to the kind of dynamics, and this involves the initial growth as well as the saturation

OTOCS AND WSE

MODEL SYSTEM

RESULTS

CONCLUSION