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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

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Out-of-time-order fluctuation-dissipation theorem.

Naoto Tsuji¹, Tomohiro Shitara², Masahito Ueda^1,2

¹RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan.

Physical Review. E

|February 17, 2018

Summary

We introduce bipartite out-of-time-ordered correlators (OTOCs) to generalize fluctuation-dissipation theorems in quantum systems. This reveals a universal link between quantum chaos and nonlinear response involving time-reversed processes.

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Area of Science:

Quantum Mechanics
Statistical Mechanics
Condensed Matter Physics

Background:

Out-of-time-ordered correlators (OTOCs) are crucial for understanding quantum chaos.
Traditional fluctuation-dissipation theorems describe equilibrium systems.
Generalizing these concepts is key to exploring complex quantum dynamics.

Purpose of the Study:

To generalize the fluctuation-dissipation theorem for quantum systems in thermal equilibrium.
To introduce and analyze bipartite OTOCs.
To establish a universal relation between quantum chaos and nonlinear response.

Main Methods:

Development of a modified statistical average for bipartite OTOCs.
Quantification of differences between bipartite and physical OTOCs using Wigner-Yanase skew information.
Analysis of nonlinear-response functions involving time-reversed processes.

Main Results:

A generalized fluctuation-dissipation theorem for bipartite OTOCs is proven.
A universal relationship is established between quantum chaotic behavior and a specific nonlinear-response function.
The theorem is shown to be generalizable to higher-order n-partite OTOCs and generalized covariance.

Conclusions:

Bipartite OTOCs offer a new framework for fluctuation-dissipation relations in quantum systems.
The findings provide insights into the interplay of quantum fluctuations, chaos, and response functions.
The generalization to n-partite OTOCs broadens the applicability of the theorem.