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Quantum Lyapunov exponent in dissipative systems.

Pablo D Bergamasco¹, Gabriel G Carlo², Alejandro M F Rivas²

¹Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina.

Physical Review. E

|September 19, 2023

Summary

This summary is machine-generated.

We investigated the out-of-time-order correlator (OTOC) in open quantum systems, revealing its decay rate is sensitive to chaos and linked to classical Lyapunov exponents. This study explores the interplay of scrambling and dissipation.

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Area of Science:

Quantum Dynamics
Statistical Mechanics
Chaos Theory

Background:

Out-of-time-order correlators (OTOCs) are key measures of quantum chaos, extensively studied in closed systems.
Research on OTOCs in open quantum systems often separates scrambling from decoherence effects.
Dissipative processes are common in quantum devices and classical dynamical systems.

Purpose of the Study:

To investigate the interplay between quantum scrambling and decoherence in open systems.
To explain the behavior of OTOCs in the presence of phase-space contracting dissipation.
To identify sensitive measures for distinguishing chaotic from regular behavior in quantum systems.

Main Methods:

Analysis of OTOCs in open quantum systems with dissipation.
Comparison of OTOC decay rates with classical Lyapunov exponents.
Investigation of the relationship between OTOCs and quantum evolution operator eigenvalues.
Modeling classical systems with Gaussian noise to explore the correspondence principle.

Main Results:

The OTOC decay rate in dissipative systems is closely related to the classical Lyapunov exponent.
OTOCs prove more sensitive than other measures for distinguishing chaotic from regular dynamics.
The OTOC decay rate is a function of the longest-lived eigenvalues of the quantum evolution operator.
Adding Gaussian noise to classical systems recovers the OTOC decay rate, consistent with the correspondence principle.

Conclusions:

The interplay of scrambling and dissipation is crucial for understanding OTOC behavior in open quantum systems.
OTOCs offer a sensitive probe of chaos in dissipative quantum dynamics.
The correspondence principle provides a framework for linking classical noise and quantum OTOC decay.