Classical approach to equilibrium of out-of-time ordered correlators in mixed systems

Abstract

The out-of-time ordered correlator (OTOC) is a measure of scrambling of quantum information. Scrambling is intuitively considered to be a significant feature of chaotic systems and thus the OTOC is widely used as a measure of chaos. For short times exponential growth is related to the classical Lyapunov exponent, sometimes known as butterfly effect. At long times the OTOC attains an average equilibrium value with possible oscillations. For fully chaotic systems the approach to the asymptotic regime is exponential with a rate given by the classical Ruelle-Pollicott resonances. In this work, we extend this notion by showing that classical generalized resonances govern the relaxation to equilibrium of the OTOC in the ubiquitous case of a system with mixed dynamics, in particular, the standard map.

9 pages, 9 figures. Closest to published version

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Cited by in corpus (8)

• Momentum dependent quantum Ruelle-Pollicott resonances in translationally invariant many-body systems
• Quantum Lyapunov exponent in dissipative systems
• Exploring quantum ergodicity of unitary evolution through the Krylov approach
• Out-of-Time Ordered Correlators in Kicked Coupled Tops: Information Scrambling in Mixed Phase Space and the Role of Conserved Quantities
• Control of spatiotemporal chaos by stochastic resetting
• Quantum Liang Information Flow Probe of Causality across Critical Points
• Ruelle-Pollicott Decay of Out-of-Time-Order Correlators in Many-Body Systems
• Localization of information driven by stochastic resetting