Quantum Lyapunov exponent in dissipative systems
arXiv:2211.06353 · doi:10.1103/PhysRevE.108.024208
Abstract
The out-of-time order correlator (OTOC) has been widely studied in closed quantum systems. However, there are very few studies for open systems and they are mainly focused on isolating the effects of scrambling from those of decoherence. Adopting a different point of view, we study the interplay between these two processes. This proves crucial in order to explain the OTOC behavior when a phase space contracting dissipation is present, ubiquitous not only in real life quantum devices but in the dynamical systems area. The OTOC decay rate is closely related to the classical Lyapunov exponent -- with some differences -- and more sensitive in order to distinguish the chaotic from the regular behavior than other measures. On the other hand, it reveals as a generally simple function of the longest lived eigenvalues of the quantum evolution operator. We find no simple connection with the Ruelle-Pollicott resonances, but by adding Gaussian noise of size to the classical system we recover the OTOC decay rate, being this a consequence of the correspondence principle put forward in [Physical Review Letters 108 210605 (2012) and Physical Review E 99 042214 (2019)]
arXiv comment5 pages, 7 figures
References in corpus (34)
- A bound on chaos
- Black holes and the butterfly effect
- Chaos in quantum channels
- Out-of-Time-Order Correlation for Many-Body Localization
- Out-of-time-ordered correlators in many-body localized systems
- Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
- Scrambling and entanglement spreading in long-range spin chains
- Out-of-time-order correlations in many-body localized and thermal phases
- Chaos signatures in the short and long time behavior of the out-of-time ordered correlator
- Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling
- Thermodynamics of quantum information scrambling
- Information Scrambling and Chaos in Open Quantum Systems
- Quantum ratchets in dissipative chaotic systems
- Semiclassical theory of out-of-time-order correlators for low-dimensional classically chaotic systems
- Information scrambling in chaotic systems with dissipation
- Resilience of scrambling measurements
- Out-of-Time-Order Correlation in Marginal Many-Body Localized Systems
- Out-of-time-order correlator in coupled harmonic oscillators
- Information scrambling vs. decoherence -- two competing sinks for entropy
- Quantum Chaos and the Correspondence Principle
- Out-of-time-ordered correlator in the quantum bakers map and truncated unitary matrices
- Scrambling in strongly chaotic weakly coupled bipartite systems: Universality beyond the Ehrenfest time-scale
- Quantum scrambling and the growth of mutual information
- Resonances in a Chaotic Attractor Crisis of the Lorenz Flow
- Signatures of quantum chaos transition in short spin chains
- OTOC, complexity and entropy in bi-partite systems
- From ETH to algebraic relaxation of OTOCs in systems with conserved quantities
- Complexity of quantum motion and quantum-classical correspondence: A phase-space approach
- Emergence of correlations in the process of thermalization of interacting bosons
- Wigner separability entropy and complexity of quantum dynamics
- Quantum Parameter Space of Dissipative Directed Transport
- Classical approach to equilibrium of out-of-time ordered correlators in mixed systems
- Relevant OTOC operators: footprints of the classical dynamics
- Quantum and classical complexity in coupled maps
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- Chaos and magic in the dissipative quantum kicked top
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- A universal constraint for relaxation rates for quantum Markov generators: complete positivity and beyond
- Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model
- Out-of-time ordered correlation functions for the localized electrons in the Falicov-Kimball model