Control of spatiotemporal chaos by stochastic resetting
arXiv:2412.21043 · doi:10.1103/zlm4-zrnx
Abstract
We study how spatiotemporal chaos in dynamical systems can be controlled by stochastically returning them to their initial conditions. Focusing on discrete nonlinear maps, we analyze how key measures of chaos -- the Lyapunov exponent and butterfly velocity, which quantify sensitivity to initial perturbations and the ballistic spread of information, respectively -- are reduced by stochastic resetting. We identify a critical resetting rate that induces a dynamical phase transition, characterized by the simultaneous vanishing of the Lyapunov exponent and butterfly velocity, effectively arresting the spread of information. These theoretical predictions are validated and illustrated with numerical simulations of the celebrated logistic map and its lattice extension. Beyond discrete maps, our findings are applicable to virtually any chaotic extended classical many-body system.
(4+) pages + Appendix. v2: minor revision (published version)
References in corpus (50)
- A bound on chaos
- Black holes and the butterfly effect
- Diffusion with Stochastic Resetting
- Stochastic Resetting and Applications
- Measuring the scrambling of quantum information
- Diffusion with Optimal Resetting
- First order transition for the optimal search time of Lévy flights with resetting
- Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
- Lieb-Robinson and the butterfly effect
- Experimental realization of diffusion with stochastic resetting
- Scrambling and thermalization in a diffusive quantum many-body system
- Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
- Diffusion with resetting in arbitrary spatial dimension
- Information propagation in isolated quantum systems
- Fluctuating interfaces subject to stochastic resetting
- Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
- Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics
- Stochastic resetting: A (very) brief review
- Stochastic thermodynamics of resetting
- Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation
- Quantum dynamics with stochastic reset
- Symmetric Exclusion Process under Stochastic Resetting
- Pesin-Type Identity for Weak Chaos
- Ising model with stochastic resetting
- Spectral properties of simple classical and quantum reset processes
- Light-cone spreading of perturbations and the butterfly effect in a classical spin chain
- Extreme statistics and spacing distribution in a Brownian gas correlated by resetting
- Stochastic resetting in interacting particle systems: A review
- Temperature dependence of butterfly effect in a classical many-body system
- Nonlinear sigma model approach to many-body quantum chaos: Regularized and unregularized out-of-time-ordered correlators
- Classical many-body chaos with and without quasiparticles
- Many-body Chaos in Thermalised Fluids
- Emergent quantum correlations and collective behavior in non-interacting quantum systems subject to stochastic resetting
- Reducing mean first passage times with intermittent confining potentials: a realization of resetting processes
- Exact extreme, order and sum statistics in a class of strongly correlated system
- Universal scrambling in gapless quantum spin chains
- Spatio-temporal spread of perturbations in a driven dissipative Duffing chain: an OTOC approach
- Arresting classical many-body chaos by kinetic constraints
- Generating Entanglement by Quantum Resetting
- Zero-current Nonequilibrium State in Symmetric Exclusion Process with Dichotomous Stochastic Resetting
- Dynamically emergent correlations in bosons via quantum resetting
- Transport, correlations, and chaos in a classical disordered anharmonic chain
- Spatio-temporal spread of perturbations in power-law models at low temperatures: Exact results for OTOC
- Non-Analytic Non-Equilibrium Field Theory: Stochastic Reheating of the Ising Model
- Classical approach to equilibrium of out-of-time ordered correlators in mixed systems
- Local and nonlocal stochastic control of quantum chaos: Measurement- and control-induced criticality
- Out-of-time-ordered correlator in the one-dimensional Kuramoto-Sivashinsky and Kardar-Parisi-Zhang equations
- Manifestation of strange nonchaotic attractors in extended systems: A study through out-of-time-ordered correlators
- Out of Time Order Correlation of the Hubbard Model with Random Local Disorder
- Kinetics of information scrambling in correlated electrons: disorder-driven transition from shock-wave to FKPP dynamics