Out-of-time-ordered correlator in the one-dimensional Kuramoto-Sivashinsky and Kardar-Parisi-Zhang equations
arXiv:2303.08049 · doi:10.1103/PhysRevE.108.054112
Abstract
The out-of-time-ordered correlator (OTOC) has emerged as an interesting object in both classical and quantum systems for probing the spatial spread and temporal growth of initially local perturbations in spatially extended chaotic systems. Here, we study the (classical) OTOC and its ``light-cone'' in the nonlinear Kuramoto-Sivashinsky (KS) equation, using extensive numerical simulations. We also show that the linearized KS equation exhibits a qualitatively similar OTOC and light-cone, which can be understood via a saddle-point analysis of the linearly unstable modes. Given the deep connection between the KS (deterministic) and the Kardar-Parisi-Zhang (KPZ which is stochastic) equations, we also explore the OTOC in the KPZ equation. While our numerical results in the KS case are expected to hold in the continuum limit, for the KPZ case it is valid in a discretized version of the KPZ equation. More broadly, our work unravels the intrinsic interplay between noise/instability, nonlinearity and dissipation in partial differential equations (deterministic or stochastic) through the lens of OTOC.
arXiv comment8 pages (including supplemental material), 5 figures, updated
References in corpus (25)
- A bound on chaos
- Black holes and the butterfly effect
- Fast Scramblers
- Chaos in quantum channels
- Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
- Towards the fast scrambling conjecture
- A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
- An appetizer to modern developments on the Kardar-Parisi-Zhang universality class
- Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
- Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields
- Light-cone spreading of perturbations and the butterfly effect in a classical spin chain
- Semiclassical theory of out-of-time-order correlators for low-dimensional classically chaotic systems
- Temperature dependence of butterfly effect in a classical many-body system
- Coupled Kardar-Parisi-Zhang Equations in One Dimension
- Classical many-body chaos with and without quasiparticles
- Many-body Chaos in Thermalised Fluids
- Defect-Mediated Stability: An Effective Hydrodynamic Theory of Spatio-Temporal Chaos
- Weak and strong dynamic scaling in a one-dimensional driven coupled-field model: Effects of kinematic waves
- Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
- Spatio-temporal spread of perturbations in a driven dissipative Duffing chain: an OTOC approach
- Arresting classical many-body chaos by kinetic constraints
- The one-dimensional Kardar-Parisi-Zhang and Kuramoto-Sivashinsky universality class: limit distributions
- 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
- Manifestation of strange nonchaotic attractors in extended systems: A study through out-of-time-ordered correlators