Perturbation spreading in many-particle systems: a random walk approach

Abstract

The propagation of an initially localized perturbation via an interacting many-particle Hamiltonian dynamics is investigated. We argue that the propagation of the perturbation can be captured by the use of a continuous-time random walk where a single particle is traveling through an active, fluctuating medium. Employing two archetype ergodic many-particle systems, namely (i) a hard-point gas composed of two unequal masses and (ii) a Fermi-Pasta-Ulam chain we demonstrate that the corresponding perturbation profiles coincide with the diffusion profiles of the single-particle Lévy walk approach. The parameters of the random walk can be related through elementary algebraic expressions to the physical parameters of the corresponding test many-body systems.

References in corpus (4)

• Relativistic Brownian Motion
• Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
• Relativistic diffusion processes and random walk models
• Energy diffusion in hard-point systems

Cited by in corpus (43)

• Lévy walks
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Heat transport in low dimensions: introduction and phenomenology
• Anomalous Heat Diffusion
• Anomalous Heat Diffusion
• Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics
• Anomalous Heat Conduction and Anomalous Diffusion in Low Dimensional Nanoscale Systems
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• The Continuous Time Random Walk, still trendy: Fifty-year history, state of art, and outlook
• Non-normalizable densities in strong anomalous diffusion: beyond the central limit theorem
• Time averaged Einstein relation and fluctuating diffusivities for the Lévy walk
• Exact solution of a Levy walk model for anomalous heat transport
• Diffusion of heat, energy, momentum, and mass in one-dimensional systems
• Equilibrium time-correlation functions for one-dimensional hard-point systems
• Random time averaged diffusivities for Lévy walks
• Mixing properties of stochastic quantum Hamiltonians
• Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation
• 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
• Crossover from ballistic to normal heat transport in the ${\varphi }^4$ lattice: If nonconservation of momentum is the reason, what is the mechanism?
• Space-time velocity correlation function for random walks
• Wave Turbulence and thermalization in one-dimensional chains
• Crossover between different universality classes: Scaling for thermal transport in one dimension
• Levy walks with velocity fluctuations
• Additivity Principle in High-dimensional Deterministic Systems
• Temperature profile and boundary conditions in an anomalous heat transport model
• Langevin dynamics for Lévy walk with memory
• Thermoelectricity of interacting particles: A numerical approach
• One-dimensional Superdiffusive Heat Propagation Induced by Optical Phonon-Phonon Interactions
• Observing Golden Mean Universality Class in the Scaling of Thermal Transport
• Heat conduction and energy diffusion in momentum-conserving 1D full lattice ding-a-ling model
• Nonergodicity of $d$-dimensional generalized Lévy walks and their relation to other space-time coupled models
• Energy spread and current-current correlation in quantum systems
• Using Hilbert transform and classical chains to simulate quantum walks
• Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices
• Universality in the Onset of Super-Diffusion in Lévy Walks
• Large deviations of the ballistic Lévy walk model
• Anomalous temperature-dependent heat transport in one-dimensional momentum-conserving systems with soft-type interparticle interaction
• Mapping the Arnold web with a GPU-supercomputer
• Heat perturbations spreading in the Fermi-Pasta-Ulam-$\beta$ system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity
• L{é}vy walks on finite intervals: A step beyond asymptotics
• Dynamics of a randomly kicked particle
• Origin of universality in the onset of superdiffusion in Lévy walks
• Complete Decomposition of Anomalous Diffusion in Variable Speed Generalized Lévy Walks