Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion

Abstract

Energy transport in one-dimensional chains of particles with three conservation laws is generically anomalous and belongs to the Kardar-Parisi-Zhang dynamical universality class. Surprisingly, some examples where an apparent normal heat diffusion is found over a large range of length scales were reported. We propose a novel physical explanation of these intriguing observations. We develop a scaling analysis which explains how this may happen in the vicinity of an integrable limit, such as, but not only, the famous Toda model. In this limit, heat transport is mostly supplied by quasi-particles with a very large mean free path $\ell$. Upon increasing the system size $L$, three different regimes can be observed: a ballistic one, an intermediate diffusive range, and, eventually, the crossover to the anomalous (hydrodynamic) regime. Our theoretical considerations are supported by numerical simulations of a gas of diatomic hard-point particles for almost equal masses and of a weakly perturbed Toda chain. Finally, we discuss the case of the perturbed harmonic chain, which exhibits a yet different scenario.

arXiv commentPublished version

References in corpus (45)

• Thermal conduction in classical low-dimensional lattices
• Heat Transport in low-dimensional systems
• Lévy walks
• Fundamental aspects of steady-state conversion of heat to work at the nanoscale
• Anomalous heat conduction in one dimensional momentum-conserving systems
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Exact results for anomalous transport in one dimensional Hamiltonian systems
• A momentum conserving model with anomalous thermal conductivity in low dimension
• Heat conduction in the diatomic Toda lattice revisited
• Heat Conduction and Entropy Production in a One-Dimensional Hard-Particle Gas
• Anomalous Heat Diffusion
• Anomalous Heat Diffusion
• From anomalous energy diffusion to Levy walks and heat conductivity in one-dimensional systems
• Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics
• Fermi-Pasta-Ulam $\beta$ lattice: Peierls equation and anomalous heat conductivity
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• FPU $\beta$ model: Boundary Jumps, Fourier's Law and Scaling
• On the universality of anomalous one-dimensional heat conductivity
• Self-Consistent Mode-Coupling Approach to 1D Heat Transport
• Normal heat conduction in one dimensional momentum conserving lattices with asymmetric interactions
• Heat conduction in the α-β-Fermi-Pasta-Ulam chain
• Studies of thermal conductivity in Fermi-Pasta-Ulam like lattices
• Validity of Fourier's law in one-dimensional momentum-conserving lattices with asymmetric interparticle interactions
• Exact solution of a Levy walk model for anomalous heat transport
• Non-integrability and the Fourier heat conduction law
• Anomalous energy transport in the FPU-beta chain
• A stochastic model of anomalous heat transport: analytical solution of the steady state
• Equilibrium time-correlation functions for one-dimensional hard-point systems
• Interacting and noninteracting integrable systems
• Density Profiles in Open Superdiffusive Systems
• A violation of universality in anomalous Fourier's law
• Equilibrium dynamical correlations in the Toda chain and other integrable models
• Non-diffusive Lattice Thermal Transport in Si-Ge Alloy Nanowires
• Normal heat conductivity in chains capable of dissociation
• Anomalous fluctuations for a perturbed Hamiltonian system with exponential interactions
• Transport in perturbed classical integrable systems: the pinned Toda chain
• Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas
• The Fourier heat conduction as a strong kinetic effect
• Nonequilibrium dynamics of a stochastic model of anomalous heat transport: numerical analysis
• Thermal conductivity of the Toda lattice with conservative noise
• Transport properties of the classical Toda chain: effect of a pinning potential
• Nonintegrability and thermalization of one-dimensional diatomic lattices
• Dynamics of Energy Transport in a Toda Ring
• Underlying mechanisms for normal heat transport in one-dimensional anharmonic oscillator systems with a double-well interparticle interaction
• Temperature dependent divergence of thermal conductivity in momentum conserving 1D lattice with asymmetric potential

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• Anomalous Dynamics and Equilibration in the Classical Heisenberg Chain
• Microscopic theory of the fluctuating hydrodynamics in nonlinear lattices
• The Taylor-von Neumann-Sedov blast-wave solution: comparisons with microscopic simulations of a one-dimensional gas
• Long-lived Solitons and Their Signatures in the Classical Heisenberg Chain
• Thermalization of two- and three-dimensional classical lattices
• Effect of pressure on thermalization of one-dimensional nonlinear chains
• Kinetic and hydrodynamic regimes in multi-particle-collision dynamics of a one-dimensional fluid with thermal walls
• Heat conduction in a three-dimensional momentum-conserving fluid
• A splash in a one-dimensional cold gas
• Hydrodynamics and transport in the long-range-interacting ${\phi }^4$ chain
• Conformal order and Poincar$\acute{\mathrm{e}}$-Klein mapping underlying electrostatics-driven inhomogeneity in tethered membranes
• Non-equilibrium steady states of long-range coupled harmonic chains
• Thermalization of isolated harmonic networks under conservative noise
• Super-diffusion and crossover from diffusive to anomalous transport in a one-dimensional system
• Simulating generalised fluids via interacting wave packets evolution
• Effective and asymptotic scaling in a one-dimensional billiard problem
• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases
• Onsager coefficients in a coupled-transport model displaying a condensation transition
• Relaxation dynamics and finite-size effects in a simple model of condensation
• Nonanomalous heat transport in a one-dimensional composite chain
• Revisiting a Low-Dimensional Model with Short Range Interactions and Mean Field Critical Behavior
• Large-deviations approach to thermalization: the case of harmonic chains with conservative noise
• Recent progress on thermal transport in one-dimensional long-range interacting Fermi-Pasta-Ulam-Tsingou lattice systems
• Thermalization in asymmetric harmonic chains
• Lax dynamics
• Classical and quantum harmonic mean-field models coupled intensively and extensively with external baths
• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport
• Symmetry-based nonlinear fluctuating hydrodynamics in one dimension