Non-integrability and the Fourier heat conduction law

Abstract

We study in momentum-conserving systems, how nonintegrable dynamics may affect thermal transport properties. As illustrating examples, two one-dimensional (1D) diatomic chains, representing 1D fluids and lattices, respectively, are numerically investigated. In both models, the two species of atoms are assigned two different masses and are arranged alternatively. The systems are nonintegrable unless the mass ratio is one. We find that when the mass ratio is slightly different from one, the heat conductivity may keep significantly unchanged over a certain range of the system size and as the mass ratio tends to one, this range may expand rapidly. These results establish a new connection between the macroscopic thermal transport properties and the underlying dynamics.

References in corpus (17)

• Thermal conduction in classical low-dimensional lattices
• Heat Transport in low-dimensional systems
• Transport and conservation laws
• Exact results for anomalous transport in one dimensional Hamiltonian systems
• Heat conduction in the diatomic Toda lattice revisited
• Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses
• Local Temperature and Universal Heat Conduction in FPU chains
• Anomalous Heat Conduction in a Di-atomic One-Dimensional Ideal Gas
• 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
• Thermodyamic bounds on Drude weights in terms of almost-conserved quantities
• Anomalous kinetics and transport from 1D self--consistent mode--coupling theory
• Validity of Fourier's law in one-dimensional momentum-conserving lattices with asymmetric interparticle interactions
• Detailed Examination of Transport Coefficients in Cubic-Plus-Quartic Oscillator Chains
• Conservation Laws and Thermodynamic Efficiencies
• Finite-size effects on current correlation functions

Cited by in corpus (38)

• Phononic thermal properties of two-dimensional materials
• High-temperature coherent transport in the XXZ chain in the presence of an impurity
• Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion
• Anomalous heat transport in classical many-body systems: overview and perspectives
• Non-Fourier heat transport in nanosystems
• Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation
• Crossover from ballistic to normal heat transport in the ${\varphi }^4$ lattice: If nonconservation of momentum is the reason, what is the mechanism?
• A violation of universality in anomalous Fourier's law
• Blast in a One-Dimensional Cold Gas: From Newtonian Dynamics to Hydrodynamics
• Key role of asymmetric interactions in low-dimensional heat transport
• From thermal rectifiers to thermoelectric devices
• Transport in perturbed classical integrable systems: the pinned Toda chain
• The Fourier heat conduction as a strong kinetic effect
• The Taylor-von Neumann-Sedov blast-wave solution: comparisons with microscopic simulations of a one-dimensional gas
• Transport properties of the classical Toda chain: effect of a pinning potential
• Nonintegrability and thermalization of one-dimensional diatomic lattices
• Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions
• Pressure-induced recovery of Fourier's law in one dimensional momentum-conserving systems
• Thermoelectricity of interacting particles: A numerical approach
• One-Dimensional Self-Organization and Nonequilibrium Phase Transition in a Hamiltonian System
• Underlying mechanisms for normal heat transport in one-dimensional anharmonic oscillator systems with a double-well interparticle interaction
• Dynamics and transport in the boundary-driven dissipative Klein-Gordon chain
• Effect of pressure on thermalization of one-dimensional nonlinear chains
• Thermal conductance of the coupled-rotator chain: Influence of temperature and size
• Heat conduction in a three-dimensional momentum-conserving fluid
• Anomalous temperature-dependent heat transport in one-dimensional momentum-conserving systems with soft-type interparticle interaction
• Universal scaling for recovery of Fourier's law in low-dimensional solids under momentum conservation
• A splash in a one-dimensional cold gas
• Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport
• Superdiffusive transport on lattices with nodal impurities
• Heat conduction in a chain of colliding particles with stiff repulsive potential
• Optimal qubit-mediated quantum heat transfer via noncommuting operators and strong coupling effects
• Calculating the free energy difference by applying the Jarzynski equality to a virtual integrable system
• Energy current cumulants in one-dimensional systems in equilibrium
• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases
• Dynamical correlations of conserved quantities in the one-dimensional equal mass hard particle gas
• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport
• Thermalization in asymmetric harmonic chains