1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport

Abstract

Transport and diffusion of heat in one dimensional (1D) nonlinear systems which {\it conserve momentum} is typically thought to proceed anomalously. Notable exceptions, however, exist of which the rotator model is a prominent case. Therefore, the quest arises to identify the origin of manifest anomalous transport in those low dimensional systems. Here, we develop the theory for both, momentum/heat diffusion and its corresponding momentum/heat transport. We demonstrate that the second temporal derivative of the mean squared deviation of the momentum spread is proportional to the equilibrium correlation of the total momentum flux. This result in turn relates, via the integrated momentum flux correlation, to an effective viscosity, or equivalently, to the underlying momentum diffusivity. We put forward the intriguing hypothesis that a fluid-like momentum dynamics with a {\it finite viscosity} causes {\it normal} heat transport; its corollary being that superdiffusive momentum diffusion with an intrinsic {\it diverging viscosity} in turn yields {\it anomalous} heat transport. This very hypothesis is corroborated over wide extended time scales by use of precise molecular dynamics simulations. The numerical validation of the hypothesis involves three distinct archetype classes of nonlinear pair-interaction potentials: (i) a globally bounded pair interaction (the noted rotator model), (ii) unbounded interactions acting at large distances (the Fermi-Pasta-Ulam $\beta$ model, or the rotator model amended with harmonic pair interactions) and (iii), a pair interaction potential being unbounded at short distances while displaying an asymptotic free part (Lennard-Jones model).

arXiv commentNew J. Phys. (in press)

References in corpus (32)

• Thermal conduction in classical low-dimensional lattices
• Phononics: Manipulating heat flow with electronic analogs and beyond
• Length-dependent thermal conductivity in suspended single-layer graphene
• Heat Transport in low-dimensional systems
• Anomalous heat conduction in one dimensional momentum-conserving systems
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• High order symplectic integrators for perturbed Hamiltonian systems
• Heat conduction in one dimensional chains
• Finite thermal conductivity in 1d lattices
• Exact results for anomalous transport in one dimensional Hamiltonian systems
• Heat conduction in one dimensional nonintegrable systems
• Delocalization of wave packets in disordered nonlinear chains
• Heat conduction in the diatomic Toda lattice revisited
• Momentum conservation implies anomalous energy transport in 1d classical lattices
• 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
• Bulk Properties of Anharmonic Chains in Strong Thermal Gradients: Non-Equilibrium ${\varphi }^4$ Theory
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels
• Dynamical heat channels
• Energy carriers in the Fermi-Pasta-Ulam $\beta$ lattice: Solitons or Phonons?
• Exact solution of a Levy walk model for anomalous heat transport
• Perturbation spreading in many-particle systems: a random walk approach
• Diffusion of heat, energy, momentum, and mass in one-dimensional systems
• Equilibrium time-correlation functions for one-dimensional hard-point systems
• Wave scattering by discrete breathers
• Triggering waves in nonlinear lattices: Quest for anharmonic phonons and corresponding mean free paths
• Fourier law in a momentum-conserving chain
• Fluctuating hydrodynamics for a chain of nonlinearly coupled rotators
• Role of conserved quantities in normal heat transport in one dimenison

Cited by in corpus (25)

• Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation
• Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions
• Crossover from ballistic to normal heat transport in the ${\varphi }^4$ lattice: If nonconservation of momentum is the reason, what is the mechanism?
• Role of the range of the interactions in thermal conduction
• 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
• Crossover behavior of the thermal conductance and Kramers' transition rate theory
• Energy transport in the presence of long-range interactions
• Coupled transport in rotor models
• Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map
• Pressure-induced recovery of Fourier's law in one dimensional momentum-conserving systems
• Anomalous energy diffusion in two-dimensional nonlinear lattices
• Heat conduction and energy diffusion in momentum-conserving 1D full lattice ding-a-ling model
• Heat conduction in chains of non-locally coupled harmonic oscillators: mean-field limit
• Fluctuating hydrodynamics for a chain of nonlinearly coupled rotators
• Anomalous temperature-dependent heat transport in one-dimensional momentum-conserving systems with soft-type interparticle interaction
• Stretch diffusion and heat conduction in 1D nonlinear lattices
• Heat perturbations spreading in the Fermi-Pasta-Ulam-$\beta$ system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity
• Hydrodynamics and transport in the long-range-interacting ${\phi }^4$ chain
• Thermal Conduction in one dimensional ${\Phi }^4$ chains with colliding particles
• Temperature dependent divergence of thermal conductivity in momentum conserving 1D lattice with asymmetric potential
• Cluster sizes in a classical Lennard-Jones chain
• Confinement and non-universality of anomalous heat transport and superdiffusion of energy in low-dimensional systems
• Thermal transport characteristics of Fermi-Pasta-Ulam chains undergoing soft-sphere type collisions