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).

New J. Phys. (in press)

References in corpus (6)

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• Heat Transport in low-dimensional systems
• Anomalous Heat Conduction and Anomalous Diffusion in Low Dimensional Nanoscale Systems
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Cited by in corpus (10)

• 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?
• Equilibrium dynamical correlations in the Toda chain and other integrable models
• Non-diffusive Lattice Thermal Transport in Si-Ge Alloy Nanowires
• Energy transport in the presence of long-range interactions
• Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map
• Fluctuating hydrodynamics for a chain of nonlinearly coupled rotators
• Cluster sizes in a classical Lennard-Jones chain
• Thermal transport characteristics of Fermi-Pasta-Ulam chains undergoing soft-sphere type collisions