Thermal conductivity and bulk viscosity in quartic oscillator chains

Abstract

We propose a relation which predicts the low-frequency thermal conductivity of a one-dimensional (1D) system from the thermal conductivity and bulk viscosity at higher frequency. Our theory is based on the assumption that "ballistic" transport by sound waves dominates the heat transport. For a system with equal heat capacities (c(p) = c(v)) this relation is particularly simple. We test the prediction by simulating a chain of particles with quartic interparticle potentials under zero pressure conditions. As the frequency omega --> 0 the theory predicts that the energy current power spectrum diverges as omega(-1/2), not seen in previous simulations. Because we simulate very long chains to long times we do observe the crossover into this regime. The bulk viscosity of a 1D chain has been determined via simulation. It is found to be finite for our system, in contrast to the thermal conductivity which is infinite.

Anomalous kinetics and transport from 1D self-consistent mode-coupling theory

“…In fact, taking the oscillations into account, we find that the decay of the envelope M (q, t) depends on the order of the leading nonlinearity of the theory. In the cubic case, M ∝ t −2/3 , while a faster decay, M ∝ t −1 , is found in the quartic one, see equations (17,31). As a consequence, in the two cases, the decay of G(q, t) is, respectively, anomalous (i.e.…”

“…Such an analysis, that applies to quartic nonlinearity, predicts the same behavior for κ as ours, as well as a finite η. As the Authors of reference [31] pointed out, the cubic case requires a fully self-consistent calculation which is precisely the task we accomplished here. Moreover, as already remarked, we conclude that both transport coefficients diverge.…”

“…In addition, we argue that since M and J(t)J(0) decay with the same power-law, η should scale in the same way as κ. A few words are also needed to comment about the definition of the second class, which is identified in the present paper from the vanishing of the cubic term in the expansion of the effective potential (1), while in [31] from the equality between constant-pressure and constant-volume specific heats. At least in the FPU-β model both constraints are simultaneously fulfilled.…”

Fluctuating Hydrodynamics Approach to Equilibrium Time Correlations for Anharmonic Chains

“…Because of the relation (5.3), in many MD simulations the total energy current correlation J 3 (t); J 3 (0) is measured as an addition to steady state transport [51,52]. There are also MD simulations exclusively focussed on momentum and energy current correlations [53]. However simulations of correlations of the conserved fields have been fairly scarce until recently.…”

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

“…It has been argued that this case belongs to a different universality class. This has been tested numerically in the FPU-β model, where the displacement symmetry is a straightforward consequence of a purely quartic nonlinearity [13][14][15], in the hard-point-chain model at zero pressure [16], and in the FPU-α + β model, where the displacement symmetry can be imposed by applying suitable pressure at the chain boundaries [17]. It has been further pointed out that such a case corresponds to the special thermodynamic condition, for which the specific heat capacities at constant volume and pressure are equal [18].…”