Fourier heat conduction as a strong kinetic effect in one-dimensional hard-core gases

Effect of pressure on thermalization of one-dimensional nonlinear chains

Pressure plays a vital role in changing the transport properties of matter. To understand this phenomenon at a microscopic level, we here focus on a more fundamental problem, i.e., how pressure affects the thermalization properties of solids. As illustrating examples, we study the thermalization behavior of the monatomic chain and the mass-disordered chain of Fermi-Pasta-Ulam-Tsingou-β under different strains in the thermodynamic limit. It is found that the pressure-induced change in integrability results in qualitatively different thermalization processes for the two kinds of chains. However, for both cases, the thermalization time follows the same law-it is inversely proportional to the square of the nonintegrability strength. This result suggests that pressure can significantly change the integrability of a system, which provides a new perspective for understanding the pressure-dependent thermal transport behavior.

Blast in a One-Dimensional Cold Gas: From Newtonian Dynamics to Hydrodynamics

A gas composed of a large number of atoms evolving according to Newtonian dynamics is often described by continuum hydrodynamics. Proving this rigorously is an outstanding open problem, and precise numerical demonstrations of the equivalence of the hydrodynamic and microscopic descriptions are rare. We test this equivalence in the context of the evolution of a blast wave, a problem that is expected to be at the limit where hydrodynamics could work. We study a one-dimensional gas at rest with instantaneous localized release of energy for which the hydrodynamic Euler equations admit a self-similar scaling solution. Our microscopic model consists of hard point particles with alternating masses, which is a nonintegrable system with strong mixing dynamics. Our extensive microscopic simulations find a remarkable agreement with Euler hydrodynamics, with deviations in a small core region that are understood as arising due to heat conduction.

Heat conduction in a three-dimensional momentum-conserving fluid

Size dependence of energy transport and the effects of reduced dimensionality on transport coefficients are of key importance for understanding nonequilibrium properties of matter on the nanoscale. Here, we perform nonequilibrium and equilibrium simulations of heat conduction in a three-dimensional (3D) fluid with the multiparticle collision dynamics, interacting with two thermal walls. We find that the bulk 3D momentum-conserving fluid has a finite nondiverging thermal conductivity. However, for large aspect ratios of the simulation box, a crossover from 3D to one-dimensional (1D) abnormal behavior of the thermal conductivity occurs. In this case, we demonstrate a transition from normal to abnormal transport by a suitable decomposition of the energy current. These results not only provide a direct verification of Fourier's law, but also further confirm the validity of existing theories for 3D fluids. Moreover, they indicate that abnormal heat transport persists also for almost 1D fluids over a large range of sizes.

Heat conduction in two-dimensional momentum-conserving and -nonconserving gases

Compared to that for two-dimensional (2D) lattices, our understanding of heat conduction in 2D gases is still limited. Here we study heat conduction behavior of 2D gas systems with momentum-conserving and -nonconserving interparticle interactions by using the nonequilibrium and equilibrium molecular dynamics methods. For the momentum-conserving system, we find that when the dimensionality of the system is changed from 2D to quasi-one-dimensional (quasi-1D), the heat conductivity κ diverges with the system size L as κ∼lnL (the theoretical prediction for 2D systems) for a short L and shows, in the thermodynamic limit, a tendency to κ∼L^{1/3} like that predicted in 1D fluids. This suggests that the dimensional-crossover effect of heat conduction exists in 2D systems with conserved momentum. In contrast, for the momentum-nonconserving system, as L increases, finite heat conductivity independent of L is observed. These findings are in agreement with the predictions given by hydrodynamic theory and thus further confirm the validity of the theory in 2D gases.

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

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 that 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 quasiparticles with a very large mean free path ℓ. 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.

Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas

A recently developed nonlinear fluctuating hydrodynamics theory has been quite successful in describing various features of anomalous energy transport. However, the diffusion and the noise terms present in this theory are not derived from microscopic descriptions but rather added phenomenologically. We here derive these hydrodynamic equations with explicit calculation of the diffusion and noise terms in a one-dimensional model. We show that in this model the energy current scales anomalously with system size L as ∼L^{-2/3} in the leading order with a diffusive correction of order ∼L^{-1}. The crossover length ℓ_{c} from diffusive to anomalous transport is expressed in terms of microscopic parameters. Our theoretical predictions are verified numerically.