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

Abstract

For a one-dimensional (1D) momentum conserving system, intensive studies have shown that generally its heat current autocorrelation function (HCAF) tends to decay in a power-law manner and results in the breakdown of the Fourier heat conduction law in the thermodynamic limit. This has been recognized to be a dominant hydrodynamic effect. Here we show that, instead, the kinetic effect can be dominant in some cases and leads to the Fourier law for finite-size systems. Usually the HCAF undergoes a fast decaying kinetic stage followed by a long slowly decaying hydrodynamic tail. In a finite range of the system size, we find that whether the system follows the Fourier law depends on whether the kinetic stage dominates. Our Rapid Communication is illustrated by the 1D hard-core gas models with which the HCAF is derived analytically and verified numerically by molecular dynamics simulations.

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

“…Yet, more compelling evidence of a seemingly normal transport has been found in a Toda lattice under the action of an additional conservative noise [35] and in the diatomic hard point gas (HPG) [36] (see also Ref. [37]). In the first context, successive studies showed that the diffusive regime is a finite-size effect, whereby anomalous behavior is recovered for large enough L [38,39] (see also the discussion based on mode-coupling arguments in Ref.…”

“…Nevertheless, the successful implementation of our scaling arguments provides a convincing explanation of the seemingly normal diffusion observed not only in Refs. [35][36][37], used as our test beds, but also in many nonlinear chains like those discussed in Refs. [38,39] where the potential is "well approximated" by the Toda one.…”

Heat conduction in a three-dimensional momentum-conserving fluid

“…In addition, our results suggest that the dimensionality-crossover behavior of heat conduction in 3D lattices [30,31] can also take place in 3D fluids. Remarkably, the quasi-1D fluid displays the same transition from a normal to abnormal behavior for large enough longitudinal sizes, characteristic of strictly 1D models [40,[49][50][51]. This stems from the fact that abnormal (hydrodynamic) effects can be only observed on scales that can be much larger than the typical kinetic mean-free-path [40].…”

A splash in a one-dimensional cold gas

“…This system is non-integrable, has good thermalization behavior, and continues to have an ideal gas equation of state. The alternating hard particle (AHP) gas has been extensively investigated in the context of studies on heat transport and hydrodynamics in one dimension [5][6][7][8][9][10][11][12][13][14][15]. In recent work [16,17], the AHP model was used for a numerical verification of the equivalence of the continuum hydrodynamics description and the Newtonian description in the context of the socalled blast problem.…”