Simple One-Dimensional Model of Heat Conduction which Obeys Fourier’s Law

Abstract

We present the computer simulation results of a chain of hard-point particles with alternating masses interacting on its extremes with two thermal baths at different temperatures. We found that the system obeys Fourier's law at the thermodynamic limit. This result is against the actual belief that one-dimensional systems with momentum conservative dynamics and nonzero pressure have infinite thermal conductivity. It seems that thermal resistivity occurs in our system due to a cooperative behavior in which light particles tend to absorb much more energy than the heavier ones.

Nonequilibrium stationary state of a harmonic crystal with alternating masses

“…Temperature oscillations have earlier been observed in the steady state of the alternate mass hard particle gas [9] and in the Fermi-Pasta-Ulam chain [10] but in these cases the oscillations decay with system size. The case of temperature oscillations persisting for infinite system sizes is thus special to harmonic systems where heat is transmitted by non-interacting phonons.…”

“…In the context of testing Fourier's law and investigating the size-dependence of the current, various one-dimensional models with alternate masses have been studied [8][9][10]. Temperature oscillations have earlier been observed in the steady state of the alternate mass hard particle gas [9] and in the Fermi-Pasta-Ulam chain [10] but in these cases the oscillations decay with system size.…”

Nonequilibrium Energy Profiles for a Class of 1-D Models

“…In this respect, these models are closer to our earlier work [5] in which locked-in tracers were considered. Ding-a-ling and ding-dong models belong essentially to the same class [2,16,6,15].…”

Limited validity of the Kubo formula for thermal conduction in modular quantum systems

“…Thus it has often been pointed out that those concepts do not provide a rigorous justification of the KF for thermal conduction 5,11,12,13,14,15,16 which remains an open question. Furthermore, the KF has been counterchecked only for few concrete systems, see Refs.…”