Heat conduction in a chain of colliding particles with a stiff repulsive potential
Abstract
Onedimensional billiards, i.e., a chain of colliding particles with equal masses, is a wellknown example of a completely integrable system. Billiards with different particle masses is generically not integrable, but it still exhibits divergence of a heat conduction coefficient (HCC) in the thermodynamic limit. Traditional billiards models imply instantaneous (zerotime) collisions between the particles. We relax this condition of instantaneous impact and consider heat transport in a chain of stiff colliding particles with the powerlaw potential of the nearestneighbor interaction. The instantaneous collisions correspond to the limit of infinite power in the interaction potential; for finite powers, the interactions take nonzero time. This modification of the model leads to a profound physical consequence—the probability of multiple (in particular triple) particle collisions becomes nonzero. Contrary to the integrable billiards of equal particles, the modified model exhibits saturation of the heat conduction coefficient for a large system size. Moreover, the identification of scattering events with tripleparticle collisions leads to a simple definition of the characteristic mean free path and a kinetic description of heat transport. This approach allows us to predict both the temperature and density dependencies for the HCC limit values. The latter dependence is quite counterintuitive—the HCC is inversely proportional to the particle density in the chain. Both predictions are confirmed by direct numerical simulations.
 Publication:

Physical Review E
 Pub Date:
 November 2016
 DOI:
 10.1103/PhysRevE.94.052137
 arXiv:
 arXiv:1609.00564
 Bibcode:
 2016PhRvE..94e2137G
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 6 pages, 7 figures