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One-dimensional billiard, i.e. a chain of colliding particles with equalmasses, is well-known example of completely integrable system. Billiards withdifferent particles are generically not integrable, but still exhibitdivergence of a heat conduction coefficient (HCC) in thermodynamic limit.Traditional billiard models imply instantaneous (zero-time) collisions betweenthe particles. We lift this condition and consider the heat transport in achain of stiff colliding particles with power-law potential of thenearest-neighbor interaction. The instantaneous collisions correspond to thelimit of infinite power in the interaction potential; for finite powers, theinteractions take nonzero time. This modification of the model leads toprofound physical consequence -- probability of multiple, in particular, tripleparticle collisions becomes nonzero. Contrary to the integrable billiard ofequal particles, the modified model exhibits saturation of the heat conductioncoefficient for large system size. Moreover, identification of scatteringevents with the triple particle collisions leads to simple definition ofcharacteristic mean free path and kinetic description of the heat transport.This approach allows prediction both of temperature and density dependenciesfor the HCC limit values. The latter dependence is quite counterintuitive - theHCC is inversely proportional to the particle density in the chain. Bothpredictions are confirmed by direct numeric simulations.

Heat conduction in a chain of colliding particles with stiff repulsive potential