  One-dimensional billiard, i.e. a chain of colliding particles with equal
masses, is well-known example of completely integrable system. Billiards with
different particles are generically not integrable, but still exhibit
divergence of a heat conduction coefficient (HCC) in thermodynamic limit.
Traditional billiard models imply instantaneous (zero-time) collisions between
the particles. We lift this condition and consider the heat transport in a
chain of stiff colliding particles with power-law potential of the
nearest-neighbor 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
profound physical consequence -- probability of multiple, in particular, triple
particle collisions becomes nonzero. Contrary to the integrable billiard of
equal particles, the modified model exhibits saturation of the heat conduction
coefficient for large system size. Moreover, identification of scattering
events with the triple particle collisions leads to simple definition of
characteristic mean free path and kinetic description of the heat transport.
This approach allows prediction both of 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 numeric simulations.
