Asymptotics of the scattering problem for a system of one-dimensional particles

It was shown by Sinai [1] that an infinite ensemble of one-dimensional particles interacting through a finite-range potential with a hard core breaks up into clusters, each of which moves for a certain time independently of the others. The present paper investigates the evolution of a cluster that collides with a “hot” particle. It is shown that as a result of the collision the particle at the extreme end of the cluster acquires a velocity close to the initial velocity of the “hot” particle. The asymptotic behavior of the difference between the velocities of the incident particle and the separated particle when the initial velocity of the hot particle tends to infinity is found.