Collision properties of one-dimensional granular particles with internal degrees of freedom

Starting from a microscopic model of interacting elastic rods, we derive an effective dissipative dynamics for the translational motion, when the internal degrees of freedom, i.e., the vibrations of the rods, are represented by a thermalized bath. Focusing on two-particle collisions, we calculate the coefficient of restitution epsilon as a function of the relative length of the colliding rods, the center of mass velocity, and the degree of excitation of the internal vibrations. In general, epsilon is a stochastic quantity; its distribution is interpreted as the transition probability for the Markovian jump process, which describes the loss of translational energy in successive two-particle collisions.