2ND-ORDER DICHOTOMOUS PROCESSES - DAMPED FREE MOTION, CRITICAL-BEHAVIOR, AND ANOMALOUS SUPERDIFFUSION

We study damped inertial processes driven by dichotomous Markov noise in the absence of a potential. We obtain exact differential equations for the joint probability density and for the marginal densities of ve locity and position. Several aspects of the critical behavior of the s ystem are examined in detail. The exact equation for the displacement of a free Brownian particle is also found, and from this equation we s tudy the damping effects on the mean-square displacement [X2(t)], by e valuating the dynamical exponent and showing a crossover from a superd iffusive motion of the form [X2(t)] approximately t3 to ordinary diffu sion where [X2(t)] approximately t.