Abstract
We consider a particle randomly accelerated by Gaussian white noise on the half-line x>0. The collisions of the particle with the wall at x=0 are inelastic. The velocities just before and after reflection are related by v(f)=-rv(i), where r is the coefficient of restitution. Cornell, Swift, and Bray have shown that for r<r(c)=e(-pi/sqrt[3])=0.163, there is inelastic collapse, i.e., boundary collisions localize the particle at x=0. The probability that the particle is not yet absorbed at the boundary after a time t decays, for long times, as t(-straight theta(r)). The exponent straight theta(r) is calculated exactly. We also consider the case of "partial-survival" boundary conditions, i.e., elastic reflection with probability p and absorption with probability 1-p, and derive the analogous persistence exponent straight phi(p). The exact exponents satisfy the Swift-Bray conjecture straight theta(r)=straight phi(r(2straight theta(r))).
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