First-passage times in phase space for the strong collision model

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Abstract
We consider the dynamics in phase space in which particles follow Newtonian trajectories that are randomly interrupted by collisions which equilibrate both the velocity and position of the particles. Collisions are assumed to be statistically independent events of zero duration and the intercollision time is a random variable with a negative exponential distribution. For this model, we derive an analytical expression for the Laplace transform of the survival probability and quadrature expressions for mean first-passage times.