Many random transport phenomena, such as radiation propagation, chemical/biological species migration, or electron motion, can be described in terms of particles performing { \em exponential flights}. For such processes, we sketch a general approach (based on the Feynman-Kac formalism) that is amenable to explicit expressions for the moments of the number of collisions and the residence time that the walker spends in a given volume as a function of the particle equilibrium distribution. We then illustrate the proposed method in the case of the so-called { \em rod problem} (a 1d system), and discuss the relevance of the obtained results in the context of Monte Carlo estimators.
Categories: cond-mat.stat-mech