title: Slow encounters of particle pairs in branched structures.
abstract: On infinite homogeneous structures, two random walkers meet with certainty if and only if the structure is recurrent; i.e., a single random walker returns to its starting point with probability 1. However, on general inhomogeneous structures this property does not hold, and, although a single random walker will certainly return to its starting point, two moving particles may never meet. This striking property has been shown to hold, for instance, on infinite combs. Due to the huge variety of natural phenomena which can be modeled in terms of encounters between two (or more) particles diffusing in comblike structures, it is fundamental to investigate if and, if so, to what extent similar effects may take place in finite structures. By means of numerical simulations we provide evidence that, indeed, even on finite structures, the topological inhomogeneity can qualitatively affect the two-particle problem. In particular, the mean encounter time can be polynomially larger than the time expected from the related one-particle problem.
authors.affiliation: Dipartimento di Fisica, Sapienza Università di Roma, Rome, Italy and INdAM, Gruppo Collegato di "Tor Vergata," Rome, Italy.
authors.forename: Elena
authors.initials: E
authors.lastname: Agliari
authors.affiliation: Theoretische Polymerphysik, Universität Freiburg, Freiburg, Germany.
authors.forename: Alexander
authors.initials: A
authors.lastname: Blumen
authors.affiliation: Dipartimento di Fisica, Università di Parma, Parma, Italy.
authors.forename: Davide
authors.initials: D
authors.lastname: Cassi