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 comb-like 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 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.

8 pages, 12 figures; accepted for publication in Physical Review E

References in corpus (2)

• First-passage times in complex scale-invariant media
• Fractal and Transfractal Recursive Scale-Free Nets

Cited by in corpus (17)

• Diffusion and subdiffusion of interacting particles on comb-like structures
• From compact localized states to many-body scars in the random quantum comb
• The two-particle problem in comb-like structures
• Statistics of boundary encounters by a particle diffusing outside a compact planar domain
• First-encounter time of two diffusing particles in confinement
• Hitting and Trapping Times on Branched Structures
• Mesoscopic description of random walks on combs
• Statistics of diffusive encounters with a small target: Three complementary approaches
• First encounters on Bethe Lattices and Cayley Trees
• Mean encounter times for multiple random walkers on networks
• Interplay between particle trapping and heterogeneity in anomalous diffusion
• Biased random walk on random networks in presence of stochastic resetting: Exact results
• First-encounter time of two diffusing particles in two- and three-dimensional confinement
• Information Dimension of Stochastic Processes on Networks: Relating Entropy Production to Spectral Properties
• Asymmetric simple exclusion process on a random comb: Transport properties in the stationary state
• Smart Walkers in Discrete Space
• Dynamics of soft interacting particles on a comb