Localization in simple multiparticle catalytic absorption model

TL;DR

This paper investigates a phase transition phenomenon in a system of many independent random walks on a halfline, where localization at the origin occurs depending on the well depth's growth rate, with implications for polymer physics.

Contribution

It introduces a model of multiparticle random walks with a variable well depth at the origin and analyzes the conditions leading to simultaneous localization.

Findings

Localization occurs when well depth grows faster than 3/2 n ln(n).

All walks become localized at the origin under certain growth conditions.

Connects the phase transition to copolymer chain behavior with quenched disorder.

Abstract

We consider the phase transition in the system of n simultaneously developing random walks on the halfline x>=0. All walks are independent on each others in all points except the origin x=0, where the point well is located. The well depth depends on the number of particles simultaneously staying at x=0. We consider the limit n>>1 and show that if the depth growth faster than 3/2 n ln(n) with n, then all random walks become localized simultaneously at the origin. In conclusion we discuss the connection of that problem with the phase transition in the copolymer chain with quenched random sequence of monomers considered in the frameworks of replica approach.