Localization of a pair of bound particles in a random potential

TL;DR

This paper investigates how the localization length of a bound particle pair in a 1D random potential depends on the interaction potential and the number of bound states, revealing proportionality to the number of states and sensitivity to interaction shape.

Contribution

It provides an analytical understanding of how interaction potential shape and bound state number influence localization length in disordered systems.

Findings

Localization length is proportional to the number of bound states N.

Exact solution for two bound states shows dependence on interaction shape.

Localization length varies with interaction potential symmetry.

Abstract

We study the localization length of a pair of two attractively bound particles moving in a one-dimensional random potential. We show in which way it depends on the interaction potential between the constituents of this composite particle. For a pair with many bound states N the localization length is proportional to N, independently of the form of the two particle interaction. For the case of two bound states we present an exact solution for the corresponding Fokker-Planck equation and demonstrate that the localization length depends sensitively on the shape of the interaction potential and the symmetry of the bound state wave functions.