Coherent propagation of interacting particles in a random potential: the Mechanism of enhancement

TL;DR

This paper investigates how interactions between two particles in a one-dimensional weak random potential can enhance their localization length, revealing a different mechanism than previously thought, supported by analytical and numerical analysis.

Contribution

It introduces a new mechanism for localization length enhancement in interacting particles and provides an analytical and numerical framework to understand it.

Findings

Enhancement mechanism differs from previous models.

Numerical simulations support the relation l_2/l_1 ~ l_1^γ.

Strong interactions do not enhance propagation, l_2 ≈ l_1.

Abstract

Coherent propagation of two interacting particles in $1d$ weak random potential is considered. An accurate estimate of the matrix element of interaction in the basis of localized states leads to mapping onto the relevant matrix model. This mapping allows to clarify the mechanism of enhancement of the localization length which turns out to be rather different from the one considered in the literature. Although the existence of enhancement is transparent, an analytical solution of the matrix model was found only for very short samples. For a more realistic situation numerical simulations were performed. The result of these simulations is consistent with l_{2}/l_1 \sim l_1^{\gamma} , where $l_1$ and $l_2$ are the single and two particle localization lengths and the exponent $\gamma$ depends on the strength of the interaction. In particular, in the limit of strong particle-particle interaction there is no enhancement of the coherent propagation at all ($l_{2} \approx l_1$).