Delocalization of two interacting particles in a random potential: One-dimensional electric interaction

We consider a continuous one-dimensional model of two charged interacting particles in a random potential. The electric repulsion is strictly one dimensional and it inhibits Anderson localization. In fact, the spectrum is continuous. The case of electrical attraction is briefly studied and it shows bounded states. So, the dynamics is sign dependent for this model. We support our analytical results with numerical simulations where the effect of repulsion breaking localization is clearly observed.