A simple model of the charge transfer in DNA-like substances

Abstract

We present a very simple model for the study of charge transport in a molecule patterned on B-DNA. In this model we use a discrete non-linear Schr\"{o}dinger equation to describe electrons propagating along the sugar-phosphate backbone of the DNA molecule. We find that in this model, for a given nonlinearity, the transport is controlled by $J$, a parameter which relates to the electronic coupling between different molecules on the backbone. For smaller values of $J$ we have localised states while at higher values of $J$ the soliton field is spread out and through its interaction with the lattice it has stronger effects on the distortion of the lattice.