Charged polymer in an electric field

The Brownian motion random-walk model of a polymer gives unphysical results for the case of a charged polymer in an electric field. To avoid these difficulties we use two stochastic processes in which the finiteness of the monomer size is retained. For a continuum model we use Kac’s telegrapher process. The relation of this to the Brownian motion picture corresponds to the relation between a Poisson process and its corresponding Wiener process. In both cases idealized and unrealistic properties of the Wiener process are avoided. Explicit results in any dimension are obtained by going over to a completely discrete process. By both methods, and in contrast to Brownian motion predictions, physically reasonable O(${\mathit{N}}^2$) dependence is found for the mean-squared extension of the size-N polymer. We also examine the breakdown of the Brownian motion approach by considering the effect of the electric field on the usual limiting process by which the discrete model becomes Brownian motion.