Statistics of Gaussian Polymer Chains in Quadratic Applied Fields

This work derives statistics for a continuous Gaussian chain exposed to multidimensional, quadratic applied fields. Results include closed-form expressions for the partition function, moment generating function of the spatial distribution, total and potential energies, and radius of gyration of the chain. The sensitivity of the statistics to different initial distributions, chain lengths, and field strengths is discussed. The result is shown to be consistent with Monte Carlo simulations of discrete Gaussian chains for a wide logarithmic range of the aforementioned input parameters. The general nature of both the potential and the chain model allows for a variety of applications, including polymer confinement in a tube or channel, response of a polymeric material to traveling waves, etc.