A gaussian model of the dynamics of an inextensible chain

TL;DR

This paper introduces an approximate path integral model for the dynamics of an inextensible chain, relaxing nonlinear constraints and computing the probability function exactly under certain assumptions.

Contribution

It presents a novel approximation method for modeling inextensible chain dynamics using a relaxed constraint approach and solves the resulting nonlinear equations for long chains.

Findings

Probability function of chain configurations computed exactly.

Nonlinear equations for Lagrange multipliers solved for very long chains.

Method extends previous models for semi-flexible polymers to dynamic cases.

Abstract

In this work an approximated path integral model describing the dynamics of a inextensible chain is presented. To this purpose, the nonlinear constraints which enforce the property of inextensibility of the chain are relaxed and are just imposed in an average sense. This strategy, which has been originally proposed for semi-flexible polymers in statistical mechanics, is complicated in the case of dynamics by the extra dependence on the time variable and by the presence of nontrivial boundary conditions. Despite these complications, the probability function of the chain, which measures the probability to pass to a given initial conformation to a final one, is computed exactly. The Lagrange multiplier imposing the relaxed condition satisfies a complicated nonlinear equation, which has been solved assuming that the chain is very long.