Dynamics of a three-dimensional inextensible chain

TL;DR

This paper explores the classical and statistical dynamics of a 3D inextensible chain, including a special case with fixed angles, using path integral methods to reduce the problem to a 2D scenario.

Contribution

It introduces a novel analysis of inextensible chain dynamics in three dimensions and reduces a special fixed-angle case to a two-dimensional problem via path integrals.

Findings

Classical and statistical dynamics of 3D inextensible chains are characterized.

A reduction method for fixed-angle chains to 2D is developed.

Path integral approach simplifies the analysis of specialized chain configurations.

Abstract

In the first part of this work the classical and statistical aspects of the dynamics of an inextensible chain in three dimensions are investigated. In the second part the special case of a chain admitting only fixed angles with respect to the $z-$axis is studied using a path integral approach. It is shown that it is possible to reduce this problem to a two-dimensional case, in a way which is similar to the reduction of the statistical mechanics of a directed polymer to the random walk of a two-dimensional particle.