Description of the dynamics of a random chain with rigid constraints in the path integral framework

TL;DR

This paper analyzes the dynamics of a three-dimensional chain with rigid constraints using the path integral framework, providing probability distributions for entangled chains and special cases with discrete angles.

Contribution

It introduces a path integral approach to model the dynamics of constrained chains and derives probability distributions for entangled configurations.

Findings

Probability distribution for two topologically entangled chains

Analysis of chains with discrete angle constraints

Application of nonlinear sigma model to chain dynamics

Abstract

In this work we discuss the dynamics of a three dimensional chain which is described by generalized nonlinear sigma model The formula of the probability distribution of two topologically entangled chain is provided. The interesting case of a chain which can form only discrete angles with respect to the $z-$axis is also presented.