Applications of a generalization of the nonlinear sigma model with O(d) group of symmetry to the dynamics of a constrained chain

TL;DR

This paper extends the generalized nonlinear sigma model to d-dimensional constrained chains, incorporating bending energy, and computes key dynamical observables for stiff chains, including form factors and topological constraints.

Contribution

The work generalizes the GNLSM to higher dimensions with added bending energy and introduces a topological variant using the Gauss linking invariant.

Findings

Computed the dynamical form factor for a ring chain.

Generalized the static form factor to dynamics.

Presented a topological model with linked chain constraints.

Abstract

Subject of this work are the applications of a field theoretical model, called here generalized nonlinear sigma model or simply GNLSM,to the dynamics of a chain subjected to constraints. Chains with similar properties and constraints have been discussed in a seminal paper of Edwards and Goodyear using an approach based on the Langevin equation. The GNLSM has been proposed in a previous publication in order to describe the dynamics of a two dimensional chain. In this paper the model is extended to d dimensions and a bending energy term is added to its action. As an application, two observables are computed in the case of a very stiff chain. The first observable is the dynamical form factor of a ring shaped chain. The second observable is a straightforward generalization to dynamics of the static form factor. This observable is relevant in order to estimate the average distance between two arbitrary points of the chain. Finally, a variant of the GNLNM is presented, in which the topological conditions which constrain the motion of two linked chains are imposed with the help of the Gauss linking invariant.