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arXiv · 0807.4045

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

Franco Ferrari·Jaroslaw Paturej·T. A. Vilgis
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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.

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Franco Ferrari, Jaroslaw Paturej, T. A. Vilgis. 2008-10-25. Applications of a generalization of the nonlinear sigma model with O(d) group of symmetry to the dynamics of a constrained chain. https://arxiv.org/abs/0807.4045

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