Exact Solution to Ideal Chain with Fixed Angular Momentum

TL;DR

This paper derives an exact analytical expression for the radius of gyration of a ring polymer with fixed angular momentum, revealing how angular momentum influences polymer size in statistical mechanics.

Contribution

It provides the first exact solution for the radius of gyration of a polymer with fixed angular momentum using functional integration techniques.

Findings

Radius of gyration differs from a random walk even at zero angular momentum

Exact closed-form expression for the radius of gyration with fixed angular momentum

Large angular momentum limit explained by physical arguments

Abstract

The statistical mechanics of a non-interacting polymer chain in the limit of a large number of monomers is considered when the total angular momentum, L, is fixed. The radius of gyration for a ring polymer in this situation is derived exactly in closed form by functional integration techniques. Even when L = 0 the radius of gyration differs from that of a random walk by a prefactor of order unity. The dependence on L is discussed qualitatively and the large L limit can be understood by physical arguments.