Abstract
In the present work, a method to impose the inextensibility constraints on the dynamics of a chain fluctuating in a thermal bath at fixed temperature is investigated. The final goal is to construct the probability function of the chain and the generating functional of the correlation functions of the relevant degrees of freedom of the system. First, we study the dynamics of a freely hinged chain composed by massive beads connected together by massless segments of fixed length. It is shown that a system of this kind may be described by a set of Langevin equations in which the noise is characterized by a non-gaussian probability distribution. Starting from these Langevin equations, the generating functional of the freely hinged chain is derived in path integral form. A connection with a stochastic process governed by a Fokker–Planck equation is established. Next, a chain composed by one-dimensional bars with constant mass distribution is considered. A path integral expression of the generating functional for a chain of this type is derived. Finally, it is verified that in the limit in which the chain becomes continuous, both generating functionals of the freely hinged chain and of the freely jointed bar chain converge to the same result as expected.
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