A path integral approach to the dynamics of random chains

Abstract

In this work the dynamics of a freely jointed random chain with small masses attached to the joints is studied from a microscopic point of view. The chain is treated using a stringy approach, in which a statistical sum is performed over all two dimensional trajectories spanned by the chain during its fluctuations. In the limit in which the chain becomes a continuous curve, the probability function for such a system coincides with the partition function of a generalized nonlinear sigma model. The cases of open or closed chains in two and three dimensions are discussed. In three dimensions it is possible also to introduce some rigidity at the joints, allowing the segments of the chain to take only particular angles with respect to a given direction.

arXiv comment23 pages, 4 figures, LaTeX + RevTeX 4

References in corpus (6)

• Addendum to paper: Strong-Coupling Behavior of ${\varphi }^4$-Theories and Critical Exponents [Phys. Rev. D 57, 2264 (1998)]
• Tension dynamics in semiflexible polymers. Part I: Coarse-grained equations of motion
• Propagation and Relaxation of Tension in Stiff Polymers
• Strong-Coupling ${\varphi }^4$-Theory in $4-\epsilon$ Dimensions and Critical Exponents
• Field Theory of N Entangled Polymers
• Constrained dynamics of a polymer ring enclosing a constant area

Cited by in corpus (3)

• On the connection of the generalized nonlinear sigma model with constrained stochastic dynamics
• From constrained stochastic processes to the nonlinear sigma model. Two old problems revisited
• Dynamical aspects of inextensible chains