Coherent state field theory: A tool for inhomogeneous polymer dynamics and rheology

Abstract

A non-equilibrium framework is introduced for recasting microscopic kinetic models of polymer dynamics into a compact field-theoretic form. Specifically, we adapt the Doi–Peliti formalism, which transforms a classical many-body problem into a second-quantized Schrödinger equation that is subsequently expressed as a real-time path integral using a boson coherent state basis. The framework is well-suited to the analysis of non-equilibrium, spatially inhomogeneous systems, which is illustrated using a simple Brownian dynamics model of dumbbell polymers in implicit solvent. By invoking a mean-field approximation, equations are derived that describe the coupled dynamics of polymer concentration and stress to second order in spatial gradients. New stress–concentration coupling and stress diffusion terms are found to arise from non-bonded interactions and serve to generalize previous theories beyond the dilute limit. Strategies are discussed for exploring fluctuation effects beyond the mean-field approximation, both analytically and numerically via field-theoretic simulation. The method can be extended to a wide variety of non-equilibrium polymer models, including those with reversible or irreversible chemical reactions.