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

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.