  A stochastic field theory approach is applied to a coarse-grained polymer
model that will enable studies of polymer behavior under non-equilibrium
conditions. This article is focused on the validation of the new model in
comparison to explicit Langevin equation simulations under conditions with
analytical solutions. The polymers are modeled as Hookean dumbbells in one
dimension, without including hydrodynamic interactions and polymer-polymer
interactions. Stochastic moment equations are derived from the full field
theory. The accuracy of the field theory and moment equations are quantified
using autocorrelation functions. The full field theory is only accurate for
large number of polymers due to keeping track of rare occurrences of polymers
with a large stretch. The moment equations do not have this error because they
do not explicitly track these configurations. The accuracy of both methods
depends on the spatial degree of discretization. The timescale of decorrelation
over length scales bigger than the spatial discretization is accurate, while
there is an error over the scale of single mesh points.
