The Hartree approximation in dynamics of polymeric manifolds in the melt

The Martin-Siggia-Rose functional integral technique is applied to the dyna mics of a D-dimensional manifold in a melt of similar manifolds. The integr ation over the collective variables of the melt can be simply implemented i n the framework of the dynamical random phase approximation. The resulting effective action functional of the test manifold is treated by making use o f the self-consistent Hartree approximation. As an outcome the generalized Rouse equation of the test manifold is derived and its static and dynamic p roperties are studied. It was found that the static upper critical dimensio n, d(uc)= 2D/(2-D), discriminates between Gaussian (or screened) and non-Ga ussian regimes, whereas its dynamical counterpart, (d) over tilde(uc) = 2d( uc), distinguishes between the simple Rouse and the renormalized Rouse beha vior. We have argued that the Rouse mode correlation function has a stretch ed exponential form. The subdiffusional exponents for this regime are calcu lated explicitly. The special case of linear chains, D = 1, shows good agre ement with Monte-Carlo simulations. (C) 1999 American Institute of Physics. [S0021-9606(99)50601-6].