VARIATIONAL-METHODS FOR CONSTRAINED POLYMER DYNAMICS

The dynamics of an idealized polymer chain (bead-spring model) is trea ted as a special case of Brownian motion in a potential. In free space the corresponding Langevin description is sufficient. In the presence of constraints on the dynamics one has to apply the full Fokker-Planc k formalism. In general, the ensuing boundary value problem is not ana lytically solvable, so we resort to approximation methods. For diffusi ve motion in a potential there exists a natural Hilbert space on which the Fokker-Planck operator is positive (semi-)definite. Consequently, the problem is amenable to variational methods. Here, we investigate exemplarily the relaxation of a Rouse chain fixed with one end to a pl anar, impenetrable surface and obtain the relaxation spectrum approxim ately using the Rayleigh-Ritz scheme. This may be the first instance i n which this formalism is applied to polymer dynamics.