Dynamical Eigenmodes of a Polymerized Membrane

Abstract

We study the bead-spring model for a polymerized phantom membrane in the overdamped limit, which is the two-dimensional generalization of the well-known Rouse model for polymers. We derive the {\it exact} eigenmodes of the membrane dynamics (the "Rouse modes"). This allows us to obtain exact analytical expressions for virtually any equilibrium or dynamical quantity for the membrane. As examples we determine the radius of gyration, the mean square displacement of a tagged bead, and the autocorrelation function of the difference vector between two tagged beads. Interestingly, even in the presence of tensile forces of any magnitude the Rouse modes remain the exact eigenmodes for the membrane. With stronger forces the membrane becomes essentially flat, and does not get the opportunity to intersect itself; in such a situation our analysis provides a useful and exactly soluble approach to the dynamics for a realistic model flat membrane under tension.

17 pages, 4 figures, minor changes, references updated, to appear in JSTAT

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Cited by in corpus (5)

• Dynamics of a tagged monomer: Effects of elastic pinning and harmonic absorption
• Dynamical Scaling of Polymerized Membranes
• Complementary mode analyses between sub- and super-diffusions
• Generalised Langevin Equation Formulation for Anomalous Diffusion in the Ising Model at the Critical Temperature
• Approximate dynamical eigenmodes of the Ising model with local spin-exchange moves