Dynamics of Selfavoiding Tethered Membranes II, Inclusion of Hydrodynamic Interaction (Zimm Model)

TL;DR

This paper investigates how hydrodynamic interactions influence the dynamic scaling of self-avoiding polymerized membranes and polymers, establishing a renormalizable theory and deriving the dynamical exponent z as equal to the embedding dimension d.

Contribution

It extends the understanding of membrane dynamics by including hydrodynamic interactions within a renormalizable framework applicable to both membranes and polymers.

Findings

The theory is renormalizable to all orders in perturbation theory.

The dynamical scaling exponent z equals the embedding dimension d.

Discussion of crossover behavior when hydrodynamic interactions become irrelevant.

Abstract

The dynamical scaling properties of selfavoiding polymerized membranes with internal dimension D embedded into d dimensions are studied including hydrodynamical interactions. It is shown that the theory is renormalizable to all orders in perturbation theory and that the dynamical scaling exponent z is given by z=d. The crossover to the region, where the membrane is crumpled swollen but the hydrodynamic interaction irrelevant is discussed. The results apply as well to polymers (D=1) as to membranes (D=2).