Rigorous Study of the Unbinding Transition of Biomembranes and Strings from Morse Potentials

Abstract

The purpose is an exact study of the unbinding transition from two interacting manifolds (strings or bilayer membranes). These systems have similar scaling behavior, and then it is sufficient to consider only the strings’ problem. We assume that the manifolds interact via a realistic potential of Morse type. To this end, the use is made of the transfer matrix method, based on the resolution of a Schrödinger equation. We first determine the associated bound states and energy spectrum. Second, the exact ground state energy gives the free energy density, from which we extract the expression of the unbinding temperature. Third, we determine the contact probability between manifolds, from which we compute the (diverging) average separation and roughness of the manifolds. It is found that their critical behavior is close to that obtained using Field-Theoretical Renormalization-Group. The conclusion is that these analytical studies reveal that the Morse potential is a good candidate for the study of the unbinding phenomenon within manifolds. Finally, the discussion is extended to generalized Morse potential.

Mechanics of Twisted DNA Molecule Adsorbed on a Biological Membrane

“…We take the results obtained in the case of unbinding transition from two interacting manifolds (strings or bilayer membranes), we find that near the transition temperature (is the similar case) [28], this average distance scale exactly as follows 1 1 , .…”