Path integrals for stiff polymers applied to membrane physics

Abstract

Path integrals similar to those describing stiff polymers arise in the Helfrich model for membranes. We show how these types of path integrals can be evaluated and apply our results to study the thermodynamics of a minority stripe phase in a bulk membrane. The fluctuation induced contribution to the line tension between the stripe and the bulk phase is computed, as well as the effective interaction between the two phases in the tensionless case where the two phases have differing bending rigidities.

11 pages RevTex, 4 figures

References in corpus (6)

• Phase ordering and shape deformation of two-phase membranes
• The two loop calculation of the disjoining pressure of a symmetric electrolyte soap film
• Field theoretic calculation of the surface tension for a model electrolyte system
• Electrostatic Fluctuations in Soap Films
• Fluctuation induced interactions between domains in membranes
• The thermal Casimir effect in lipid bilayer tubules

Cited by in corpus (11)

• Main phase transition in lipid bilayers: phase coexistence and line tension in a soft, solvent-free, coarse-grained model
• The out of equilibrium behavior of Casimir type fluctuation induced forces for free classical fields
• The effects of dielectric disorder on van der Waals interactions in slab geometries
• Thermal Casimir effect between random layered dielectrics
• On the distribution of estimators of diffusion constants for Brownian motion
• Distribution of the least-squares estimators of a single Brownian trajectory diffusion coefficient
• Path integrals for fractional Brownian motion and fractional Gaussian noise
• Thermal Casimir effect with soft boundary conditions
• Fluctuation mediated interactions due to rigidity mismatch and their effect on miscibility of lipid mixtures in multicomponent membranes
• Path integrals for higher derivative actions
• Pseudo-Casimir interactions and surface anchoring duality in bookshelf geometry of smectic-A liquid crystals