Spinor representation of surfaces and complex stresses on membranes and interfaces

Details Spinor representation of surfaces and complex stresses on membranes and interfaces Spinor representation of surfaces and complex stresses on membranes and interfaces

2010-01-08

arxiv.org/abs/1001.1183v2

Phy. Rev. E 82, 041604 (2010)

Physics

Condensed Matter

Soft Condensed Matter

17 pages

Scientific paper

10.1103/PhysRevE.82.041604

Variational principles are developed within the framework of a spinor representation of the surface geometry to examine the equilibrium properties of a membrane or interface. This is a far-reaching generalization of the Weierstrass-Enneper representation for minimal surfaces, introduced by mathematicians in the nineties, permitting the relaxation of the vanishing mean curvature constraint. In this representation the surface geometry is described by a spinor field, satisfying a two-dimensional Dirac equation, coupled through a potential associated with the mean curvature. As an application, the mesoscopic model for a fluid membrane as a surface described by the Canham-Helfrich energy quadratic in the mean curvature is examined. An explicit construction is provided of the conserved complex-valued stress tensor characterizing this surface.

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