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Applied Mathematics Colloquium

Friday, December 9,  2005, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

A Second Modulus of Elasticity For an Ensemble of Vortex Lines - new vortex matter in

superfluid He4 and superconductors

Chjan Lim

Department of Mathematical Sciences

RPI    

Troy, NY

Abstract

Ensembles of vortex lines have been found in rotating superfluid He 4, high temperature superconductors and more recently in Bose-Einstein condensates of trapped ions, where they appear as quantized line defects. It is well known in the new vortex matter community, that at lower temperatures, the vortex line ensemble form a crystalline solid and has an elastic modulus associated with its 2D cross-sectional lattice structure. At high temperatures T >> 1, this vortex lattice melts and Monte-Carlo simulations of Andersen and Lim show that it then behaves like a vortex liquid of hard disks of radius r(T) (non-interacting except for the non-overlap condition). In this talk, I will derive a second modulus of elasticity E for the vortex line ensemble at high temperatures. Unlike the first elastic modulus of the vortex lattice which is energetic in nature (calculated on the basis of minimizing the internal energy), the second modulus of elasticity is entropic in nature. Numerical evidence of my theoretical prediction of a second (entropic) elastic modulus for vortex lines is found in the incompressibility of the vortex liquid of hard disks. Moduli of elasticity of an entropic nature have been found in cross-linked polymer chains such as natural vulcanized Rubber and in soft condensed matter such as actin bundles.