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Topological properties of static and dynamic defect configurations in ordered liquids

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  • Holz, A.

Abstract

The topology of linked disclinations is studied in uniaxial nematic liquids and in anisotropic liquids with an order parameter space SO(3)/Pi(3). In these models {Pi(3)} are the finite point symmetry groups of 3-space with applications to helium 3 (Pi(3) = I), biaxial nematic liquid (Pi(3) = D2), and anisotropic super cooled liquids (Pi(3) = groups of Platonic solids). The topological properties are studied via Hopf's invariant of the O(3) σ model and its relation to the Wess-Zumino term of the SO(3)/Pi(3) σ model in an orthonormal drei-bein representation of SO(3). Dynamic processes are topology changing during intersection of disclinations and are studied via “magnetic” N-pole singularities and the instanton number η in an “electromagnetic” formalism. The connection with tunneling amplitudes in a SO(3) Yang-Mills theory is indicated. Applications of the theory to topological fluid dynamics is worked out for the uniaxial nematic liquid and indicated for the SO(3) spin liquid.

Suggested Citation

  • Holz, A., 1992. "Topological properties of static and dynamic defect configurations in ordered liquids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 182(1), pages 240-278.
    • Handle: RePEc:eee:phsmap:v:182:y:1992:i:1:p:240-278
    DOI: 10.1016/0378-4371(92)90241-H
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    1. Gong, Shang-Chi, 1988. "The Taiwanese livestock and feedgrain markets and policies," ISU General Staff Papers 198801010800009845, Iowa State University, Department of Economics.
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