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Mathematical Physics Seminar

Geometrical frustration and fractional defect charges on cones

David R. Nelson - Harvard University

Location:  Zoom
Date & time: Wednesday, 13 July 2022 at 10:45AM - 11:45AM

Abstract: The difficulty of constructing ordered states on spheres, an example of geometrical frustration, was recognized by J. J. Thomson, who discovered the electron and then attempted regular tilings of the sphere in an ill-fated attempt to explain the periodic table. We first discuss how protein packings in virus shells (like the corona virus) solve a related “Thomson problem”, and the remarkable modifications in the theory necessary to account for grain boundary scars in colloidal particles packed on spheres. We then demonstrate that liquid crystals on cones provide a soft matter analog of the Aharonov-Bohm effect, with defect textures again frustrated due to parallel transport. These materials are characterized by a fractional topological charges at the apex, and an unusual defect-unbinding transition at finite temperatures. We check our predictions numerically for a set of commensurate cone angles, whose surfaces can be polygonized as a perfect triangular or square meshes. When tangential boundary conditions are applied at the base, the cone apex absorbs and emits quantized defect charges into the ground state, as function of cone angle.

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