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Condensed Matter Theory Group Seminar
The Casimir effect in two dimensions and the Weyl problem
Date: Monday, June 6th
Time: 10:00 am
Place: 5280 Chamberlin
Speaker: Luke Langsjoen, University of Virginia
Abstract: A field theoretical technique for a massless scalar field is used to calculate the Casimir energy of the modes removed by the introduction of a smooth, Dirichlet boundary into two dimensional space. There are formally divergent, cutoff dependent parts of the Casimir energy that are disregarded as unphysical in many treatments of the Casimir effect. However, we show that these contributions are related to geometric properties of the boundary and may be physically relevant. These formally divergent contributions are shown to be closely related to the Weyl problem of the asymptotic distribution of the eigenvalues of the Laplacian. Our results explain why formal regularization techniques fail in even dimension, and we correct the sign of the vacuum induced coefficient of linear tension given in previous treatments. <br>
Host: Maxim Vavilov & Robert Joynt
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