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Some variational problems arising in condensed matter physics

Abstract : In chapter 1, we compute the infimum of an energy with measurable weight over a class of S2-valued maps with prescribed singularities. We prove that such quantity induces a distance. This result allows us to determine in chapter 2, a relaxed type energy for maps with values into the sphere. The explicit formula involves the length of a minimal connection between the topological singularities. In chapter 3, we investigate the physical model for a 2d rotating Bose-Einstein condensate. We estimate the critical velocity of rotation for having d vortices and we determine their location. In chapter 4, we study the asymptotic behavior of minimizers of a Ginzburg-Landau energy with epsilon-depending weight. We prove a pinning effect of the limiting singularities. In chapter 5, we present a set of results on the stabilization in finite time of some mechanical processes where a dry friction coexists with other physical frameworks leading to oscillations in absence of friction.
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Contributor : Vincent Millot <>
Submitted on : Friday, January 19, 2007 - 8:33:16 AM
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  • HAL Id : tel-00125312, version 1

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Vincent Millot. Some variational problems arising in condensed matter physics. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2005. English. ⟨tel-00125312⟩

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