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arXiv · 1305.7193

The laminations of a crystal near an anti-continuum limit

Vincent Knibbeler·Blaz Mramor·Bob Rink
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Abstract

The anti-continuum limit of a monotone variational recurrence relation consists of a lattice of uncoupled particles in a periodic background. This limit supports many trivial equilibrium states that persist as solutions of the model with small coupling. We investigate when a persisting solution generates a so-called lamination and prove that near the anti-continuum limit the collection of laminations of solutions is homeomorphic to the (N-1)-dimensional simplex, with N the number of distinct local minima of the background potential. This generalizes a result by Baesens and MacKay on twist maps near an anti-integrable limit.

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Vincent Knibbeler, Blaz Mramor, Bob Rink. 2013-05-30. The laminations of a crystal near an anti-continuum limit. https://doi.org/10.1088/0951-7715%2F27%2F5%2F927

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