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Title:
Periodic Approximations to Aperiodic Hamiltonians
Speaker:
Abstract:
Computing the energy spectrum of electrons in a quasicrystal or any other aperiodic solid is still a challenge today. A review of techniques and mathematical methods available will be presented. Most of the methods are restricted to one dimensional systems and short range interactions. We will present a different approach using the full force of the theory of groupoid C*-algebras and continuous fields of C*-algebras. The main result will be a series of criteria allowing to approximate the aperiodic system by periodic ones, together with precise statement concerning the convergence of the spectrum as a set.
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