Spectral Properties of Schrödinger Operators Arising in the Study of Quasicrystals

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dc.contributor.authorDamanik, David
dc.contributor.authorEmbree, Mark
dc.contributor.authorGorodetski, Anton
dc.date.accessioned2018-06-19T17:48:01Z
dc.date.available2018-06-19T17:48:01Z
dc.date.issued2012-10
dc.date.noteOctober 2012
dc.description.abstractWe survey results that have been obtained for self-adjoint operators, and especially Schrödinger operators, associated with mathematical models of quasicrystals. After presenting general results that hold in arbitrary dimensions, we focus our attention on the one-dimensional case, and in particular on several key examples. The most prominent of these is the Fibonacci Hamiltonian, for which much is known by now and to which an entire section is devoted here. Other examples that are discussed in detail are given by the more general class of Schrödinger operators with Sturmian potentials. We put some emphasis on the methods that have been introduced quite recently in the study of these operators, many of them coming from hyperbolic dynamics. We conclude with a multitude of numerical calculations that illustrate the validity of the known rigorous results and suggest conjectures for further exploration.
dc.format.extent51 pp
dc.identifier.citationDamanik, David, Embree, Mark and Gorodetski, Anton. "Spectral Properties of Schrödinger Operators Arising in the Study of Quasicrystals." (2012) <a href="https://hdl.handle.net/1911/102210">https://hdl.handle.net/1911/102210</a>.
dc.identifier.digitalTR12-21
dc.identifier.urihttps://hdl.handle.net/1911/102210
dc.language.isoeng
dc.titleSpectral Properties of Schrödinger Operators Arising in the Study of Quasicrystals
dc.typeTechnical report
dc.type.dcmiText
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