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arXiv · 1704.01609

Spectra of Magnetic Operators on the Diamond Lattice Fractal

Antoni Brzoska·Aubrey Coffey·Madeline Rooney·Stephen Loew·Luke G. Rogers
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Abstract

We adapt the well-known spectral decimation technique for computing spectra of Laplacians on certain symmetric self-similar sets to the case of magnetic Schrodinger operators and work through this method completely for the diamond lattice fractal. This connects results of physicists from the 1980's, who used similar techniques to compute spectra of sequences of magnetic operators on graph approximations to fractals but did not verify existence of a limiting fractal operator, to recent work describing magnetic operators on fractals via functional analytic techniques.

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Antoni Brzoska, Aubrey Coffey, Madeline Rooney, Stephen Loew, Luke G. Rogers. 2017-04-05. Spectra of Magnetic Operators on the Diamond Lattice Fractal. https://arxiv.org/abs/1704.01609

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