by Antoni Brzoska, Aubrey Coffey, Madeline Hansalik, Stephen Loew, Luke G. Rogers
We adapt the well-known spectral decimation technique for computing spectra of Laplacians on certain symmetric self-similar sets to the case of magnetic Schrödinger 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.