Magnetic Laplacians of locally exact forms on the Sierpinski Gasket

by Jessica Hyde, Daniel Kelleher, Jesse Moeller, Luke G. Rogers, Luis Seda

We give an explicit construction of a magnetic Schrödinger operator corresponding to a field with flux through finitely many holes of the Sierpinski Gasket. The operator is shown to have discrete spectrum accumulating at $$\infty$$, and it is shown that the asymptotic distribution of eigenvalues is the same as that for the Laplacian. Most eigenfunctions may be computed using gauge transformations corresponding to the magnetic field and the remainder of the spectrum may be approximated to arbitrary precision by using a sequence of approximations by magnetic operators on finite graphs.

Arxiv Preprint version

Published version in CPAA