Magnetic Laplacians of locally exact forms on the Sierpinski Gasket

Autor:	Hyde, Jessica, Kelleher, Daniel J., Moeller, Jesse, Rogers, Luke G., Seda, Luis
Rok vydání:	2016
Předmět:	Mathematics - Spectral Theory Primary: 28A80 Secondary: 31E05 47A07 60J35 81Q10 81Q35
Druh dokumentu:	Working Paper
Popis:	We give a mathematically rigorous construction of a magnetic Schr\"odinger 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. Comment: 20 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1604.01340 Zobrazit plný text záznamu View this record from Arxiv