Normalized Laplace operators for hypergraphs with real coefficients

Chemical hypergraphs and their associated normalized Laplace operators are generalized and studied in the case where each vertex–hyperedge incidence has a real coefficient. We systematically study the effect of symmetries of a hypergraph on the spectrum of the Laplacian.

Coherent state transform for Landau levels on quasi-tori

The spectrum of the Laplacian operator on the positive theta line bundle over the quasi-torus reduces to eigenvalues \pi\ell, \ell=0,1,\ldots{}, which are called Landau levels. This paper discusses the coherent state transform for each eigenspace associated with a Landau level. We construct a unitary transform valid for each eigenspace. A concrete form of the inverse formula for the proposed transform is also obtained.