



01224nas a2200145   4500008004100000245013100041210006900172260001500241300001400256490000800270520068500278100002000963700002400983856007101007       2017                        eng d00aModulus of continuity eigenvalue bounds for homogeneous graphs and  convex subgraphs with applications to quantum Hamiltonians0 aModulus of continuity eigenvalue bounds for homogeneous graphs a  c2017/03/03  a1269-12900 v4523 a<p>We adapt modulus of continuity estimates to the study of spectra of combinatorial graph Laplacians, as well as the Dirichlet spectra of certain weighted Laplacians. The latter case is equivalent to stoquastic Hamiltonians and is of current interest in both condensed matter physics and quantum computing. In particular, we introduce a new technique which bounds the spectral gap of such Laplacians (Hamiltonians) by studying the limiting behavior of the oscillations of their eigenvectors when introduced into the heat equation. Our approach is based on recent advances in the PDE literature, which include a proof of the fundamental gap theorem by Andrews and Clutterbuck.</p>1 aJarret, Michael1 aJordan, Stephen, P.  uhttp://www.sciencedirect.com/science/article/pii/S0022247X1730272X