Modulus of continuity eigenvalue bounds for homogeneous graphs and convex subgraphs with applications to quantum Hamiltonians

Published: August 15, 2017

Author(s)

Stephen P. Jordan, Michael Jarret

Abstract

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.
Citation: Journal of Mathematical Analysis and Applications
Volume: 452
Issue: 2
Pub Type: Journals

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Keywords

spectral graph theory, quantum mechanics, quantum computation
Created August 15, 2017, Updated April 17, 2017