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

Download Paper

DOI Link

Keywords

spectral graph theory, quantum mechanics, quantum computation

Citation

Jordan, S. and Jarret, M. (2017), Modulus of continuity eigenvalue bounds for homogeneous graphs and convex subgraphs with applications to quantum Hamiltonians, Journal of Mathematical Analysis and Applications, [online], https://doi.org/10.1016/j.jmaa.2017.03.030 (Accessed March 19, 2025)