Tunneling on graphs: an approach "a la Helffer-Sjoestrand"
Y. Colin de Verdiere
TL;DR
This paper adapts the Helffer-Sjoestrand approach to analyze quantum tunneling phenomena on graphs, providing a novel perspective inspired by methods used for Schrödinger operators on manifolds.
Contribution
It introduces a new application of Helffer-Sjoestrand techniques to graph-based quantum tunneling, bridging methods from differential geometry and graph theory.
Findings
New framework for tunneling on graphs
Insights into spectral properties of graph Schrödinger operators
Potential applications in quantum computing and network analysis
Abstract
We revisit a paper of Li-Gabor-Yau on quantum tunneling on graphs using the approach of Helffer-Sjoestrand for the study of tunneling for Schroedinger operators on manifolds.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Quantum chaos and dynamical systems · Spectral Theory in Mathematical Physics