Trace formulas for Schr\"odinger operators on star graphs
Semra Demirel-Frank, Laura Shou
TL;DR
This paper derives trace formulas for Schrödinger operators on star graphs, utilizing high energy asymptotics of the perturbation determinant to extend existing mathematical frameworks.
Contribution
It introduces new trace formulas for quantum star graphs, incorporating high energy asymptotics of the perturbation determinant, advancing spectral analysis methods.
Findings
Derived trace formulas of Buslaev-Faddeev type for star graphs
Established high energy asymptotics of the perturbation determinant
Extended spectral analysis techniques for quantum graphs
Abstract
We derive trace formulas of the Buslaev-Faddeev type for quantum star graphs. One of the new ingredients is high energy asymptotics of the perturbation determinant.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Random Matrices and Applications · Markov Chains and Monte Carlo Methods