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On Aharonov-Bohm Operators with Two Colliding Poles
Laura Abatangelo1, Veronica Felli2, Corentin Léna3
1Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Cozzi 55, 20125 Milano, Italy.
Advanced Nonlinear Studies
|September 20, 2023
Summary
We analyze Aharonov-Bohm operators with two poles, proving precise eigenvalue behavior as poles merge. This reveals insights into quantum mechanics and spectral theory.
Area of Science:
- Quantum mechanics
- Mathematical physics
- Spectral theory
Background:
- Aharonov-Bohm operators are crucial in quantum mechanics.
- Understanding eigenvalue asymptotics is vital for spectral analysis.
Purpose of the Study:
- To investigate the behavior of simple eigenvalues for Aharonov-Bohm operators with two poles.
- To establish sharp asymptotic formulas as the poles coalesce.
Main Methods:
- Analysis of Aharonov-Bohm operators.
- Perturbation theory.
- Asymptotic analysis of eigenvalues.
Main Results:
- Derived sharp asymptotic formulas for simple eigenvalues.
- Demonstrated eigenvalue behavior as poles approach an interior point.
- Showed the limit eigenfunction's nodal lines are avoided.
Conclusions:
- The study provides precise mathematical descriptions of spectral properties.
- Results contribute to the understanding of quantum systems with specific potential configurations.
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