Semiclassical Birkhoff-Gustavson normal forms and spectral asymptotics for nearly resonant Schr\"odinger operators
Spectral Theory
2024-10-16 v1 Mathematical Physics
math.MP
Abstract
The concept of near resonances for harmonic approximations of semiclassical Schr\"odinger operators is introduced and explored. Combined with a natural extension of the Birkhoff-Gustavson normal form, we obtain formulas for approaching the discrete spectrum of such operators which are both accurate and easy to implement. We apply the theory to the physically important case of the near Fermi 1:2 resonance, for which we propose explicit expressions and numerical computations.
Keywords
Cite
@article{arxiv.2410.11440,
title = {Semiclassical Birkhoff-Gustavson normal forms and spectral asymptotics for nearly resonant Schr\"odinger operators},
author = {Abdelkader Bourebai and Kaoutar Ghomari and San Vu Ngoc},
journal= {arXiv preprint arXiv:2410.11440},
year = {2024}
}