Spectral asymptotics of all the eigenvalues of Schrödinger operators on flat tori

2020/07/15 by Bambusi, Dario, Langella, Beatrice, Montalto, Riccardo
#35Q55 #37K10 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2007.07865

Abstract

We study Schrödinger operators with Floquet boundary conditions on flat tori obtaining a spectral result giving an asymptotic expansion of all the eigenvalues. The expansion is in λ^-δ with δ∈(0,1) for most of the eigenvalues λ (stable eigenvalues), while it is a "directional expansion" for the remaining eigenvalues (unstable eigenvalues). The proof is based on a structure theorem which is a variant of the one proved in \citePS10,PS12 and on a new iterative quasimode argument.

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