Sharp spectral asymptotics for four-dimensional Schrödinger operator with a strong degenerating magnetic field

2006/05/11 by Victor Ivrii, Ivrii, Victor
Computer Science · Mathematics · #35P20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0605298

openalex publication_date 2006/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I continue analysis of the Schrödinger operator with the strong degenerating magnetic field, started in \citeIRO6. Now I consider 4-dimensional case, assuming that magnetic field is generic degenerated and under certain conditions I derive spectral asymptotics with the principal part \asymp h^-4 and the remainder estimate O(μ^-1/2h^-3) where μ≫ 1 is the intensity of the field and h≪ 1 is the Plank constant; μh≤ 1. These asymptotics can contain correction terms of magnitude μ^5/4h^-3/2 corresponding to the short periodic trajectories.

Related

• Sharp Spectral Asymptotics for four-dimensional Schroedinger operator with a strong magnetic field. II
• Sharp Spectral Asymptotics for two-dimensional Schrödinger operator with a strong degenerating magnetic field
• Sharp Spectral Asymptotics for Operators with Irregular Coefficients. IV. Multidimensional Schroedinger operator with a strong magnetic field. Full-rank case
• Sharp Spectral Asymptotics for 2-dimensional Schrödinger operator with a strong magnetic field. Note about forgotten generic case
• Sharp Spectral Asymptotics for 2-dimensional Schrödinger operator with a strong but degenerating magnetic field. II