2017/04/12 by Pablo Miranda, Miranda, Pablo, Nicolas Popoff +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP
paper · pdf · doi:10.48550/arxiv.1704.03759
openalex publication_date 2017/04/12 · arxiv created 2017/06/27 · arxiv updated 2017/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the bi-dimensional Schrödinger operator with unidirectionally constant magnetic field, H0, sometimes known as the "Iwatsuka Hamiltonian". This operator is analytically fibered, with band functions converging to finite limits at infinity. We first obtain the asymptotic behavior of the band functions and its derivatives. Using this results we give estimates on the current and on the localization of states whose energy value is close to a given threshold in the spectrum of H0. In addition, for a non-negative electric perturbation V we study the spectral density of H0± V by considering the Spectral Shift Function associated to the operator pair (H0± V,H0). We describe the continuity and boundedness properties of the spectral shift function, and we compute the asymptotic behavior at the thresholds, which are the only points where it can grows to infinity.