Spectral Properties of 2D Pauli Operators with Almost-Periodic Electromagnetic Fields
Language
en
Article de revue
This item was published in
Publications of the Research Institute for Mathematical Sciences. 2019, vol. 55, n° 3, p. 453-487
European Mathematical Society
English Abstract
We consider a 2D Pauli operator with almost periodic field b and electric potential V. First, we study the ergodic properties of H and show, in particular, that its discrete spectrum is empty if there exists a magnetic ...Read more >
We consider a 2D Pauli operator with almost periodic field b and electric potential V. First, we study the ergodic properties of H and show, in particular, that its discrete spectrum is empty if there exists a magnetic potential which generates the magnetic field b − b0, b0 being the mean value of b. Next, we assume that V = 0, and investigate the zero modes of H. As expected, if b0 = 0, then generically dim Ker H = ∞. If b0 = 0, then for each m ∈ N ∪ {∞}, we construct almost periodic b such that dim Ker H = m. This construction depends strongly on results concerning the asymptotic behavior of Dirichlet series, also obtained in the present article.Read less <
English Keywords
Pauli operators
almost periodic functions
ergodic operator families
zero modes
asymptotics of Dirichlet series.
Origin
Hal imported