On effective Hamiltonians for adiabatic perturbations of magnetic Schrödinger operators

Article type: Research Article

Authors: Dimassi, Mouez^; | Guillot, Jean‐Claude | Ralston, James

Affiliations: Département de Mathématiques, Université Paris 13, Villetaneuse, France E‐mails: dimassi@math.univ‐paris13.fr, guillot@math.univ‐paris13.fr | University of California, Los Angeles, CA 90095, USA E‐mail: ralston@math.ucla.edu

Note: [] Corresponding author.

Abstract: We construct almost invariant subspaces and the corresponding effective Hamiltonian for magnetic Bloch bands. We also discuss the question of the dynamics related to the effective Hamiltonian. We assume that the magnetic and electric potentials are slowly varying perturbations of the potential of a constant magnetic field and a periodic lattice potential, respectively.

Journal: Asymptotic Analysis, vol. 40, no. 2, pp. 137-146, 2004