On the tunneling effect for magnetic Schroedinger operators in antidot lattices

摘要

We study the Schroedinger operator (hD - A)~2 with periodic magnetic field B = curl A in an antidot lattice Ω_∞ = R~2U_(α ∈ Γ)(U + α). Neumann boundary conditions lead to spectrum below h inf B. Under suitable assumptions on a "one-well problem" we prove that this spectrum is localized inside an exponentially small interval in the semi-classical limit h → 0. For this purpose we construct a basis of the corresponding spectral subspace with natural localization and symmetry properties.