Rupert L. Frank
On the tunneling effect for magnetic Schr\"odinger operators in antidot lattices
(356K, postscript)

ABSTRACT.  We study the Schr\"odinger operator $(h\mathbf{D}-\mathbf{A})^2$ with periodic magnetic field $B= \text{curl}\,\mathbf{A}$ in an antidot lattice $\Omega_\infty=\R^2\setminus\bigcup_{\alpha\in\Gamma}(U+\alpha)$. 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 $h\rightarrow 0$. For this purpose we construct a basis of the corresponding spectral subspace with natural localization and symmetry properties.