Dimitri Yafaev: Spectral properties of magnetic Hamiltonians

We discuss spectral properties of quantum magnetic Hamiltonians for several physically important classes of magnetic fields $B(x,y,z)$: 1. $B(x,y,z)=constant$ 2. $B(x,y,z)$ is a function decaying sufficiently rapidly at infinity In the following two cases $B(x,y,z)$ is translationally invariant, that is, it does not depend on $z$ and $B(x,y)$ decays sufficiently rapidly as $(x,y)\to \infty$ 3. The vectors $B(x,y)$ are directed along the $z$-axis 4. The vectors $B(x,y)$ are orthogonal to the $z$-axis A behavior of the corresponding classical systems is also discussed.