Motion of electrons in adiabatically perturbed periodic structures

G. Panati, H. Spohn, S. Teufel

In A. Mielke (Hrsg.), Analysis, Modeling and Simulation of Multiscale Problems, pp. 595-617.
Springer-Verlag, Berlin Heidelberg, 2006.

Zusammenfassung

We study the motion of electrons in a periodic background potential (usually resulting from a crystalline solid). For small velocities one would use either the non-magnetic or the magnetic Bloch hamiltonian, while in the relativistic regime one would use the Dirac equation with a periodic potential. The dynamics, with the background potential included, is perturbed either through slowly varying external
electromagnetic potentials or through a slow deformation of the crystal. In either case we discuss how the Hilbert space of states decouples into almost invariant subspaces and explain the effective dynamics within such a subspace.