Motions of electrons in adiabatically perturbed periodic structures

Details Motions of electrons in adiabatically perturbed periodic structures Motions of electrons in adiabatically perturbed periodic structures

2007-12-28

arxiv.org/abs/0712.4365v1

in A. Mielke (editor), "Analysis, Modeling and Simulation of Multiscale Problems" (Final Report of the DFG Priority Program SP

Physics

Mathematical Physics

23 pages, no figures

Scientific paper

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.

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