Motion of Electrons in Adiabatically Perturbed Periodic Structures

Gianluca Panati (), Herbert Spohn () and Stefan Teufel ()
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Gianluca Panati: TU München, Zentrum Mathematik
Herbert Spohn: TU München, Zentrum Mathematik
Stefan Teufel: Universität Tübingen, Mathematisches Institut

A chapter in Analysis, Modeling and Simulation of Multiscale Problems, 2006, pp 595-617 from Springer

Abstract: Summary 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.

Keywords: Invariant Subspace; Geometric Phase; Bloch Function; Chern Number; Periodicity Lattice (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-35657-8_22

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DOI: 10.1007/3-540-35657-6_22

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