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Motion of Electrons in Adiabatically Perturbed Periodic Structures

  • Gianluca Panati
  • Herbert Spohn
  • Stefan Teufel

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gianluca Panati
    • 1
  • Herbert Spohn
    • 1
  • Stefan Teufel
    • 2
  1. 1.Zentrum MathematikTU MünchenGarching
  2. 2.Mathematisches InstitutUniversität TübingenTübingen

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