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Motion of Electrons in Adiabatically Perturbed Periodic Structures

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Analysis, Modeling and Simulation of Multiscale Problems

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.

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Author information

Authors and Affiliations

  1. Zentrum Mathematik, TU München, Boltzmannstraße 3, 85747, Garching

    Gianluca Panati & Herbert Spohn

  2. Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen

    Stefan Teufel

Authors
  1. Gianluca Panati
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  2. Herbert Spohn
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  3. Stefan Teufel
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Editor information

Editors and Affiliations

  1. Weierstraß-Institut für Angewandte, Analysis und Stochastik, Mohrenstraße 39, 10117, Berlin, Germany

    Alexander Mielke

  2. Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489, Berlin, Germany

    Alexander Mielke

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Panati, G., Spohn, H., Teufel, S. (2006). Motion of Electrons in Adiabatically Perturbed Periodic Structures. In: Mielke, A. (eds) Analysis, Modeling and Simulation of Multiscale Problems. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-35657-6_22

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