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Motion of Electrons in Adiabatically Perturbed Periodic Structures

In: Analysis, Modeling and Simulation of Multiscale Problems

Author

Listed:
  • Gianluca Panati

    (TU München, Zentrum Mathematik)

  • Herbert Spohn

    (TU München, Zentrum Mathematik)

  • Stefan Teufel

    (Universität Tübingen, Mathematisches Institut)

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.

Suggested Citation

  • Gianluca Panati & Herbert Spohn & Stefan Teufel, 2006. "Motion of Electrons in Adiabatically Perturbed Periodic Structures," Springer Books, in: Alexander Mielke (ed.), Analysis, Modeling and Simulation of Multiscale Problems, pages 595-617, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-35657-8_22
    DOI: 10.1007/3-540-35657-6_22
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