Quantum Tunnelling for Bloch Electrons in Small Electric Fields

  • J. M. Combes
  • P. Hislop
Part of the Mathematical Physics Studies book series (MPST, volume 12)


We consider the quantum Hamiltonian describing a one dimensional particle in a periodic potential plus constant electric field and show that it exhibits an infinite ladder of resonances in the semi-classical regime. The lifetime of these resonances is related to tunnelling phenomena. This provides in this particular case a positive answer to the question of the existence of Stark Ladders.


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Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • J. M. Combes
    • 1
  • P. Hislop
    • 2
  1. 1.PHYMAT, Departement de MathématiquesUniversité de Toulon et du VarLa GardeFrance
  2. 2.Mathematics DepartmentUniversity of KentuckyLexingtonUSA

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