Landau-Zener problem for energies close to potential crossing points

  • V. A. Benderskii
  • E. V. Vetoshkin
  • E. I. Kats
Methods of Theoretical Physics


We examine a previously overlooked aspect of the well-known Landau-Zener (LZ) problem, namely, the behavior in the intermediate, i.e., close to a crossing point, energy region, when all four LZ states are coupled and should be taken into account. We calculate the 4×4 connection matrix in this intermediate energy region, possessing the same block structure as the known connection matrices for the tunneling and in the over-barrier regions of the energy and continuously matching those in the corresponding energy regions. Applications of the results may concern various systems of physics, chemistry, or biology, ranging from molecular magnets and glasses to Bose condensed atomic gases.

PACS numbers

05.45.−a 31.50.Gh 72.10.−d 


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Copyright information

© MAIK "Nauka/Interperiodica" 2004

Authors and Affiliations

  • V. A. Benderskii
    • 1
    • 3
  • E. V. Vetoshkin
    • 1
  • E. I. Kats
    • 2
    • 3
  1. 1.Institute of Problems of Chemical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia
  2. 2.Laue-Langevin InstituteGrenobleFrance
  3. 3.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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