INSTANTON VERSUS TRADITIONAL WKB APPROACH TO THE LANDAU-ZENER PROBLEM
Benderskii V.A., Vetoshkin E.V., Kats E.I.

Received: March 14, 2003

PACS: 05.45.-a, 72.10.-d

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Different theoretical approaches to the famous two-state Landau-Zener problem are briefly discussed. Apart from traditional methods of the adiabatic perturbation theory, Born-Oppenheimer approximation with geometric phase effects, two-level approach, and momentum space representation, the problem is treated semiclassically in the coordinate space. In the framework of the instanton approach, we present a full and unified description of the 1D Landau-Zener problem of level crossing. The method enables us to treat all four transition points (appearing at two-level crossing) accurately, while the standard WKB approach takes only two of them into account. The latter approximation is adequate for calculating the transition probability or for studying scattering processes, but it does not work in finding the corresponding chemical reactions rates, where all four transition points can often be relevant in the typical range of parameters. Applications of the method and of the results may concern various systems in physics, chemistry, and biology.