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Multistate Landau–Zener problem

Nikolai A. Sinitsyn, V. L. Pokrovsky

Published Feb 5, 2026• 0 citations
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Abstract

Abstract This chapter is introduction to multistate Landau-Zener theory. We prove and solve various general formulas and conclude with a section that describes the solution of the driven Tavis-Cummigs model.
DOI
10.1093/oso/9780198988007.003.0011

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Nanoscale systems have sizes intermediate between atomic and macroscopic ones. Therefore their treatment often requires a combination of methods from atomic and condensed matter physics. The conventional Landau-Zener theory, being a powerful tool in atomic physics, often fails to predict correctly nonadiabatic transition probabilities in various nanostructures because it does not include many-body effects typical for mesoscopics. In this research project the generalizations of the Landau-Zener theory that solve this problem were studied. The multistate, multiparticle and nonunitary extensions of the theory have been proposed and investigated. New classes of exactly solvable models have been derived. I discuss their applications in problems of the molecular condensate dissociation and of the driven charge transport. In application to the physics of nanomagnets new approaches in modeling the influence of the environment on the Landau-Zener evolution are proposed and simple universal formulas are derived for the extensions of the theory that include the coupling to noise and the nuclear spin bath.