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We formulate and approximately solve a specific many-body generalization ofthe Landau-Zener problem. Unlike with the single particle Landau-Zener problem,our system does not abide in the adiabatic ground state, even at very slowdriving rates. The structure of the theory suggests that this finding reflectsa more general phenomenon in the physics of adiabatically driven many particlesystems. Our solution can be used to understand, for example, the behavior oftwo-level systems coupled to an electromagnetic field, as realized in cavityQED experiments.

Many body generalization of the Landau Zener problem