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Quantum adiabatic expansion for dynamics in strong magnetic fields.

Landau level mixing by external potentials is considered in a Born-Oppenheimer expansion which separates the dynamics of the fast velocities of cyclotron rotation and the slow coordinates of the guiding centers. Level mixing is present already in the extreme adiabatic limit and in transitions at avoided crossings. Nonvanishing Berry's phase adds effective magnetic field depending on external potential. Explicit results are given for weakly inhomogeneous potentials. The projection on a single Landau level appears as an extreme limit of the formalism