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The quantum adiabatic theorem incorporating the Berry phase phenomenon can becharacterized as a factorization of the time evolution operator into apath-dependent geometric factor, a usual dynamical factor and a non-adiabaticfactor that approaches the identity in the adiabatic limit. We study a casewhere all these three factors can be constructed explicitly and where theinstantaneous Hamiltonian has infinitely degenerate energy eigenstatesassociated with magnetic translation symmetry. Significance of thenon-adiabatic factor in terms of transition probabilities is discussed.

Nonadiabatic factor accompanying magnetic translation of a charged particle