Joye A:, Pfister C.-E.
Quantum adiabatic evolution
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ABSTRACT. This is a review about recent results for the adiabatic evolution for
quantum systems with analytic Hamiltonians. A new version of the adiabatic
theorem in Quantum Mechanics is given and the geometrical aspects of the
evolution is discussed. For two-level systems various rigourous formulas
given the transition probability between the two energy-levels,
like the Landau-Zener formula, are reviewed.