EXPONENTIAL APPROACH TO THE ADIABATIC LIMIT AND THE LANDAU-ZENER FORMULA

We study the adiabatic limit for Hamiltonians with certain complex-analytic dependence on the time variable We show that the transition probability from a spectral band that is separated by gaps is exponentially small in the adiabatic parameter We find sufficient conditions for the Landau-Zener formula, and its generalization to nondiscrete spectrum, to bound the transition probability