Adiabatic Theorem without a Gap Condition

  title={Adiabatic Theorem without a Gap Condition},
  author={J. Avron and Alexander Elgart},
  journal={Communications in Mathematical Physics},
  • J. Avron, A. Elgart
  • Published 25 May 1998
  • Physics, Mathematics
  • Communications in Mathematical Physics
Abstract:We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the adiabatic theorem holds for the ground state of atoms in quantized radiation field. The general result we prove gives no information on the rate at which the adiabatic limit is approached. With additional spectral information one can also estimate this… 
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