Adiabatic theorem without a gap condition

Joseph E. Avron, Alexander Elgart

Research output: Contribution to journalArticlepeer-review

161 Scopus citations


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 rate.

Original languageEnglish
Pages (from-to)445-463
Number of pages19
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - 1 Jan 1999
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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