Communications in Mathematical Physics

, Volume 203, Issue 2, pp 445–463

Adiabatic Theorem without a Gap Condition

  • Joseph E. Avron
  • Alexander Elgart

DOI: 10.1007/s002200050620

Cite this article as:
Avron, J. & Elgart, A. Comm Math Phys (1999) 203: 445. doi:10.1007/s002200050620

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 rate.

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Joseph E. Avron
    • 1
  • Alexander Elgart
    • 1
  1. 1.Department of Physics, Technion, 32000 Haifa, Israel. E-mail: avron@physics.technion.ac.ilIL