Adiabatic Evolution for Systems with Infinitely many Eigenvalue Crossings

Details Adiabatic Evolution for Systems with Infinitely many Eigenvalue Crossings Adiabatic Evolution for Systems with Infinitely many Eigenvalue Crossings

1998-12-23

arxiv.org/abs/math-ph/9812024v1

Physics

Mathematical Physics

Scientific paper

10.1063/1.533039

We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to the adiabatic limit. The result requires only differentiability of the considered spectral projector, and some geometric hypothesis on the local behaviour of the eigenvalues at the crossings.

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