A.Joye, F.Monti, S. Guerin, H.R. Jauslin
Adiabatic Evolution for Systems with Infinitely many Eigenvalue Crossings
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ABSTRACT. 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.