Adiabatic evolution for systems with infinitely many eigenvalue crossings

Alain Joye (1) , F. Monti (2) , S. Guérin (2) , H. R. Jauslin (2)

1 IF - Institut Fourier
2 LPUB - Laboratoire de Physique de l'Université de Bourgogne

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 projector, and some geometric hypothesis on the local behavior of the eigenvalues at the crossings.

Domaines: Mathématiques [math]

Alain Joye, F. Monti, S. Guérin, H. R. Jauslin. Adiabatic evolution for systems with infinitely many eigenvalue crossings. Journal of Mathematical Physics, 1999, 40 (11), pp.5456-5472. ⟨10.1063/1.533039⟩. ⟨hal-01233203⟩