Abstract
The evolution equation
in the limit ε → 0, is considered. Various methods to construct asymptotically invariant (up to exponentially small errors) subspaces are reviewed. Then, following the basic idea of the reduction theory, the so called “superadiabatic evolution” is written down. In the second part some applications of the general theory are presented: theory of adiabatic invariants for linear Hamiltonian systems and spectral properties of periodic Dirac hamiltonian.
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Nenciu, G. (1996). Linear Adiabatic Theory: Exponential Estimates and Applications. In: de Monvel, A.B., Marchenko, V. (eds) Algebraic and Geometric Methods in Mathematical Physics. Mathematical Physics Studies, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0693-3_6
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DOI: https://doi.org/10.1007/978-94-017-0693-3_6
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