Abstract
We consider the evolution iε \(frac{{\text{d}}}{{{\text{ds}}}}\)U(s) = H(s)U(s), U(0) = 1 fore ε→ 0. A recurrence procedure providing arbitrary order asymptotic invariant subspaces of U(s) corresponding to the isolated parts of the spectrum of H(s) is written down. The point of the construction is that at the kth step the invariant subspaces at the “time” s are constructed from H and its first k derivatives at the same time. As consequences we give a hierarchy of adiabatic theorems as well as a block diagonalisation scheme.
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© 1991 Springer Science+Business Media Dordrecht
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Nenciu, G. (1991). Asymptotic Invariant Subspaces, Adiabatic Theorems and Block Diagonalisation. In: Boutet de Monvel, A., Dita, P., Nenciu, G., Purice, R. (eds) Recent Developments in Quantum Mechanics. Mathematical Physics Studies, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3282-4_7
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DOI: https://doi.org/10.1007/978-94-011-3282-4_7
Publisher Name: Springer, Dordrecht
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