Progressive diagonalization and applications

Details Progressive diagonalization and applications Progressive diagonalization and applications

2004-05-06

arxiv.org/abs/math-ph/0405014v1

Proceedings of the Conference "Operator Algebras & Mathematical Physics", Constanta (Roumanie, 2001), R. Purice Ed., Theta Fou

Physics

Mathematical Physics

16 pages, Latex2e

Scientific paper

We give a partial review of what is known so far on stability of periodically driven quantum systems versus regularity of the bounded driven force. In particular we emphasize the fact that unbounded degeneracies of the unperturbed Hamiltonian are allowed. Then we give a detailed description of an extension to some unbounded driven forces. This is done by representing the Schroedinger equation in the instantaneous basis of the time dependent Hamiltonian with a method that we call progressive diagonalization.

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