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arXiv · 1504.05113

Kato expansion in quantum canonical perturbation theory

A. S. Nikolaev
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Abstract

This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson's ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.

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A. S. Nikolaev. 2015-08-05. Kato expansion in quantum canonical perturbation theory. https://doi.org/10.1063/1.4953639

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