Kato expansion in quantum canonical perturbation theory

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.

18 pages. Version 2: Additional discussion of the computational algorithms

References in corpus (3)

• The Magnus expansion and some of its applications
• FORM version 4.0
• Kato perturbation expansion in classical mechanics and an explicit expression for a Deprit generator

Cited by in corpus (1)

• Parametric approximation as open quantum systems problem