Kato expansion in quantum canonical perturbation theory

TL;DR

This paper links quantum canonical perturbation series with Kato expansion, providing explicit formulas for block-diagonalization and comparing computational efficiency with existing methods.

Contribution

It introduces a novel connection between Kato expansion and quantum perturbation theory, offering explicit generator expressions and analyzing computational advantages.

Findings

Derived explicit generator expressions for block-diagonalization.

Established a connection between Kato expansion and quantum perturbation series.

Compared efficiency with Van Vleck and Magnus methods.

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.