The Rayleigh-Schrödinger perturbation series of quasi-degenerate systems

Abstract

We present the first representation of the general term of the Rayleigh-Schrödinger series for quasidegenerate systems. Each term of the series is represented by a tree and there is a straightforward relation between the tree and the analytical expression of the corresponding term. The combinatorial and graphical techniques used in the proof of the series expansion allow us to derive various resummation formulas of the series. The relation with several combinatorial objects used for special cases (degenerate or non-degenerate systems) is established.

16 pages, 3 figures

References in corpus (8)

• Shell-model calculations and realistic effective interactions
• Bounds on variation of spectral subspaces under J-self-adjoint perturbations
• The many-body Green function of degenerate systems
• Gell-Mann and Low formula for degenerate unperturbed states
• Tree expansion in time-dependent perturbation theory
• Riccati Diagonalization of Hermitian Matrices
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• Householder transformed density matrix functional embedding theory
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• From iterated integrals and chronological calculus to Hopf and Rota-Baxter algebras
• Explicit diagrammatic solution of normalised, nondegenerate Rayleigh-Schrödinger perturbation theory