Physics – Quantum Physics
Scientific paper
2010-09-15
Physics
Quantum Physics
11 figures, submitted
Scientific paper
Many properties of current \emph{ab initio} approaches to the quantum many-body problem, both perturbational or otherwise, are related to the singularity structure of Rayleigh--Schr\"odinger perturbation theory. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the perturbed Hamiltonian on a vector, and does not rely on the terms in the perturbation series. Some illustrative model problems are studied, including a Helium-like model with $\delta$-function interactions for which M{\o}ller--Plesset perturbation theory is considered and the radius of convergence found.
Jarlebring Elias
Kvaal Simen
Michiels Wim
No associations
LandOfFree
Computing singularities of perturbation series does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Computing singularities of perturbation series, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computing singularities of perturbation series will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-77268