Bounds on variation of the spectrum and spectral subspaces of a few-body Hamiltonian

Abstract

We overview the recent results on the shift of the spectrum and norm bounds for variation of spectral subspaces of a Hermitian operator under an additive Hermitian perturbation. Along with the known results, we present a new subspace variation bound for the generic off-diagonal subspace perturbation problem. We also demonstrate how some of the abstract results may work for few-body Hamiltonians.

arXiv admin note: text overlap with arXiv:1311.6604

References in corpus (2)

• On the existence of solutions to the operator Riccati equation and the tanΘtheorem
• On applying the subspace perturbation theory to few-body Hamiltonians

Cited by in corpus (2)

• Solvability of the operator Riccati equation in the Feshbach case
• An alternative proof of the a priori $\tan \Theta$ Theorem