TY  - JOUR
UR  - http://stacks.iop.org/1751-8121/46/i=20/a=205302
T1  - Convexity and the quantum many-body problem
A1  - P Chau Huu-Tai and P Van Isacker
Y1  - 2013
SP  - 205302
JF  - Journal of Physics A: Mathematical and Theoretical
VL  - 46
IS  - 20
SN  - 1751-8121
N2  - We recall some properties of convex functions and, in particular, of the sum of the largest
eigenvalues of a Hermitian matrix. From these properties a new estimate of an arbitrary eigenvalue
of a sum of Hermitian matrices is derived, which in turn is used to compute an approximate
associated spectral projector. These estimates are applied for the first time to explain the generic
spectral features of quantum systems. As an application of the formalism, we explain the
preponderance of certain ground-state angular momenta as observed in the vibron model with random
interactions. We show that the evolution of eigenstates can be predicted from the knowledge of a
limited number of spectra and investigate the effect of a three-body interaction in the vibron model
on eigenenergies and eigenvectors.
ER  -