Structure of eigenstates and local spectral density of states: A three-orbital schematic shell model

Abstract

The average shape of the spectral local density of states (LDOS) and eigenfunctions (EFs) has been studied numerically for a conservative dynamical model (three-orbital Lipkin-Meshkov-Glick model) that can exhibit strong chaos in the classical limit. Attention is paid to the comparison of the shape of the LDOS with that known for random matrix models, as well as to the shape of the EFs, for different values of the perturbation strength. The classical counterparts of the LDOS has also been studied and found to be in remarkable agreement with the quantum calculations. Finally, by making use of a generalization of Brillouin-Wigner perturbation expansion, the form of the long tails of the LDOS and EFs is given analytically and confirmed numerically.