Approximate Scaling Behaviour of Local Spectral Density of States at Relatively Weak Perturbation: a Schematic Shell Model

For a schematic shell model,we show numerically that,contrary to the behaviour of eigenfunctions,the shapes of the so-called local spectral density of states become close to their forms at extremely strong perturbation(after rescaling)even when the perturbation is relatively weak.The same phenomenon is also found for the random version of the schematic shell model.We suggest that this property of the local spectral density of states may be common to models in which the Hamiltonian matrices in independent particle states have a banded and regular structure.