Partial Weyl law for billiards
Partial Weyl law for billiards
For two-dimensional quantum billiards we derive the partial Weyl law, i.e. the average density of states, for a subset of eigenstates concentrating on an invariant region Γ of phase space. The leading term is proportional to the area of the billiard times the phase-space fraction of Γ. The boundary term …