Localization of eigenfunctions in the stadium billiard - art. no. 066214

We present a systematic survey of scarring and symmetry effects in the stad ium billiard. The localization of individual eigenfunctions in Husimi phase space is studied first, and it is demonstrated that on average there is mo re localization than can be accounted for by random-matrix theory, even aft er removal of bouncing-ball stares and visible scars. A major point of the paper is that symmetry considerations, including parity and time-reversal s ymmetries, enter to influence the total amount of localization. The propert ies of the local density of states are also investigated, as a function of phase space location. Aside from the bouncing-ball region of phase space, e xcess localization is found on short periodic orbits and along certain symm etry-related lines: the origin of all these sources of localization is disc ussed quantitatively and comparison is made with analytical predictions. Sc arring is observed to be present in all the energy ranges considered. In li ght of our results, the excess localization in individual eigenstates is in terpreted as being primarily due to symmetry effects.