Structure and far-infrared edge modes of quantum antidots at zero   magnetic field
  We have investigated edge modes of different multipolarity sustained by quantum antidots at zero magnetic field. The ground state of the antidot is described within a local density functional formalism. Two sum rules, which are exact within this formalism, have been derived and used to evaluate the energy of edge collective modes as a function of the surface density and the size of the antidot. 
Agusti Emperador, Marti Pi, Manuel Barranco, Enrico Lipparini, and   Llorens Serra