ELEMENTARY EXCITATIONS IN A FINITE FRACTIONAL QUANTUM HALL DROPLET

We have carried out a numerical study of elementary excitations in a f inite droplet of an incompressible quantum Hall liquid by using the fe w-particle exact diagonalization technique on disks and spheres in the presence of an external confining potential. We study both weak and s trong confinements in a spherical droplet, finding in the latter case a possible destruction of the incompressibility gap for high-enough co nfinement strength. In the disk geometry, we find evidence for a linea r gap mode and for a second edge mode at a fractional filling of 2/5.