Elementary excitations in a finite fractional quantum Hall droplet

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