Collective excitations of quantum Hall states under tilted magnetic field

We study the neutral excitations of quantum Hall systems under external anisotropy introduced by tilting the magnetic field. In the isotropic case, the neutral collective excitation can be worked out through the conserving method of composite fermions satisfying integer quantum Hall effects in the Hamiltonian theory. We show how such a computation can be carried out perturbatively for an anisotropic interaction. We find that unlike the charge gap, the neutral collective gap is much more easily destroyed by the parallel component of the magnetic field. We also address the issue about the convergence of the collective spectrum to the activation gap.