  The pygmy dipole resonance in neutron-rich nuclei is studied within the
framework of the Vlasov equation which is solved numerically. The interaction
used in the Thomas-Fermi ground state and in the Vlasov equation is derived
from an energy functional which correctly describes the equation of state of
nuclear matter and neutron matter. It is found that the pygmy resonance appears
in the electric dipole response of all nuclei with strong neutron excess, the
energies and transition probabilities being in reasonable agreement with
experimental results. Since the Vlasov equation does not account for any shell
effects, this indicates that the existence of the pygmy resonance is a generic
phenomenon and does not rely on the specific shell structure. Besides the
electric dipole response, the isoscalar toroidal response is calculated. The
transition densities and velocity fields are discussed. A comparison of the
peak positions and velocity fields suggests that the pygmy resonance can be
identified with one of the low-lying modes excited by the isoscalar toroidal
operator.
