  Although the adiabatic heuristic argument of the fractional quantum Hall
states has been successful, continuous modification of the flux/statistics of
anyons is strictly prohibited due to algebraic constrains of the braid group on
a torus. We have numerically shown that the adiabatic heuristic principle for
anyons is still valid even though the Hamiltonians cannot be modified
continuously. The Chern number of the ground state multiplet is the adiabatic
invariant, while the number of the topological degeneracy behaves wildly. A
generalized Streda formula is proposed that explains the degeneracy pattern.
Nambu-Goldston modes associated with the anyon superconductivity are also
suggested numerically.
