  General properties of the tunnelling-charging Hamiltonian of a Cooper pair
pump are examined with emphasis on the symmetries of the model. An efficient
block-diagonalisation scheme and a compatible Fourier expansion of the
eigenstates is constructed and applied in order to gather information on
important observables. Systematics of the adiabatic pumping with respect to all
of the model parameters are obtained and the link to the geometrical Berry's
phase is identified.
