New regimes of junction arrays

1. Build an explicit wave function for the eigen- states on the charge lattice
2. Clarify how degeneracy arises in the spectrum
3. Determine the lowest-order correction to ener- gies and wave function when EJa is included perturbatively.
4. Perform parameter sweeps of matrix elements of the operators of the system as a function of: N, ECa,b, EJa,b, external flux and off-set charge. This include matrix elements among all the first- excited states and the ground state.
5. Use explicit expressions of wave functions to study matrix elements in the EJa = 0 limit.