FLUCTUATION MODES OF THE FRUSTRATED XY-MODEL

The spectrum of fluctuations around the flux density wave 'staircase' states of the frustrated XY-model of Josephson junction arrays is studied for rational values of the flux per plaquette, f = p/q. The structure of the Brillouin zone is discussed and the reduced eigenvalue equation for the Hessian matrix derived. The eigenvalue equation is studied analytically in two regions: (i) the zone boundary and (ii) the zone centre for the lowest band; in various limits as q --> infinity. Numerical diagonalization is employed for a sequence of values of f and the band structures and densities of states calculated. The simple harmonic approximation is modified to include the strong anisotropy of the states and is shown to explain the lowest band density of states well at low energy.