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We present a detailed study of the dynamic response of a ring of N equally spaced Josephson junctions to a time-periodic external flux, including screening current effects. The dynamics are described by the resistively shunted Josephson junction model, appropriate for proximity effect junctions, and we include Faraday's law for the flux. We find that the time-averaged I −V characteristics show novel subharmonic giant Shapiro voltage resonances, which strongly depend on having phase slips or not, on N , on the inductance and on the external drive frequency. We include an estimate of the possible experimental parameters needed to observe these quantized voltage spikes.

We study the classical and quantum mechanics of a two-dimensional version of a Fermi accelerator. The model consists of a free particle that collides elastically with the walls of a circular disk with the radius varying periodically in time. A complete quantum mechanical solution of the problem is possible for a specific choice of the time-periodic oscillating radius. The quasi-energy spectral properties of the model are obtained from direct evaluation of finitedimensional approximations to the time evolution operator. As the scaledh is changed from large to small the statistics of the Quasienergy Eigenvalues (QEE) change from Poisson to circular orthogonal ensemble (COE). Different statistical tests are used to characterize this transition. The transition of the Quasienergy Eigenfunctions (QEF ) is also studied using the χ 2 test with ν degrees of freedom. The Porter-Thomas distribution is shown to apply in the COE regime, while the Poisson regime does not fit the χ 2 test with ν = 0. We find that the Poisson regime is associated with exponentially localized QEF whereas the eigenfunctions are extended in the COE regime. 1To make a direct comparison between the classical and quantum solutions we change the representation of the model to one in which the boundary is fixed and the Hamiltonian acquires a quadratic term with a time-periodic frequency. We then carry out a successful comparison between specific classical phase space surface-of-section solutions and their corresponding quasi-energy eigenfunctions in the Husimi representation.