HISTORY DEPENDENCE AND AGING IN A PERIODIC LONG-RANGE JOSEPHSON ARRAY

History dependence and aging are studied in the low-temperature glass phase of a long-range periodic Josephson array. This model is characte rized by two parameters, the number of wires (2N) and the flux per uni t strip (alpha); in the limit N-->infinity and fixed alpha much less t han 1 the dynamics of the model are described by the set of coupled in tegral equations, which coincide with those for the p=4 disordered sph erical model. Below the glass transition we have solved these equation s numerically in a number of different regimes. We observe power-law a ging after a fast quench with an exponent that decreases rapidly with temperature. After slow cooling to a not-too-low temperature, we see a ging characterized by the appearance of a time scale which has a power -law dependence on the cooling rate. By contrast, if the array is cool ed slowly to very low temperatures, the aging disappears. The physical consequences of these results in different cooling regimes are discus sed for future experiment. We also study the structure of the phase sp ace in the low-temperature glassy regime. Analytically. we expect an e xponential number of metastable states just below the glass-transition temperature with vanishing mutual overlap, and numerical results indi cate that this scenario remains valid down to zero temperature. Thus i n this array there is no further subdivision of metastable states. We also investigate the probability to evolve to different states given a starting overlap, and our results suggest a broad distribution of bar riers. [S0163-1829(97)05838-4].