Phase dynamics in SQUID’s: Anomalous diffusion and irregular energy dependence of diffusion coefficients

Deterministic diffusions of superconducting phases in extremely underdamped SQUID’s are studied. It is found that, by controlling the total energy, two types of diffusion, i.e., anomalous and normal ones, appear. In the anomalous diffusion, the orbit in the phase space is trapped mainly into the jump-related hierarchy structure so that the mean-square displacement behaves as $t^{\gamma }$ with $1<\mathrm{}\gamma <2.\mathrm{}$ This enhanced diffusion is analyzed from a viewpoint of the Lévy walk. Even in the normal diffusion, it is revealed that the diffusion coefficient has the amazing irregular energy dependence, which reflects an extreme sensitivity of the phase-space structure to a small change of the energy.