Current responses and voltage fluctuations in Josephson-junction systems

– We consider arrays of Josephson junctions as well as single junctions in both the classical and quantum-mechanical regimes, and examine the generalized (frequency-dependent) resistance, which describes the dynamic responses of such Josephson-junction systems to external currents. It is shown that the generalized resistance and the power spectrum of voltage fluctuations are related via the fluctuation-dissipation theorem. Implications of the obtained relations are also discussed in various experimental situations. There has been much interest in the dynamics of Josephson junctions [1] and Josephsonjunction arrays [2], e.g., current-voltage characteristics, dynamic resistivity, and voltage fluctuations. Among these, the voltage fluctuations provide direct information about the dynamic correlations in equilibrium [3, 4], whereas the resistivity probes the response to external currents [5]. The latter is also closely related to the relaxation function, which describes the relaxation behavior towards the equilibrium state. These two probes are therefore complementary to each other, and one may expect, in view of the general idea of the fluctuation-dissipation (FD) theorem, that there exists a FD relation between them. Nevertheless most existing studies have been devoted either to the resistivity or to the voltage fluctuations, and the relation between the two has hardly been investigated. Here we thus make use of the linear-response theory to derive the generalized frequency-dependent resistance, and examine the relation between the generalized resistance and the power spectrum of the voltage fluctuations in Josephson-junction systems. There are three energy scales in a Josephson-junction system: the Josephson coupling energy EJ ≡ h̄IJ/2|e|, the self-charging energy E0 ≡ e/2C0, and the junction-charging energy EC ≡ e/2C, where IJ is the Josephson critical current and C0 and C are the self-capacitance