The standard theory of dynamical Coulomb blockade [ P ( E ) theory] in ultra-small tunnel junctions has been formulated on the basis of phase-phase correlations by several authors. It was recently extended by several experimental and theoretical works to account for novel features such as electromagnetic environment-based renormalization effects. Despite this progress, aspects of the theory remain elusive especially in the case of linear arrays. Here, we apply path integral formalism to re-derive the Cooper-pair current and the BCS quasi-particle current in single small Josephson junctions and extend it to include long Josephson junction arrays as effective single junctions. We consider renormalization effects of applied oscillating voltages due to the impedance environment of a single junction as well as its implication to the array. As is the case in the single junction, we find that the amplitude of applied oscillating electromagnetic fields is renormalized by the s...

中文翻译：

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在小约瑟夫逊结中施加的振荡电压的重新定标

几位作者基于相位-相位相关性，制定了超小型隧道结中的动态库仑阻塞标准理论[P（E）理论]。最近，通过一些实验和理论工作对其进行了扩展，以说明诸如基于电磁环境的重归一化效应等新功能。尽管取得了这些进展，但是在线性阵列的情况下，该理论的各个方面仍然难以捉摸。在这里，我们应用路径积分形式论来重新推导单个小的约瑟夫森结中的库珀对电流和BCS准粒子电流，并将其扩展为包括长的约瑟夫森结阵列作为有效的单个结。我们考虑了由于单个结的阻抗环境及其对阵列的影响而导致的施加振荡电压的重新归一化效应。