Resistance-shunted Josephson junctions are studied theoretically based on a tight-binding model. In addition to the effective bandwidth 2ℏΔeff, this multi-level system genuinely has a novel crossover at lower energy KℏΔeff below which the density of states becomes strongly degenerate, where K is a dimensionless damping strength. The optical responses take nearly Lorentzian forms with a width of the order of KℏΔ. The non-linear I-V characteristics is also discussed.
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