Quantum effects of resistance-shunted Josephson junctions

Thermodynamics and transport properties of resistance-shunted Josephson junctions are studied theoretically in the tight-binding limit E_C/E_J ≪ 1, where E_C and E_J are a charging energy and a Josephson coupling energy respectively. Based on a phenomenological harmonic-oscillator model, weak coupling region K = R_Q/R ≪ 1 is analytically studied, where R and R_Q = h/(2e)² are a shunt resistance and the quantum resistance. In addition to an effective bandwidth 2ℏΔ_eff, we find that this multi-level system genuinely has a novel crossover at lower energy KℏΔ_eff below which the density of states becomes strongly degenerate. These two energy scales control the linear DC responses, optical responses, and nonlinear I-V characteristics. The lower energy crossover indicates the existence of a new class of strongly-correlated phenomena beyond the framework of the Kondo problem.