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The quantum Smoluchowski equation for the reduced Wigner function in configuration space pertaining to the quantum Brownian motion of a particle in a tilted cosine potential in the high dissipation or noninertial limit as applied to a model point Josephson junction namely, a resistively shunted junction in the presence of noise and an arbitrarily large microwave ac driving current is considered. The solution of the resulting recurrence relations for the Fourier amplitudes of the statistical moments describing the nonlinear dynamics of the junction ignoring the capacitance is obtained using the matrix continued fractions previously developed for the stationary ac field solution of the corresponding classical problem. Quantum effects in the nonlinear response of the junction to an ac microwave current of arbitrary amplitude nonlinear microwave impedance, frequency dependence of the dc current-voltage characteristic, etc. are estimated.

physical review b

Nonlinear noninertial response of a quantum Brownian particle in a tilted periodic potential to a strong ac force as applied to a point Josephson junction