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

Abstract

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 noninertial͒ 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 current͒ 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 capacitance͒ 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.

Quantum effects in the Brownian motion of a particle in a double well potential in the overdamped limit

“…͑4͒. The estimations show 27 that for various physical systems T 0 can be very low in comparison with the temperatures of interest, which can also very low. For example, for point Josephson junctions, which are usually treated using the model of Brownian motion in a tilted periodic potential, 4 T ϳ 1.5-4 K and T 0 ϳ 0.01.…”

“…͑8͒ as described in Ref. 27. Thus higher order quantum correction terms to the classical results may be calculated, in principle, to any desired degree r of ប 2r .…”

“…16,26,27 Here, having determined the quantum Smoluchowski equation in the manner outlined above, we shall use it to evaluate quantum corrections in the Brownian motion of the particle moving in the double well potential given by Eq. ͑1͒.…”

Fokker-Planck equation with arbitrary dc and ac fields: Continued fraction method

“…Finally, it is worth noting that CFM has recently been applied to solve the Bloch-Redfield equation [21] and the quantum Smoluchowski equation [22][23][24] with an ac field. Thus, our methodology is also expected to be useful in solving driven quantum Brownian systems.…”

“…III [see Eqs (21),(22),. and(23)]. Note that only Q n is related to the ac field strength because the Fourier series {e inx } are eigenfunctions of the term ∂ ∂x F ext (t) in Eq.…”