Nonlinear response of a dissipative Bloch particle in an oscillating field

We study the Caldeira-Leggett model of a particle coupled to a heat bath moving in a periodic cosine potential. In the limit of small viscosity we obtain an integral equation for the nonlinear response of the system to a constant or a slowly oscillating field. The equation is derived by a resummation of the infinite series expansion in the strength of the cosine potential. When solved via a self-consistent approximation it gives an analytic expression for the response function. Applications to Josephson junctions driven by a low-frequency source are discussed.