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The solution of the Langevin equation describing the dynamics of a Brownian particle in a tilted periodic potential in the overdamped limit is obtained in terms of a matrix continued fraction, allowing us to evaluate statistical averages governing the nonlinear response to a strong ac force. Pronounced nonlinear effects are observed for large values of the ac force. For a weak ac force and low noise strength, the results obtained agree closely with previously available linear response and noiseless solutions, respectively.

Nonlinear noninertial response of a Brownian particle in a tilted periodic potential to a strong ac force