Harmonic mixing in a cosine potential for arbitrary damping

Harmonic mixing of two alternating electric fields due to a Brownian charged particle in a nonlinear one-dimensional potential of cosine shape is investigated. The dynamics of the system are described by a time dependent Fokker-Planck equation. The appropriate distribution function is obtained by a matrix continued fraction expansion method, which is treated numerically. The dc signal due to mixing is computed for strong thermal fluctuations in all relevant parameter ranges of the pinning potential strength, damping and frequency. The dc signal without fluctuations is discussed separately. Resonance effects are shown in the electric dc field and the additional phase shift, caused by intrinsic relaxation processes.