  Transport in a one-dimensional symmetric device can be activated by the
combination of thermal noise and a bi-harmonic drive. For the study case of an
overdamped Brownian particle diffusing on a periodic one-dimensional substrate,
we distinguish two apparently different bi-harmonic regimes: (i) Harmonic
mixing, where the two drive frequencies are commensurate and of the order of
some intrinsic dynamical relaxation rate. A comparison of new simulation
results with earlier theoretical predictions shows that the analytical
understanding of this frequency mixing mechanism is not satisfactory, yet; (ii)
Vibrational mixing, where one harmonic drive component is characterized by a
high frequency but finite amplitude-to-frequency ratio. Its effect on the
device response to either a static or a low-frequency additional input signal
is accurately reproduced by rescaling each spatial Fourier component of the
substrate potential, separately. Contrary to common wisdom based on the linear
response theory, we show that extremely high-frequency modulations can indeed
influence the response of slowly (or dc) operated devices, with potential
applications in sensor technology and cellular physiology. Finally, the mixing
of two high-frequency beating signal is also investigated both numerically and
analytically.
