Particle trapping and self-focusing in temporally asymmetric ratchets with strong field gradients

We study the dynamics of a particle whose velocity is a nonlinear, monotonically increasing function of the applied field. The particle moves in a strong field gradient whose intensity and sign vary periodically. We demonstrate that if the field pulses are temporally asymmetric and biased, we can have situations where the particle always migrates towards a stable zero-velocity point. This special ratchet process can in principle be used to separate molecules and particles. An example is given for the electrophoresis of DNA.