Asymmetry Of Coordinate And Velocity In Noisy Oscillator

The velocity variable of a noise oscillator as an internal or external noise is proposed: the spectrum of which is quite different from that of the coordinate variable of the same noise oscillator. The former leads to ballistic diffusion for a free particle in long time limit and the asymptotical results of the system are sensitive to the initial condition. However, diffusion process induced by the coordinate of noise oscillator is a normal one and depends on the initial condition only in the transient time. This allows us to classify two kinds of non-Markovian processes: normal one and strong one, just like the processes induced by the coordinate and the velocity of noise oscillator. respectively. Applying to a correlation ratchet, we have found that the steady current of a particle subjected to the velocity of noise oscillator is opposite to that subjected to its coordinate, thus the former shows greenness and the latter redness.