Dissipation and transport dynamics in a ratchet coupled to a discrete bath.

We investigate a particle in a ratchet potential (the system) coupled to an harmonic bath of N=1-500 degrees of freedom (the discrete bath). The dynamics of the energy exchange between the system and the discrete bath is studied in the transition regime from low to high values of N . First manifestation of dissipation (energy lost by the system) appears for the bath composed of 10 less, similar N less, similar 20 oscillators, as expected. For low values of N , beside small dissipation effects, the system experiences the bath-induced particle transfer between different potential wells from the ratchet. We show that this effect decreases the mobility of particles along the ratchet. The hopping probability along the ratchet and the energy decay rates for the system are shown to obey the power law for late times, a behavior typical of discrete baths which for low and intermediate values of N always induce a non-Markovian process. The exponential decay is recovered for high bath frequencies distribution and for high values of N , where the Markovian limit is expected. Moreover, by including the external oscillating field with intensity F , we show that current reversal occurs in two situations: By increasing N and by switching from low to high frequencies distribution of the bath. The mobility of particles is shown to have a maximum at F=0.1 , which is N independent (for higher values of N ).