Non-Feynman Deterministic Pulsing Ratchet Based on a Symmetric Periodic Potential with Harmonic Time Modulation

The deterministic mechanism of directed particle motion in a symmetric periodic potential with harmonic time modulation is theoretically examined. We show that directed particle motion can be established with a symmetric potential in the absence of thermal motion, provided the spatial particle shift is synchronized with the period of temporal change in the potential and the characteristic time required for the particle to pass through the interval between neighboring extremes in potential is equal to the half-period of the time modulation. Ratchet behavior is demonstrated using a simple symmetric force potential consisting of a square wave with opposite but equal amplitude regions. By establishing spatiotemporal synchronization between the particle shift in space and the time modulation, nonreversible directed particle motion is provided by inertia that is maintained as the potential profile approaches zero in the time modulation process.