Mechanisms of Symmetry Breaking in a Multidimensional Flashing Particle Ratchet

Ratcheting is a mechanism
that produces directional transport of
particles by rectifying nondirectional energy using local asymmetries
rather than a net bias in the direction of transport. In a flashing
ratchet, an oscillating force (here, an AC field) is applied perpendicular
to the direction of transport. In an effort to explore the properties
of current experimentally realizable ratchet systems, and to design
new ones, this paper describes classical simulations of a damped flashing
ratchet that transports charged nanoparticles within a transport layer
of finite, non-zero thickness. The thickness of the layer, and the
decay of the applied field in the z-direction throughout
that thickness, provide a mechanism of symmetry breaking in the system
that allows the ratchet to produce directional transport using a temporally unbiased oscillation of the AC driving field, a sine wave.
Sine waves are conveniently produced experimentally or harvested from
natural sources but cannot produce transport in a 1D or pseudo-1D
system. The sine wave drive produces transport velocities an order
of magnitude higher than those produced by the common on/off drive,
but lower than those produced by a temporally biased square wave drive
(unequal durations of the positive and negative states). The dependence
of the particle velocity on the thickness of the transport layer,
and on the homogeneity of the oscillating field within the layer,
is presented for all three driving schemes.