A Primer on Ratchets and Brownian Motors
Example: The flashing ratchet.
Brownian particles are trapped ina periodic, asymmetric potential
that can be turned on and off. The random diffusion when the
potential is off is converted into net motion to the left
when the ratchet is switched on. A discussion of this
Brownian motor, and a nice on-line simulation can
be found at www.chaos.gwdg.de/java_gallery/brownian_motor/bm.html
Most research in the Linke lab is based on the ratchet
concept: The combination of non-equilibrium
and asymmetry generally leads to transport.
The basic physical idea is simple: a system that is not in thermal
equilibrium tends towards equilibrium. If this system lives in an
asymmetric world, then moving towards equilibrium will usually also
involve a movement in space. To keep the system moving, we need
to perpetually keep it away from thermal equilibrium, which costs
energy - this is the energy that drives the motion.
Ratchets are interesting for a number of reasons:
- The physics of precisely how transport is achieved can be very
subtle and interesting, including quantum phenomena.
- The direction of transport often depends on fine details of
the system, for instance the temperature or the size of the particles.
In principle, ratchets can therefore be used to separate particles,
for instance by their size.
- When thermal motion is important for the function of a ratchet,
the system is called a thermal ratchet or a Brownian motor. Such
systems use non-equilibrium energy to rectify Brownian motion:
a subtle, interesting phenomenon that cannot be observed in thermal
- Brownian motors are excellent model systems to understand how
nanoscale machines may operate in the presence of substantial
thermal motion. For this reason, the Brownian motor concept is
often used to model biological, molecular motors.
An accessible introduction to the physics of Brownian motors:
D. Astumian, Science 276, 917 (1997)
A popular review:
D. Astumian: Making Molecular Motors. Scientific American,
A somewhat more technical introduction to the physics of Brownian
motors, including a brief history of the ratchet idea
P. Reimann and P. Hänggi, Appl. Phys. A 75, 169 (2002)
The bible: a technical and very thorough review.
P. Reimann, Brownian motors: Noisy transport far from equilibrium.
Phys. Rep. 361, 57 (2002)
A collection of papers on experiments and applications:
H. Linke (Ed.): Ratchets and Brownian Motors: Basics, Experiments
and Applications. Applied
Physics A Vol. 75 (2) (2002).