Abstract
The ratchet effect [1–3] is the rectification of fluctuations in a periodic potential in the absence of net applied bias forces. In this way directed motion along a macroscopically flat structure is obtained. The archetypal of a ratchet consists of Brownian particles in a periodic potential. In order to obtain directed motion, two main requirements have to be fulfilled. First, the system has to be driven out of equilibrium, so to overcome the limitations imposed by the second principle of thermodynamics. Second, the relevant symmetries of the system, which would otherwise prevent the generation of a current, have to be broken. Among the different possible implementations of the ratchet effect, we mention here the flashing ratchet [1–3], the rocking ratchet [1–3], and the more recently introduced gating ratchet [4–6]. In the rocking ratchet set-up, Brownian particles in a periodic potential experience an additional time-dependent applied force F(t), which is homogeneous and has zero time-average. The oscillating applied force plays a double role. On one hand, it drives the system out of thermodynamic equilibrium, thus avoiding the restrictions imposed by the second principle of thermodynamics. On the other hand, the temporal symmetry properties of the applied force, together with the spatial symmetry properties of the periodic potential, control the directed motion.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R.D. Astumian and P. Hänggi, Phys. Today 55, 33 (2002)
P. Reimann, Phys. Rep. 361, 57 (2002)
P. Hänggi, F. Marchesoni, and F. Nori, Ann. Phys. 14, 51 (2005)
S. Savel’ev, F. Marchesoni, P. Hänggi, and F. Nori, Europhys. Lett. 67, 179 (2004)
S. Savel’ev, F. Marchesoni, P. Hänggi, and F. Nori, Eur. Phys. J. B 40, 403 (2004)
M. Borromeo and F. Marchesoni, Chaos 15, 026110 (2005)
S. Flach, O. Yevtushenko, and Y. Zolotaryuk, Phys. Rev. Lett. 84, 2358 (2000)
O. Yevtushenko, S. Flach, Y. Zolotaryuk, and A.A. Ovchinnikov, Europhys. Lett. 54, 141 (2001)
P. Reimann, Phys. Rev. Lett. 86, 4992 (2001)
S. Flach and S. Denisov, Acta Phys. Pol. B35, 1437 (2004)
E. Neumann and A. Pikovsky, Eur. Phys. J. B 26, 219 (2002)
G. Grynberg and C. Mennerat-Robillard, Phys. Rep. 255, 335 (2001)
M. Schiavoni, L. Sanchez-Palencia, F. Renzoni, and G. Grynberg, Phys. Rev. Lett. 90, 094101 (2003)
R. Gommers, S. Bergamini, and F. Renzoni, Phys. Rev. Lett. 95, 073003 (2005)
R. Gommers, S. Denisov, and F. Renzoni, Phys. Rev. Lett. 96, 240604 (2006)
R. Gommers, M. Brown, and F. Renzoni, Phys. Rev. A 75, 053406 (2007)
F. Marchesoni, Phys. Lett. A 119, 221 (1986)
P. Reimann, M. Grifoni, and P. Hänggi, Phys. Rev. Lett. 79, 10 (1997)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Renzoni, F. (2010). Symmetry and Transport in a Rocking Ratchet for Cold Atoms. In: Denz, C., Flach, S., Kivshar, Y. (eds) Nonlinearities in Periodic Structures and Metamaterials. Springer Series in Optical Sciences, vol 150. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02066-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-02066-7_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02065-0
Online ISBN: 978-3-642-02066-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)