Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Nonlinear Dynamics I

DY 17.7: Talk

Wednesday, March 16, 2011, 12:15–12:30, ZEU 255

Pushing through the Arnold web: Hamiltonian ratchets in higher dimensions — •Armin Seibert, Sergey Denisov, and Peter Hänggi — Institute of Physics, University of Augsburg, Universitätsstr. 1, D-86135 Augsburg

In ac-driven, space-periodic Hamiltonian systems a ratchet effect [1] may occur: particles start to diffuse predominantly into one direction, producing constant flux, even when the driving field has a zero dc-component. This is a well-established phenomenon in the case of one-dimensional Hamiltonian transport, with experimental validations ranging from classical [2] to quantum [3] limits. Remarkably, two- and three - dimensional stationary transport is impossible {\it ab initio} in ac-driven Hamiltonian systems. The system can diffuse in its phase space - along resonance channels, which constitute the {\it Arnold web} [4], - so that even when the particle is initially placed at the bottom of a potential well, it can eventually be accelerated to any preassigned energy threshold. We demonstrate that although the ratchet current never saturates to an asymptotic value in the case of higher-dimensional Hamiltonian ratchets, the direction of the ratchet motion is fixed by the space-time symmetries of the underlying potentials, and can be predicted by using the symmetry analysis [5].

[1] P. Hänggi and F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009) [2] M. Schiavoni et al., Phys. Rev. Lett. 90, 094101 (2003) [3] T. Salger et al., Science 326, 1241 (2009) [4] A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics (New York, Springer-Verlag, 1992) [5] S. Denisov et al., Phys. Rev. Lett. 100, 224102 (2008)