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Center for Nonlinear Studies |
In inhomogeneous sine-Gordon ratchet systems with ac driving the soliton dynamics is chaotic in certain parameter regions, nevertheless the soliton motion is unidirectional. This is qualitatively explained by a 1-Collective-Coordinate (1CC) theory which yields an equation of motion for the soliton that is identical to the equation of motion for a single particle ratchet which is known to exhibit chaotic transport in its underdamped regime. For a quantitative comparison with our simulations we use a 2CC-theory.
In contrast to this, homogeneous sine-Gordon ratchets with biharmonic driving, which breaks a
temporal shift symmetry, do not exhibit chaos. This is explained by a 2CC-theory which yields
two ODEs: one is linear, the other one describes a parametrically driven oscillator which does not
exhibit chaos. The latter ODE can be solved by a perturbation theory which yields a hierarchy of
linear equations that can be solved exactly order by order. The results agree very well with our
simulations.
Host: Avadh Saxena, T-4