Publication: Soliton ratchets in homogeneous nonlinear Klein-Gordon systems
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2006-03
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American Institute of Physics
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Abstract
We study in detail the ratchetlike dynamics of topological solitons in homogeneous nonlinear
Klein-Gordon systems driven by a biharmonic force. By using a collective coordinate approach
with two degrees of freedom, namely the center of the soliton, X t , and its width, l t , we show,
first, that energy is inhomogeneously pumped into the system, generating as result a directed
motion; and, second, that the breaking of the time shift symmetry gives rise to a resonance mechanism
that takes place whenever the width l t oscillates with at least one frequency of the external
ac force. In addition, we show that for the appearance of soliton ratchets, it is also necessary to
break the time-reversal symmetry. We analyze in detail the effects of dissipation in the system,
calculating the average velocity of the soliton as a function of the ac force and the damping.We find
current reversal phenomena depending on the parameter choice and discuss the important role
played by the phases of the ac force. Our analytical calculations are confirmed by numerical
simulations of the full partial differential equations of the sine-Gordon and 4 systems, which are
seen to exhibit the same qualitative behavior. Our results show features similar to those obtained in
recent experimental work on dissipation induced symmetry breaking.
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Chaos, vol. 16, n. 1, mar. 2006, 13 págs.