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Discrete soliton ratchets driven by biharmonic fields.

Yaroslav Zolotaryuk1, Mario Salerno

  • 1Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kyiv 03143, Ukraine.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 16, 2006
PubMed
Summary

Topological solitons in discrete sine-Gordon systems can move unidirectionally when driven by asymmetric AC fields, exhibiting ratchet-like transport. The motion

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Area of Science:

  • Condensed matter physics
  • Nonlinear dynamics
  • Soliton physics

Background:

  • Topological solitons, such as kinks and antikinks, are stable particle-like excitations in nonlinear systems.
  • The dynamics of solitons in discrete systems differ significantly from their continuum counterparts.
  • Ratchet transport and nonlinear harmonic mixing are established phenomena in driven nonlinear systems.

Purpose of the Study:

  • To investigate the directed motion of topological solitons in a damped, AC-driven discrete sine-Gordon system.
  • To identify the conditions under which unidirectional soliton motion occurs.
  • To compare the behavior of solitons in discrete versus continuum systems.

Main Methods:

  • Numerical simulations of the damped and AC-driven discrete sine-Gordon equation.
  • Analysis of the influence of driving field symmetries on soliton dynamics.
  • Formulation of necessary conditions for unidirectional motion.

Main Results:

  • Unidirectional soliton motion is achieved when the AC driving field breaks time-space symmetries.
  • The direction and velocity of motion are dependent on the AC drive's waveform.
  • Discrete systems exhibit unique features: a nonzero depinning threshold, frequency locking to rational fractions, and diffusive motion at weak coupling.

Conclusions:

  • Breaking time-space symmetries in the driving field is key to achieving directed soliton transport in discrete systems.
  • The discrete sine-Gordon model offers a richer phenomenology than the continuum case, including novel ratchet effects.
  • These findings have implications for understanding transport phenomena in discrete nonlinear systems.

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