Soliton ratchetlike dynamics by ac forces with harmonic mixing

Area of Science:

• Nonlinear Dynamics
• Condensed Matter Physics
• Statistical Mechanics

Background:

• Dissipative systems can exhibit complex behaviors like soliton motion.
• Sine-Gordon equation models various physical phenomena, including wave propagation.
• AC forces can drive particle-like solutions (solitons) in nonlinear systems.

Purpose of the Study:

• Investigate unidirectional motion of kinks (topological solitons) in a dissipative sine-Gordon equation under AC forces.
• Analyze the dependence of kink mean velocity on system parameters.
• Compare numerical results with perturbation analysis.

Main Methods:

• Numerical simulations of the dissipative sine-Gordon equation.
• Perturbation analysis using a point-particle representation of the soliton.
• Investigation of soliton-phonon interactions and temporal symmetry effects.

Main Results:

• First-order perturbation theory is insufficient due to significant soliton-phonon interactions.
• An asymmetric internal mode couples with the kink's translational mode, enabling soliton transport.
• Effective transport occurs when the internal mode and external force are phase-locked.
• Different harmonic forcings lead to distinct contributions to soliton drift velocity.
• The phenomenon is robust against thermal noise.

Conclusions:

• Soliton transport in dissipative systems is significantly influenced by internal modes and their coupling.
• Temporal symmetry plays a crucial role in creating soliton ratchets.
• The findings suggest potential applications in nanoscale devices and transport phenomena.