Comment on "Soliton ratchets induced by excitation of internal modes"

Kink ratchet induced by a time-dependent symmetric field potential

The ratchet effect of a sine-Gordon kink is investigated in the absence of any external force while the symmetry of the field potential at every time instant is maintained. The directed motion appears by a time shift of the sine-Gordon potential through a time-dependent additional phase. A symmetry analysis provides the necessary conditions for the existence of net motion. It is also shown analytically, by using a collective coordinate theory, that the novel physical mechanism responsible for the appearance of the ratchet effect is the coupled dynamics of the kink width with the background field. Biharmonic and dichotomic periodic variations of the additional phase of the sine-Gordon potential are considered. The predictions established by the symmetry analysis and the collective coordinate theory are verified by means of numerical simulations. Inversion and maximization of the resulting current as a function of the system parameters are investigated.

Driven and damped double sine-Gordon equation: the influence of internal modes on the soliton ratchet mobility

This work studies the damped double sine-Gordon equation driven by a biharmonic force, where a parameter lambda controls the existence and the frequency of an internal mode. The role of internal oscillations of the kink width in ratchet dynamics of kink is investigated within the framework of collective coordinate theories. It is found that the ratchet velocity of the kink, when an internal mode appears in this system, decreases contrary to what was expected. It is also shown that the kink exhibits a higher mobility in the double sine-Gordon without internal mode, but with a quasilocalized first phonon mode.

Chaotic transport in deterministic sine-Gordon soliton ratchets

We investigate homogeneous and inhomogeneous sine-Gordon ratchet systems in which a temporal symmetry and the spatial symmetry, respectively, are broken. We demonstrate that in the inhomogeneous systems with ac driving the soliton dynamics is chaotic in certain parameter regions, although the soliton motion is unidirectional. This is qualitatively explained by a one-collective-coordinate 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 two-collective-coordinate (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 the simulations.

Ratchet effect in a damped sine-Gordon system with additive and parametric ac driving forces

We study in detail the damped sine-Gordon equation, driven by two ac forces (one is added as a parametric perturbation and the other one in an additive way), as an example of soliton ratchets. By means of a collective coordinate approach we derive an analytical expression for the average velocity of the soliton, which allows us to show that this mechanism of transport requires certain relationships both between the frequencies and between the initial phases of the two ac forces. The control of the velocity by the damping coefficient and parameters of the ac forces is also presented and discussed. All these results are subsequently checked by means of simulations for the driven and damped sine-Gordon equation that we have studied.

Energy flow of moving dissipative topological solitons

We study the energy flow due to the motion of topological solitons in nonlinear extended systems in the presence of damping and driving. The total field momentum contribution to the energy flux, which reduces the soliton motion to that of a point particle, is insufficient. We identify an additional exchange energy flux channel mediated by the spatial and temporal inhomogeneity of the system state. In the well-known case of a dc external force the corresponding exchange current is shown to be small but nonzero. For the case of ac driving forces, which lead to a soliton ratchet, the exchange energy flux mediates the complete energy flow of the system. We also consider the case of combination of ac and dc external forces, as well as spatial discretization effects.

Soliton ratchets in homogeneous nonlinear Klein-Gordon systems

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 phi4 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.

Analytical approach to soliton ratchets in asymmetric potentials

We use soliton perturbation theory and collective coordinate ansatz to investigate the mechanism of soliton ratchets in a driven and damped asymmetric double sine-Gordon equation. We show that, at the second order of the perturbation scheme, the soliton internal vibrations can couple effectively, in presence of damping, to the motion of the center of mass, giving rise to transport. An analytical expression for the mean velocity of the soliton is derived. The results of our analysis confirm the internal mode mechanism of soliton ratchets proposed in [Phys. Rev. E 65, 025602(R) (2002)].