Resonances in the dynamics of $φ^4$ kinks perturbed by ac forces

Details Resonances in the dynamics of $φ^4$ kinks perturbed by ac forces Resonances in the dynamics of $φ^4$ kinks perturbed by ac forces

2000-06-21

arxiv.org/abs/cond-mat/0006313v1

Physics

Condensed Matter

Statistical Mechanics

23 pages, 7 figures, REVTeX, accepted for publication in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.62.5695

We study the dynamics of $\phi^4$ kinks perturbed by an ac force, both with and without damping. We address this issue by using a collective coordinate theory, which allows us to reduce the problem to the dynamics of the kink center and width. We carry out a careful analysis of the corresponding ordinary differential equations, of Mathieu type in the undamped case, finding and characterizing the resonant frequencies and the regions of existence of resonant solutions. We verify the accuracy of our predictions by numerical simulation of the full partial differential equation, showing that the collective coordinate prediction is very accurate. Numerical simulations for the damped case establish that the strongest resonance is the one at half the frequency of the internal mode of the kink. In the conclusion we discuss on the possible relevance of our results for other systems, especially the sine-Gordon equation. We also obtain additional results regarding the equivalence between different collective coordinate methods applied to this problem.

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