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Dynamical response of particles in asymmetric ratchet potential. (English) Zbl 1375.81115

Summary: The dynamics and response of particles in an asymmetric potential of the ratchet type is considered. An approximate asymmetric ratchet potential, which allows us to apply an analytical approach to investigate the systems’ response, is proposed based on the power series interpolation scheme. The method of multiple scales (MMS) is then employed to obtain an approximate solution at the principal resonance. Comparison between results obtained from the approximated and exact potentials show excellent agreement. The frequency response curves (FRCs) for different forcing are presented. The numerically computed FRCs were compared with the theoretical result to show the extent of agreement. Furthermore, by using perturbation methods, the stable and unstable domains of the solution were obtained.

MSC:

81Q50 Quantum chaos
81Q37 Quantum dots, waveguides, ratchets, etc.
81Q15 Perturbation theories for operators and differential equations in quantum theory
35B34 Resonance in context of PDEs