Zarlenga D G, Larrondo H A, Arizmendi C M, Family Fereydoon
Departamento de Física, Facultad de Ingeniería, Universidad Nacional de Mar del Plata, Avenida J.B. Justo 4302, 7600 Mar del Plata, Argentina.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jul;80(1 Pt 1):011127. doi: 10.1103/PhysRevE.80.011127. Epub 2009 Jul 22.
A deterministic overdamped ratchet driven by a periodic square driving force is shown to display chaotic behavior. The system has neither temporal nor quenched noise but the strong nonlinearity of the driving force produces a very rich bifurcation pattern with synchronized as well as chaotic regions. This pattern disappears if a sinusoidal force replaces the square force. This unexpected behavior is explained by decomposing the system into two exactly solvable subsystems, each with its own characteristic transit time, so that the ratio between the period of the driving force and the transit times can be analyzed. The transition from synchronized to chaotic motion can be explained by means of a one-dimensional Poincaré map. Our results can be experimentally confirmed in a number of systems, including the three-junction superconducting quantum interference devices ratchet, the rocking ratchet effect for cold atoms, and the Josephson vortex ratchet.
由周期性方驱动力求得的确定性过阻尼棘轮被证明会呈现混沌行为。该系统既没有时间噪声也没有猝灭噪声，但驱动力的强非线性产生了一个非常丰富的分岔模式，包括同步区域和混沌区域。如果用正弦力取代方力，这种模式就会消失。通过将系统分解为两个可精确求解的子系统来解释这种意外行为，每个子系统都有其自身的特征渡越时间，这样就可以分析驱动力周期与渡越时间之间的比率。从同步运动到混沌运动的转变可以通过一维庞加莱映射来解释。我们的结果可以在许多系统中通过实验得到证实，包括三结超导量子干涉器件棘轮、冷原子的摇摆棘轮效应以及约瑟夫森涡旋棘轮。
