Chaos and Multi-Fractal in Nonlinear Spin Dynamics

参数激励下的自旋波系统是非线性、非平衡自旋动力学系统的一个很好的例子。在平行和垂直抽运的参量激发下，自旋波对在热能级以上增长。当微波功率增加到苏尔不稳定性阈值以上时，系统变得不稳定，自旋波对随时间变化。观察到多种类型的规则和不规则自振荡，即倍周期分岔、准周期和阵发性混沌。由于微观量子理论对磁性的理解是很好的，它是混沌理论研究的一个很好的例子.分形维数，返回映射，李雅普诺夫指数，奇怪的吸引子和f（α）谱作为磁场和驱动微波功率的函数进行了研究。f（α）谱描述了混沌奇异吸引子的多重分形结构，在混沌开始时（临界区）观测到的f（α）谱与理论上的普适的倍周期通向混沌的谱非常一致.在混沌区观察到的谱与临界区不同，在交叉区同时观察到临界区和混沌区的谱。用微观模型Hamiltonian进行数值模拟，得到了f（α）谱的类似分岔现象，观察到了从准周期到混沌的转变，通过环面和相位锁定。利用庞加莱映射和层流周期长度分布研究了在自激振荡开始之前观察到的阵发性混沌。在调制抽运场作用下观察到Arnold舌和锁频态。对参激自旋波的非线性辐射阻尼进行了理论和实验研究。

A spin-wave system under parametric excitation provides a good example of nonlinear and nonequilibrium spin dynamics system. Spin-wave pairs grow far above the thermal levels under parametric excitation ehich is performed by parallel and perpendicular pumping When microwave power is increased well above the threshold of Suhl instability, the system becomes unstable and the number of spin-wave varies with time. Many types of regular and irregular auto-oscillations are observed, that is, period-doubling bifurcation, qeasi-periodic and intermittency chaos. Since magnetism is well understood by microsscopic quantum theory, it is one of excellent examples of theoretical research of chaos.Fractal dimensions, return maps, Lyapunov exponents, strange attractor and f(alpha) spectra are studied as a function of magnetic field and driving microwave power. f(alpha) spectra, which characterize the multi-fractal structure of chaotic strange attractor, observed at the onset of chaos (critical regime)are in excellent agreement with the theoretical universal spectra of period-doubling route to chaos. The spectra observed in chaotic regime is different from one in critical regime and both spectra of critical and chaotic regimes are observed in the crossover region. Numerical simulation by microscopic model Hamiltonian gives similar bifurcation phenomena of f(alpha) spectra.Transition from quasiperiodicity to chaos through a torus and phase locking is observed. Intermittency chaos observed just above the onset of auto-oscillations was studied by Poincare maps and distribution of laminar period lengths. Arnold's tongue and frequency-locked state are observed under modulated pumping field Nonlinear radiation damping of parametrically excited spin-waves are theoretically and experimentally studied.