论文标题
驱动的谐波振荡器的动力学耦合到随机场中的独立旋转
The dynamics of a driven harmonic oscillator coupled to independent Ising spins in random fields
论文作者
论文摘要
我们旨在了解定期驱动的阻尼谐波振荡器的动力学特性，该谐波振荡器在零温度下耦合到随机场ISING模型（RFIM），该模型能够显示出复杂的滞后。该系统是连续（谐波振荡器）和离散（RFIM）子系统的组合，该系统将其归类为混合系统。在本文中，我们关注系统的混合性质，并仅考虑在淬火的随机局部场中进行独立的旋转，这已经可以导致复杂的动态，例如混乱和多稳定性。我们通过使用分段平滑动力学系统和不连续映射的理论来研究该系统的动态行为。具体而言，我们提出分叉图，Lyapunov指数以及吸引子的形状和尺寸的结果以及吸引子维度的自动化行为和磁化。此外，我们研究了系统的动力学行为，用于越来越多的旋转以及向热力学极限的过渡，在该旋转中，系统的行为就像驱动的谐波振荡器，并具有额外的非线性平滑外力。
We aim at an understanding of the dynamical properties of a periodically driven damped harmonic oscillator coupled to a Random Field Ising Model (RFIM) at zero temperature, which is capable to show complex hysteresis. The system is a combination of a continuous (harmonic oscillator) and a discrete (RFIM) subsystem, which classifies it as a hybrid system. In this paper we focus on the hybrid nature of the system and consider only independent spins in quenched random local fields, which can already lead to complex dynamics such as chaos and multistability. We study the dynamic behavior of this system by using the theory of piecewise-smooth dynamical systems and discontinuity mappings. Specifically, we present bifurcation diagrams, Lyapunov exponents as well as results for the shape and the dimensions of the attractors and the self-averaging behavior of the attractor dimensions and the magnetization. Furthermore we investigate the dynamical behavior of the system for an increasing number of spins and the transition to the thermodynamic limit, where the system behaves like a driven harmonic oscillator with an additional nonlinear smooth external force.
