随机场中与独立Ising自旋耦合的受驱动谐振子的动力学
The dynamics of a driven harmonic oscillator coupled to independent Ising spins in random fields
摘要：
我们的目的是了解的动力学性质的周期性驱动的阻尼谐振子耦合到随机场伊辛模型（RISK）在零温度下，这是能够显示复杂的滞后。该系统是连续（谐振子）和离散（RFIM）子系统的组合，将其归类为混合系统。在本文中，我们专注于混合性质的系统，并考虑在淬火随机局部领域，这可能已经导致复杂的动力学，如混沌和多稳定性的独立自旋。我们利用分段光滑动力系统和不连续映射理论研究了该系统的动力学行为。具体来说，我们给出了分岔图、李雅普诺夫指数以及吸引子的形状和尺寸以及吸引子尺寸和磁化强度的自平均行为的结果。此外，我们研究了系统的动力学行为的自旋数的增加和过渡到热力学极限，其中系统的行为像一个驱动的谐振子与一个额外的非线性光滑外力。
英文摘要：
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.
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