Escobar-Ruiz A M, Quiroz-Juarez M A, Del Rio-Correa J L, Aquino N
Departamento de Física, Universidad Autónoma Metropolitana Unidad Iztapalapa, San Rafael Atlixco 186, 09340, Mexico City, Mexico.
Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Boulevard Juriquilla 3001, 76230, Juriquilla, Querétaro, Mexico.
Sci Rep. 2022 Aug 3;12(1):13346. doi: 10.1038/s41598-022-17541-0.
The classical three-body harmonic system in [Formula: see text] ([Formula: see text]) with finite rest lengths and zero total angular momentum [Formula: see text] is considered. This model describes the dynamics of the [Formula: see text] near-equilibrium configurations of three point masses [Formula: see text] with arbitrary pairwise potential [Formula: see text] that solely depends on the relative distances between bodies. It exhibits an interesting mixed regular and chaotic dynamics as a function of the energy and the system parameters. The corresponding harmonic quantum system plays a fundamental role in atomic and molecular physics. In this work we report on a novel electronic experimental realization of the model as a complementary tool to analyze the rich dynamics of the classical system. Our setup allows us to experimentally explore different regions of behavior due to the fact that the intrinsic parameters and initial states of the system are independently set by voltage inputs. Chaotic and periodic motions are characterized employing time series, phase planes, and the largest Lyapunov exponents as a function of the energy and system parameters. The results show an excellent qualitative as well as quantitative agreement between theory and experiment.
考虑了在[公式：见正文]（[公式：见正文]）中具有有限静止长度且总角动量[公式：见正文]为零的经典三体谐振子系统。该模型描述了三个点质量[公式：见正文]的[公式：见正文]近平衡构型的动力学，其具有仅取决于物体间相对距离的任意成对势[公式：见正文]。作为能量和系统参数的函数，它呈现出有趣的规则与混沌混合动力学。相应的谐振子量子系统在原子和分子物理学中起着基础性作用。在这项工作中，我们报告了该模型的一种新颖的电子实验实现方式，作为分析经典系统丰富动力学的一种补充工具。由于系统的固有参数和初始状态由电压输入独立设置，我们的装置使我们能够通过实验探索不同的行为区域。利用时间序列、相平面以及作为能量和系统参数函数的最大李雅普诺夫指数来表征混沌和周期性运动。结果表明理论与实验之间在定性和定量上都有极好的一致性。
