在带有反的最小格子模型中出现集体自我振荡
Dmitry Sinelshchikov1,2,3, Anna Poggialini4,5, Maria Francesca Abbate6,7
1Biofisika Institutua (UPV/EHU, CSIC) and Fundación Biofísica Bizkaia, Leioa E-48940, Spain.
Physical review. E
|November 18, 2023
概括
这项研究揭示了复杂系统中的集体振荡是如何出现的,它超越了平衡阶段过渡. 非线性动力学和分叉理论解释了这些现象在经典模型,如伊辛,布鲁姆-卡佩尔和波茨.
科学领域:
- 统计力学 统计力学
- 非线性动力学是一种非线性动力学.
- 复杂的系统复杂的系统.
背景情况:
- 集体振荡和同步在复杂系统中很常见,但在多体系统的失平衡阶段过渡中不太了解.
- 现有的研究主要集中在动态系统上,在阶段过渡背景下对这些现象的理解存在差距.
研究的目的:
- 调查在经历失衡阶段过渡的经典格子模型 (伊辛,布鲁姆-卡佩尔,波茨) 中非线性集体自振的出现.
- 将平均场集体行为与低维动态系统的分叉理论联系起来.
- 为集体振荡定义潜在的普遍性类.
主要方法:
- 低维非线性动态系统的推导用于使用线性响应理论的平均场例.
- 对衍生动态系统与多体随机模拟进行定量验证.
- 对分叉的分析,包括兰道理论,丁分叉,周期翻倍和体破坏场景.
主要成果:
- 平衡阶段过渡被复杂的分叉所取代,导致非线性集体自我振荡.
- 对于伊辛模型来说,在有限维度的关键点上观察到非微不足道的分叉,循环幅度遵循2D缓慢反的Onsager定律.
- 多稳定性和新出现的振荡在布鲁姆-卡佩尔模型中得到了说明,其三临界点被丁分叉所取代.
- 波茨模型 (q=3) 显示出稳定的极限周期和混乱的振荡,通过周期翻倍或体破坏.
- entropy 生产奇点与莱普诺夫指数的变化相关.
结论:
- 这些模型中的平均场集体行为可以通过低维动态系统的分叉理论有效地描述.
- 这些发现为建立集体振荡的普遍性类铺平了道路.
- 这项工作弥合了对多体系统和非线性动态中的集体现象的理解.
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