Topological phases in population dynamics with rock-paper-scissors interactions

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Jinfeng Liang, Qionglin Dai, Hancheng Li, Haihong Li, Junzhong Yang
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引用次数: 0

Abstract

Topological phases have arisen great interests of physicists. Though most works focus on quantum systems, topological phases can also be found in nonquantum systems. In this work, we study an antisymmetric Lotka-Volterra dynamics defined on a chain of two-site cells with open boundary conditions. We find two edge-localization states, left edge-localization state, and right edge-localization state. In an edge-localization state, there exists a boundary region in which mass distribution displays an exponential decay with the distance away from the boundary. The two edge-localization states are connected by a sharp transition. To comprehend the edge-localization states, we transform the population dynamics into a non-Hermitian quantum system. Based on the generalized topological band theory of the non-Hermitian system with periodic boundary conditions, we use winding number to distinguish the left and the right edge-localization states, and the transition between these two states is identified to be a topological one.

Abstract Image

具有剪刀石头布相互作用的种群动力学拓扑阶段
拓扑相引起了物理学家的极大兴趣。虽然大多数研究集中于量子系统,但拓扑相也可以在非量子系统中发现。在这项工作中,我们研究了定义在具有开放边界条件的双位单元链上的反对称洛特卡-伏特拉动力学。我们发现了两种边缘定位状态,即左边缘定位状态和右边缘定位状态。在边缘定位态中,存在一个边界区域,在该区域中,质量分布随着离边界的距离呈指数衰减。两个边缘定位态通过一个急剧的过渡连接起来。为了理解边缘定位态,我们将种群动力学转化为非赫米提量子系统。根据具有周期边界条件的非赫米提系统的广义拓扑带理论,我们用绕组数来区分左侧和右侧边缘定位态,并确定这两种态之间的转变是拓扑转变。
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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