Liu Jin, Sun Kehui, Wang Huihai
School of Physics, <a href="https://ror.org/00f1zfq44">Central South University</a>, Changsha 410083, China.
School of Electronic Information, <a href="https://ror.org/00f1zfq44">Central South University</a>, Changsha 410083, China.
Phys Rev E. 2024 Jul;110(1-1):014204. doi: 10.1103/PhysRevE.110.014204.
This study investigates the impact of external forces on the movement of particles, specifically focusing on a type of box piecewise linear map that generates normal diffusion akin to Brownian motion. Through numerical methods, the research delves into the effects of two distinct external forces: linear forces linked to the particle's current position and periodic sinusoidal forces related to time. The results uncover anomalous dynamical behavior characterized by nonlinear growth in the ensemble-averaged mean-squared displacement (EAMSD), aging, and ergodicity breaking. Notably, the diffusion pattern of particles under linear external forces resembles an Ehrenfest double urn model, with its asymptotic EAMSD coinciding with the Langevin equation under linear potential. Meanwhile, particle movement influenced by periodic sinusoidal forces corresponds to an inhomogeneous Markov chain, with its external force amplitude and diffusion coefficient function exhibiting a "multipeak" fractal structure. The study also provides insights into the formation of this structure through the turnstiles dynamics.
本研究调查了外力对粒子运动的影响，特别关注一种能产生类似于布朗运动的正态扩散的箱形分段线性映射。通过数值方法，该研究深入探讨了两种不同外力的影响：与粒子当前位置相关的线性力和与时间相关的周期性正弦力。结果揭示了异常动力学行为，其特征为系综平均均方位移（EAMSD）的非线性增长、老化和遍历性破坏。值得注意的是，线性外力作用下粒子的扩散模式类似于埃伦费斯特双瓮模型，其渐近EAMSD与线性势下的朗之万方程一致。同时，受周期性正弦力影响的粒子运动对应于一个非齐次马尔可夫链，其外力振幅和扩散系数函数呈现出“多峰”分形结构。该研究还通过旋转门动力学为这种结构的形成提供了见解。
