Title: Glassy Dynamics of Brownian Particles with Velocity-Dependent Friction Show Chinese title

Title: 布朗粒子速度依赖性摩擦的玻璃态动力学

Abstract: We consider a two-dimensional model system of Brownian particles in which slow particles are accelerated while fast particles are damped. The motion of the individual particles are described by a Langevin equation with Rayleigh-Helmholtz velocity dependent friction. In case of noninteracting particles, the time evolution equations lead to a non-Gaussian velocity distribution. The velocity dependent friction allows negative values of the friction or energy intakes by slow particles which we consider as active motion, and also causes breaking of the fluctuation dissipation relation. Defining the effective temperature proportional to the second moment of velocity, it is shown that for a constant effective temperature the higher the noise strength, the lower are the number of active particles in the system. Using the Mori-Zwanzig formalism and the mode-coupling approximation, the equation of motion for the density auto-correlation function are derived. The equations are solved using the equilibrium structure factors. The integration-through-transients approach is used to derive a relation between the structure factor in the stationary state considering the interacting forces, and the conventional equilibrium static structure factor. Show Chinese abstract

Abstract: 我们考虑一个二维布朗粒子的模型系统，在该系统中，慢速粒子被加速，而快速粒子被阻尼。 单个粒子的运动由带有瑞利-赫尔姆霍兹速度依赖摩擦力的朗之万方程描述。 在非相互作用粒子的情况下，时间演化方程导致非高斯速度分布。 速度依赖的摩擦使得慢速粒子可以具有负的摩擦或能量摄入，我们将其视为主动运动，同时也导致涨落耗散关系的破坏。 定义有效温度与速度的二阶矩成正比，结果表明，对于恒定的有效温度，噪声强度越高，系统中的主动粒子数量越少。 使用莫里-赞茨格形式主义和模耦合近似，推导出密度自相关函数的运动方程。 这些方程通过平衡结构因子进行求解。 采用瞬态积分方法，推导出考虑相互作用力的稳态结构因子与传统平衡静态结构因子之间的关系。