Yazdi Anoosheh, Sperl Matthias
Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt, 51170 Köln, Germany.
Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, 50937 Köln, Germany.
Phys Rev E. 2016 Sep;94(3-1):032602. doi: 10.1103/PhysRevE.94.032602. Epub 2016 Sep 8.
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 is described by a Langevin equation with Rayleigh-Helmholtz velocity-dependent friction. In the 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 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 the number of active particles in the system. Using the Mori-Zwanzig formalism and the mode-coupling approximation, the equations of motion for the density autocorrelation 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.
我们考虑一个二维布朗粒子模型系统，其中慢粒子被加速而快粒子被阻尼。单个粒子的运动由具有瑞利 - 亥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。速度依赖摩擦力允许慢粒子的摩擦力为负值或能量摄入，我们将其视为主动运动，并且还导致涨落耗散关系的破坏。定义与速度的二阶矩成比例的有效温度，结果表明，对于恒定的有效温度，噪声强度越高，系统中主动粒子的数量就越低。使用森 - 万齐格形式主义和模式耦合近似，推导了密度自相关函数的运动方程。使用平衡结构因子求解这些方程。采用瞬态积分方法推导了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。
