论文标题
用两个布朗颗粒的双线性模型对非线性耗散进行调和
Reconciling nonlinear dissipation with the bilinear model of two Brownian particles
论文作者
论文摘要
单个粒子的布朗运动是耗散系统非平衡动力学的范式模型。在系统加墨水方法中，人们可以从系统的可逆动力学到代表其热环境的振荡器浴的系统的可逆动力学来得出粒子的运动方程。但是，在集体环境中将系统加入的方法扩展到多个粒子并不是一件直接的，并且已经提出了相互冲突的模型。在这里，我们着手调和两个布朗颗粒的非线性和双线性模型的某些方面。我们展示了如何从双线性拉格朗日（Biinear Lagrangian）中获得最初从指数系统 - 固定耦合得出的非线性耗散，并具有明确取决于粒子之间的距离的修改光谱函数。作为应用，我们讨论了如何避免从标准的非线性模型中避免异常扩散，以及如何在粘性流体中的一对布朗尼颗粒之间的现象学上对流体动力的相互作用进行建模。
The Brownian motion of a single particle is a paradigmatic model of the nonequilibrium dynamics of dissipative systems. In the system-plus-reservoir approach, one can derive the particle's equations of motion from the reversible dynamics of the system coupled to a bath of oscillators representing its thermal environment. However, extending the system-plus-reservoir approach to multiple particles in a collective environment is not straightforward, and conflicting models have been proposed to that end. Here, we set out to reconcile some aspects of the nonlinear and the bilinear models of two Brownian particles. We show how the nonlinear dissipation originally derived from exponential system-reservoir couplings can alternatively be obtained from the bilinear Lagrangian, with a modified spectral function that explicitly depends on the distance between the particles. As applications, we discuss how to avoid the anomalous diffusion from the standard nonlinear model, as well as how to phenomenologically model a hydrodynamic interaction between a pair of Brownian particles in a viscous fluid.
