We explore the role of inertia in the properties of active Brownian particles (ABPs) immersed in an underdamped background in two dimensions using Langevin dynamics computer simulation. Similar to an equilibrium two-dimensional passive interacting particle system, the system of ABPs transits from a liquid phase to a solid phase with the change in the coupling parameter, which is the ratio of interaction potential energy and thermal energy of the background solvent. Important qualitative and quantitative differences are found in the liquid-solid phase transition with increasing strength of activity as compared to those found in the conventional overdamped background limit. In the underdamped background, inherent activity is found to lead to a temperature, called the active temperature and defined by average velocity fluctuations of the ABPs, that is different from the fixed background solvent temperature. A new scaling law for active temperature as a function of activity strength is found near the liquid-solid boundary. Active temperature, which behaves similar to the thermodynamic equilibrium temperature, is also found to depend upon the interaction strength between the active particles and the strength of the background dissipation. With an increase in background dissipation, the difference between active temperature and the background solvent temperature decreases and the difference is found to eventually vanish in the overdamped limit, demonstrating the correctness of the calculation.

中文翻译：

---

欠阻尼背景下活动布朗系统中相变和活动温度的出现

我们使用Langevin动力学计算机模拟，探索了惯性在浸入欠阻尼背景中的二维活动布朗粒子（ABP）属性中的作用。与平衡二维被动相互作用粒子系统相似，随着耦合参数（即相互作用势能与背景溶剂的热能之比）的变化，ABPs系统从液相转变为固相。与传统的超阻尼背景极限相比，在液相-固相​​转变中随着活性强度的增加，发现了重要的定性和定量差异。在欠阻尼的背景下，发现固有活动会导致一个温度，称为活动温度并由ABP的平均速度波动定义，与固定的背景溶剂温度不同。在液固边界附近发现了新的活性温度随活性强度变化的定标规律。还发现表现出类似于热力学平衡温度的活性温度取决于活性颗粒之间的相互作用强度和背景耗散的强度。随着背景耗散的增加，活性温度和背景溶剂温度之间的差异减小，并且发现该差异最终在过度衰减的极限中消失，这证明了计算的正确性。