Title: Local-time formula for dissipation in solid ionic electrolytes Show Chinese title

Title: 固态离子电解质中耗散的局部时间公式

Abstract: When ions move through solids, they interact with the solid's constituent atoms and cause them to vibrate around their equilibrium points. This vibration, in turn, modifies the potential landscape through which the mobile ions travel. Because the present-time potential depends on past interactions, the coupling is inherently non-local in time, making its numerical and analytical treatment challenging. For sufficiently slow-moving ions, we linearize the phonon spectrum to show that these non-local effects can be ignored, giving rise to a drag-like force. Unlike the more familiar drag coefficient in liquids, the drag takes on a matrix form due to the crystalline structure of the framework. We numerically simulate trajectories and dissipation rates using both the time-local and non-local formulas to validate our simplification. The time-local formula dramatically reduces the computational cost of calculating the motion of mobile particle through a crystalline framework and clearly connects the properties of the material to the drag experienced by the particle. Show Chinese abstract

Abstract: 当离子通过固体移动时，它们与固体的组成原子相互作用，并导致这些原子在其平衡点附近振动。 这种振动反过来修改了移动离子所穿越的势能景观。 由于当前的势能依赖于过去的相互作用，这种耦合在时间上本质上是非局部的，使得其数值和分析处理具有挑战性。 对于运动速度足够慢的离子，我们对声子谱进行线性化，以表明这些非局部效应可以被忽略，从而产生一种类似拖拽的力。 与液体中更为熟悉的拖拽系数不同，由于框架的晶体结构，拖拽表现为一个矩阵形式。 我们使用时间局部和非局部公式对轨迹和耗散率进行数值模拟，以验证我们的简化方法。 时间局部公式显著降低了计算通过晶体框架的移动粒子运动的计算成本，并明确地将材料的特性与粒子所经历的拖拽联系起来。