Title: No equivalence between hydrodynamic and dispersive mass of the charged polaron Show Chinese title

Title: 带电极化子的流体质量和色散质量之间没有等价性

Abstract: We consider the problem of a charged impurity exerting a weak, slowly decaying force on its surroundings, treating the latter as an ideal compressible fluid. In the semiclassical approximation, the ion is described by the Newton equation coupled to the Euler equation for the medium. After linearization, we obtain a simple closed formula for the effective mass of the impurity, depending on the interaction potential, the mean medium density, and sound velocity. Thus, once the interaction and the equation of state of the fluid is known, an estimate of the hydrodynamic effective mass can be quickly provided. Going beyond the classical case, we show that replacing the Newton with Schr\"{o}dinger equation can drastically change the behavior of the impurity. In particular, the scaling of the Fermi polaron effective mass with the medium density is opposite in quantum and classical scenario. Our results are relevant for experimental systems featuring low energy impurities in Fermi or Bose systems, such as ions immersed in neutral atomic gases. Show Chinese abstract

Abstract: 我们考虑带电杂质对其周围环境施加弱且缓慢衰减的作用力的问题，将后者视为理想可压缩流体。 在半经典近似下，离子由与介质的欧拉方程耦合的牛顿方程描述。 线性化后，我们得到了一个关于有效质量的简单封闭公式，该公式依赖于相互作用势、平均介质密度和声速。 因此，一旦知道了相互作用和流体的状态方程，就可以快速提供流体力学的有效质量估计。 超越经典情况，我们证明用薛定谔方程替换牛顿方程可以极大地改变杂质的行为。 特别是，在量子和经典场景中，费米极化子的有效质量随介质密度的变化规律相反。 我们的结果适用于实验系统中的低能杂质，例如浸没在中性原子气体中的离子。