论文标题
流行动力学液滴理论中步行液滴的不变度量
The invariant measure of a walking droplet in hydrodynamic pilot-wave theory
论文作者
论文摘要
我们研究了流体动力学驾驶器系统中步行器的长期统计数据，该系统是一种随机的Langevin动力学，具有外部电位和记忆内核。虽然先前的实验和数值模拟表明该系统可能达到统计稳定状态，但尚未严格研究其长期行为。对于广泛的外部电势和飞行员波力，我们将解决方案构建为在合适的路径空间上演变的动力学。然后，在假设前进力是由电势主导的假设下，我们证明了步行者具有独特的统计稳态状态。我们通过介绍了这样一个不变度量的示例，如从谐波电位中的步行者的数值模拟获得的示例。
We study the long time statistics of a walker in a hydrodynamic pilot-wave system, which is a stochastic Langevin dynamics with an external potential and memory kernel. While prior experiments and numerical simulations have indicated that the system may reach a statistically steady state, its long-time behavior has not been studied rigorously. For a broad class of external potentials and pilot-wave forces, we construct the solutions as a dynamics evolving on suitable path spaces. Then, under the assumption that the pilot-wave force is dominated by the potential, we demonstrate that the walker possesses a unique statistical steady state. We conclude by presenting an example of such an invariant measure, as obtained from a numerical simulation of a walker in a harmonic potential.
