论文标题
广义Langevin方程的缩放限制
Scaling limits for the generalized Langevin equation
论文作者
论文摘要
在本文中，我们研究了溶液在周期性潜力中对广义Langevin方程（GLE）的扩散极限。在假设准马尔可级的假设下，我们利用低调理论获得了GLE的长期平衡估计值。然后，我们证明了在三个限制方案中的有效扩散系数的渐近结果：短记忆，过度阻尼和引导不足的极限。最后，我们采用了最近开发的光谱数值方法，以计算多种（有效）摩擦系数的有效扩散系数，从而确认我们的渐近结果。
In this paper, we study the diffusive limit of solutions to the generalized Langevin equation (GLE) in a periodic potential. Under the assumption of quasi-Markovianity, we obtain sharp longtime equilibration estimates for the GLE using techniques from the theory of hypocoercivity. We then prove asymptotic results for the effective diffusion coefficient in three limiting regimes: the short memory, the overdamped and the underdamped limits. Finally, we employ a recently developed spectral numerical method in order to calculate the effective diffusion coefficient for a wide range of (effective) friction coefficients, confirming our asymptotic results.
