This paper is devoted to the linearized Vlasov–Poisson–Fokker–Planck system in presence of an external potential of confinement. We investigate the large time behaviour of the solutions using hypocoercivity methods and a notion of scalar product adapted to the presence of a Poisson coupling. Our framework provides estimates which are uniform in the diffusion limit. As an application in a simple case, we study the one-dimensional case and prove the exponential convergence of the nonlinear Vlasov–Poisson–Fokker–Planck system without any small mass assumption.

中文翻译：

---

$$\text {L}^2$$ L 2 -线性化 Vlasov–Poisson–Fokker–Planck 系统的低矫顽力和大时间渐近性

本文致力于在存在外部约束势的情况下线性化 Vlasov-Poisson-Fokker-Planck 系统。我们使用矫顽力方法和适用于泊松耦合存在的标量积概念来研究解决方案的长时间行为。我们的框架提供了在扩散限制中一致的估计。作为一个简单案例的应用，我们研究一维案例并证明非线性 Vlasov-Poisson-Fokker-Planck 系统的指数收敛性，无需任何小质量假设。