论文标题
二维量子涡流气体的布朗运动理论
Brownian motion theory of the two-dimensional quantum vortex gas
论文作者
论文摘要
提出了布朗运动的理论，用于涡流组装。在量子冷凝物的背景下，戴森的库仑气体实现了这种尝试。从依赖时间依赖的Landau-Ginzburg（LG）理论开始，构建了涡流气体的动力学，该动力学由运动的运动方程组成。点涡流的动力学转换为langevin方程，从而使用高斯白噪声的ANSATZ上的功能积分导致了广义的Fokker-Planck（GFP）（或Smolkovski）方程。拥有非富有财产的GFP的特点是两个称为“过度阻尼”和“失业”制度的政权。在耗散量比涡旋强度大得多的过度阻尼方案中，GFP成为标准的fokker-Planck方程，该方程转换为二维的许多粒子系统。给出了Fokker-Planck方程的几个特定应用。还讨论了两个涡流系统的小扩散极限。简要讨论了涡流电荷比耗散大得多的不足的限制。
A theory of Brownian motion is presented for an assembly of vortices. The attempt is motivated by a realization of Dyson' Coulomb gas in the context of quantum condensates. By starting with the time-dependent Landau-Ginzburg (LG) theory, the dynamics of the vortex gas is constructed, which is governed by the canonical equation of motion. The dynamics of point vortices is converted to the Langevin equation, which results in the generalized Fokker-Planck (GFP) (or Smolkovski) equation using the functional integral on the ansatz of the Gaussian white noise. The GFP, which possesses a non-Hermitian property, is characterized by two regimes called the "overdamping" and the "underdamping" regime. In the overdamping regime, where the dissipation is much larger than the vortex strength, the GFP becomes the standard Fokker-Planck equation, which is transformed to the two-dimensional many particle system. Several specific applications are given of the Fokker-Planck equation. An asymptotic limit of small diffusion is also discussed for the two vortices system. The underdamping limit, for which the vortex charge is much larger than the dissipation, is briefly discussed.
