Chavanis Pierre-Henri, Sire Clément
Laboratoire de Physique Théorique (UMR 5152 du CNRS), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jun;73(6 Pt 2):066103. doi: 10.1103/PhysRevE.73.066103. Epub 2006 Jun 1.
We derive the virial theorem appropriate to the generalized Smoluchowski-Poisson (GSP) system describing self-gravitating Brownian particles in an overdamped limit. We extend previous works by considering the case of an unbounded domain and an arbitrary equation of state. We use the virial theorem to study the diffusion (evaporation) of an isothermal Brownian gas above the critical temperature Tc in dimension d = 2 and show how the effective diffusion coefficient and the Einstein relation are modified by self-gravity. We also study the collapse at T = Tc and show that the central density increases logarithmically with time instead of exponentially in a bounded domain. Finally, for d > 2, we show that the evaporation of the system is essentially a pure diffusion slightly slowed down by self-gravity. We also study the linear dynamical stability of stationary solutions of the GSP system representing isolated clusters of particles and investigate the influence of the equation of state and of the dimension of space on the dynamical stability of the system.
我们推导了适用于广义斯莫卢霍夫斯基 - 泊松（GSP）系统的维里定理，该系统描述了在过阻尼极限下的自引力布朗粒子。我们通过考虑无界域的情况和任意状态方程扩展了先前的工作。我们使用维里定理研究二维中等温布朗气体在临界温度(Tc)以上的扩散（蒸发），并展示了自引力如何修改有效扩散系数和爱因斯坦关系。我们还研究了(T = Tc)时的坍缩，并表明在有界域中中心密度随时间呈对数增长而非指数增长。最后，对于(d > 2)，我们表明系统的蒸发本质上是一种纯扩散，只是因自引力而略有减慢。我们还研究了表示孤立粒子团簇的GSP系统稳态解的线性动力学稳定性，并研究了状态方程和空间维度对系统动力学稳定性的影响。
