Dynamics of the Bose-Einstein condensation: analogy with the collapse dynamics of a classical self-gravitating Brownian gas.
Dynamics of the Bose-Einstein condensation: analogy with the collapse dynamics of a classical self-gravitating Brownian gas.
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DOI：
10.1103/physreve.74.011112
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发表时间：
2005-11
期刊：
影响因子：
--
通讯作者：
J. Sopik;C. Sire;P. Chavanis
中科院分区：
文献类型：
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作者：
J. Sopik;C. Sire;P. Chavanis
我们在一个半经典的福克-普朗克方程中考虑自由玻色子气体的动力学，我们给出了物理证明。在这种情况下，我们发现经典系综中的玻色-爱因斯坦凝聚与经典自引力布朗粒子气体的引力坍缩之间存在惊人的相似性。本文主要致力于在该模型中对玻色-爱因斯坦“坍缩”进行全面研究。我们发现，在玻色-爱因斯坦凝聚温度Tc下，化学势(t)以我们精确计算的普遍速率指数消失。在Tc下面，我们解析地证明了平方根(t)在有限时间内线性消失。冷却后，冷凝物的质量随时间线性增长，并在长时间内呈指数饱和至其平衡值。我们还给出了密度标度函数、标度修正和指数弛豫时间的解析结果。最后，我们发现平衡时间（高于Tc）和坍缩时间（低于Tc）都表现为T -3 c ln|T-Tc|，接近Tc。
We consider the dynamics of a gas of free bosons within a semiclassical Fokker-Planck equation for which we give a physical justification. In this context, we find a striking similarity between the Bose-Einstein condensation in the canonical ensemble, and the gravitational collapse of a gas of classical self-gravitating Brownian particles. The paper is mainly devoted to the complete study of the Bose-Einstein "collapse" within this model. We find that at the Bose-Einstein condensation temperature Tc, the chemical potential mu(t) vanishes exponentially with a universal rate that we compute exactly. Below Tc, we show analytically that square root mu(t) vanishes linearly in a finite time t coll. After t coll, the mass of the condensate grows linearly with time and saturates exponentially to its equilibrium value for large time. We also give analytical results for the density scaling functions, for the corrections to scaling, and for the exponential relaxation time. Finally, we find that the equilibration time (above Tc) and the collapse time T coll(below Tc) both behave like -T -3 c ln|T-Tc|, near Tc.