量子硬球的玻色-爱因斯坦凝聚作为一种沉积相变和玻色子压力与费米压力之间的新关系
Bose-Einstein Condensation of Quantum Hard-Spheres as a Deposition Phase Transition and New Relations Between Bosonic and Fermionic Pressures
摘要：
在范德华近似下，研究了巨正则系综中具有硬核排斥的玻色-爱因斯坦粒子的相变。结果表明，非相对论性玻色-爱因斯坦粒子的压力在数学上等价于表面张力系数和Fisher指数$τ_F = \frac{5}{2}$为零的原子核多重碎裂统计模型的简化版本的压力，在这些参数下，原子核多重碎裂统计模型具有一级相变.发现这些状态方程的相似性，使我们能够表明，在本方法中的玻色-爱因斯坦粒子的高密度相是一个经典的宏观团簇消失熵在任何温度下，类似于经典的硬球，是一种固态。为了证明这一点，我们建立了新的关系，使我们能够用两种玻色-爱因斯坦粒子的压力来等同地表示费米-狄拉克粒子的压力。
英文摘要：
We investigate the phase transition of Bose-Einstein particles with the hard-core repulsion in the grand canonical ensemble within the Van der Waals approximation. It is shown that the pressure of non-relativistic Bose-Einstein particles is mathematically equivalent to the pressure of simplified version of the statistical multifragmentation model of nuclei with the vanishing surface tension coefficient and the Fisher exponent $τ_F = \frac{5}{2}$, which for such parameters has the 1-st order phase transition. The found similarity of these equations of state allows us to show that within the present approach the high density phase of Bose-Einstein particles is a classical macro-cluster with vanishing entropy at any temperature which, similarly to the classical hard spheres, is a kind of solid state. To show this we establish new relations which allow us to identically represent the pressure of Fermi-Dirac particles in terms of pressures of Bose-Einstein particles of two sorts.
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