多体引力系统中的量子效应
Quantum effects in many-body gravitating systems
摘要：
前面得到的平衡态约化密度矩阵的方程族被用来考虑仅受引力约束的无自旋玻色子系统。在玻色凝聚条件下，假设系统处于温度的绝对零度。在这种情况下，量子效应和微粒之间非常弱的引力相互作用发生了特殊的相互作用。因此，可以形成宏观尺寸的空间有界平衡结构，既不动又旋转。结构的尺寸与结构中的颗粒数量成反比。当粒子的数量相对较少时，尺寸可以是巨大的，而如果该粒子数等于阿伏伽德罗数，则在该结构由氢原子组成的情况下，该结构的半径约为30 cm。旋转的物体具有环形的形状，并表现出超流性。也考虑了可以被微小天体从周围介质捕获的大气。大气层的厚度随其质量的增加而减小。如果考虑短程分子间力，所得结果适用于寿命很长的激发态。本文的结果可用于解释星际甚至星系间气体形成天体的第一阶段。
英文摘要：
A hierarchy of equations for equilibrium reduced density matrices obtained earlier is used to consider systems of spinless bosons bound by forces of gravity alone. The systems are assumed to be at absolute zero of temperature under conditions of Bose condensation. In this case, a peculiar interplay of quantum effects and of very weak gravitational interaction between microparticles occurs. As a result, there can form spatially-bounded equilibrium structures macroscopic in size, both immobile and rotating. The size of a structure is inversely related to the number of particles in the structure. When the number of particles is relatively small the size can be enormous, whereas if this numbder equals Avogadro's number the radius of the structure is about 30 cm in the case that the structure consists of hydrogen atoms. The rotating objects have the form of rings and exhibit superfluidity. An atmosphere that can be captured by tiny celestial bodies from the ambient medium is considered too. The thickness of the atmosphere decreases as its mass increases. If short-range intermolecular forces are taken into account, the results obtained hold for excited states whose lifetime can however be very long. The results of the paper can be utilized for explaining the first stage of formation of celestial bodies from interstellar and even intergalactic gases.
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