量子多体系统的准开普勒第三定律
Quasi Kepler's third law for quantum many-body systems
摘要：
开普勒第三定律是两个经典粒子通过引力势相互作用的周期和能量之间的关系。最近的工作表明，这一定律至少可以近似地扩展到经典的三体系统，甚至是多体经典系统。因此，一个经典的准开普勒第三定律似乎是存在的。本文计算了不同质量的量子自引力粒子的近似解析解。结果给出了强有力的迹象，有利于存在一个准开普勒第三定律，这样的系统。该建议的相关性检查与精确的数值数据的基态的自引力相同的玻色子和数值估计的系统与相同的粒子加上不同的。量子和经典系统之间的连接进行了讨论。
英文摘要：
The Kepler's third law is a relation between the period and the energy of two classical particles interacting via a gravitational potential. Recent works showed that this law could be extended, at least approximately, to classical three-body systems, or even many-body classical systems. So, a classical quasi Kepler's third law seems to exist. In this paper, approximate analytical solutions are computed for quantum self-gravitating particles with different masses. The results give strong indications in favor of the existence of a quasi Kepler's third law for such systems. The relevance of the proposal is checked with accurate numerical data for the ground state of self-gravitating identical bosons and with numerical estimations for systems with identical particles plus a different one. Connections between the quantum and classical systems are discussed.
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