论文标题
准开普勒的量子多体系统的第三定律
Quasi Kepler's third law for quantum many-body systems
论文作者
论文摘要
开普勒的第三定律是通过引力潜能相互作用的两个经典粒子的时期与能量之间的关系。最近的作品表明，这一法律至少可以扩展到经典的三体系统，甚至可以扩展到多体经典系统。因此，似乎存在古典准开普勒的第三定律。在本文中，计算了近似分析解决方案，以用于具有不同质量的量子自我磨碎的颗粒。结果给出了有力的迹象，以支持存在此类系统的准开普勒第三定律。该提案的相关性与准确的数值数据相关性，以构成自我磨碎相同玻色子的基础状态，并对具有相同粒子的系统以及不同的系统进行数值估计。讨论了量子系统和经典系统之间的连接。
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.
