稀薄旋转气体的基态渐近性
Ground State Asymptotics of a Dilute, Rotating Gas
摘要：
本文研究了三维空间中相互作用粒子气体的基态性质。我们考虑稀释气体的Gross-Pitaevskii（GP）极限。分析绝对和玻色子基态的系统，我们显示，特别是，他们的不同行为的一定范围内的参数。这个参数范围是由GP泛函的极小值中的旋转对称性是否破缺决定的。对于绝对基态，我们证明了在GP极限下，依赖于密度矩阵的修正GP泛函正确地描述了能量和约化的密度矩阵，与对称性破缺无关.对于玻色子基态，当且仅当对称性未破缺时，这才成立。
英文摘要：
We investigate the ground state properties of a gas of interacting particles confined in an external potential in three dimensions and subject to rotation around an axis of symmetry. We consider the so-called Gross-Pitaevskii (GP) limit of a dilute gas. Analyzing both the absolute and the bosonic ground state of the system we show, in particular, their different behavior for a certain range of parameters. This parameter range is determined by the question whether the rotational symmetry in the minimizer of the GP functional is broken or not. For the absolute ground state, we prove that in the GP limit a modified GP functional depending on density matrices correctly describes the energy and reduced density matrices, independent of symmetry breaking. For the bosonic ground state this holds true if and only if the symmetry is unbroken.
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