囚禁理想费米子和相互作用费米子的精确基态数涨落
Exact ground state number fluctuations of trapped ideal and interacting fermions
摘要：
我们考虑一个孤立的一维陷阱（微正则系综）中的费米子的一个小的和固定的数量。系统的基态定义为T = 0，其中最低的单粒子能级被占据。处于该基态的粒子数作为激发能的函数而波动。通过将能谱分解为粒子和空穴两部分，并将问题映射到经典的数划分理论上，我们提出了一种新的方法来计算粒子数涨落，该方法比直接组合数学方法更有效.计算了粒子通过平方反比相互作用时的基态数涨落。
英文摘要：
We consider a small and fixed number of fermions in an isolated one-dimensional trap (microcanonical ensemble). The ground state of the system is defined at T=0, with the lowest single-particle levels occupied. The number of particles in this ground state fluctuates as a function of excitation energy. By breaking up the energy spectrum into particle and hole sectors, and mapping the problem onto the classic number partitioning theory, we formulate a new method to calculate the exact particle number fluctuation more efficiently than the direct combinatorics method. The exact ground state number fluctuation for particles interacting via an inverse-square pair-wise interaction is also calculated.
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