Abstract: The properties of the single-particle distribution function in nanometer scale systems are rigorously studied. First, by using the variational principle, it is shown that this function is nonincreasing with respect to the single-particle energy levels at zero temperature. Then, by applying the Klein inequality, the same conclusion can be also established in the case of nonzero temperature. These results show clearly how the behavior of the single-particle distribution function is determined by the stability condition of the systems.

Key words: nanometer scale systems, single-particle distribution function, rigorous results

摘要： 利用变分原理，首先证明在零温下，量子点系统和超导小颗粒系统的单粒子分布函数对于单粒子能量是非增的。然后利用Klein不等式证明，在非零温下，这一结论仍然正确。这些结果明确地显示，这一分布函数随单粒子能量的非增行为是由这些纳米系统的量子稳定性条件决定的。

关键词: 纳米体系, 单粒子分布函数, 严格结果