关于纳米尺度体系中单粒子分布函数的一些严格结果  

On the Single-Particle Distribution Function in the Systems of Nanometer Scale:Some Rigorous Results

作　　者：龙贤哲[1] 杨凯华[2] 何培松[1] 田光善[1] 

机构地区：[1]北京大学物理学院,北京100871 [2]北京工业大学应用数理学院,北京100022

出　　处：《北京大学学报（自然科学版）》2007年第5期630-638,共9页Acta Scientiarum Naturalium Universitatis Pekinensis

基　　金：国家自然科学基金(90403003;10674003);北京市科研新星计划(2005B11)资助项目

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。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 ease 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.

关 键 词：纳米体系 单粒子分布函数 严格结果 

分 类 号：O481[理学—固体物理]