非相互作用玻色气体的相关不等式
Correlation inequalities for noninteracting Bose gases
摘要：
对于具有固定的与粒子数无关的单体哈密顿量H^0的非相互作用玻色气体，我们导出了不等式<N_i>_N <<N_i>_{N+1}，<N_i N_j>_N <<N_i>_N<N_j>_N，其中i为\neq j，\partial<N_0>_N/ \partial β>0，<N_i>^+_N <<N_i>_N。这里N_i是H^0的第i个本征态的占据数，β是温度的倒数，上标+是指在H^0的能级上增加一个额外的能级。结果是由N粒子自由能作为N的函数的凸性得出的。
英文摘要：
For a noninteracting Bose gas with a fixed one-body Hamiltonian H^0 independent of the number of particles we derive the inequalities <N_i>_N < <N_i>_{N+1}, <N_i N_j>_N < <N_i>_N <N_j>_N for i\neq j, \partial <N_0>_N/\partial β>0 and <N_i>^+_N < <N_i>_N. Here N_i is the occupation number of the ith eigenstate of H^0, βis the inverse temperature and the superscript + refers to adding an extra level to those of H^0. The results follow from the convexity of the N-particle free energy as a function of N.
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