用费米气体表示的黎曼零点分布
Distribution of the Riemann zeros represented by the Fermi gas
摘要：
计算了任意维简并理想费米气体系统的多粒子密度矩阵。结果表示为行列式形式，其中相关核起着至关重要的作用。有趣的是，一维费米气体系统的关联结构与随机么正矩阵的本征值分布的关联结构是等价的，因而也与Riemann zeta函数的非平凡零点分布的关联结构是等价的.本研究结果的影响进行了简要讨论。
英文摘要：
The multiparticle density matrices for degenerate, ideal Fermi gas system in any dimension are calculated. The results are expressed as a determinant form, in which a correlation kernel plays a vital role. Interestingly, the correlation structure of one-dimensional Fermi gas system is essentially equivalent to that observed for the eigenvalue distribution of random unitary matrices, and thus to that conjectured for the distribution of the non-trivial zeros of the Riemann zeta function. Implications of the present findings are discussed briefly.
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