Free fermions and α-determinantal processes
Free fermions and α-determinantal processes
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DOI：
10.1088/1751-8121/ab0ebd
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发表时间：
2018-11
期刊：
影响因子：
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通讯作者：
F. D. Cunden;S. Majumdar;N. O’Connell
中科院分区：
文献类型：
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作者：
F. D. Cunden;S. Majumdar;N. O’Connell
行列式是标准行列式的单参数推广，对应于行列式，对应于永久式。本文研究了由费米子过程构造非决定点过程的一种简单极限方法.该程序示出了一个模型的N个自由费米子的谐波势。当系统处于基态时，重新标度的相关函数对于大N收敛到行列式（体中的正弦核和边缘处的艾里核的行列式）。我们分析了一个特殊的家庭费米子的激发态的点过程，并表明，适当的标度限制产生-determinantal过程。与波动光学和其他随机矩阵模型的链接建议。
The -determinant is a one-parameter generalisation of the standard determinant, with corresponding to the determinant, and corresponding to the permanent. In this paper a simple limit procedure to construct -determinantal point processes out of fermionic processes is examined. The procedure is illustrated for a model of N free fermions in a harmonic potential. When the system is in the ground state, the rescaled correlation functions converge for large N to determinants (of the sine kernel in the bulk and the Airy kernel at the edges). We analyse the point processes associated to a special family of excited states of fermions and show that appropriate scaling limits generate -determinantal processes. Links with wave optics and other random matrix models are suggested.