Second quantization approach to characteristic polynomials in RMT

Details Second quantization approach to characteristic polynomials in RMT Second quantization approach to characteristic polynomials in RMT

2000-11-07

arxiv.org/abs/nlin/0011014v1

J.Phys.A34:3553-3560,2001

Nonlinear Sciences

Chaotic Dynamics

LaTeX, 7 pages, 1 figure

Scientific paper

10.1088/0305-4470/34/17/303

The distribution of the characteristic polynomial $Z(U,\theta)$ of $N\times N$ matrices $U$ in the Circular Unitary Ensemble is studied by the method of second quantization for one-dimensional fermions. For infinite $N$ the Gaussian distribution of $Z(U,\theta)$ is established straightforwardly by bosonization. A general expression for the $n$-point correlation function of the characteristic polynomial at different points is given by this method. The case of finite $N$ is discussed.

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