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Second quantization approach to characteristic polynomials in RMT

Dimitry M. Gangardt
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Abstract

The distribution of the characteristic polynomial $Z(U,θ)$ 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 $Z(U,θ)$ 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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Dimitry M. Gangardt. 2000-11-07. Second quantization approach to characteristic polynomials in RMT. https://doi.org/10.1088/0305-4470%2F34%2F17%2F303

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