Differential Identities for the Structure Function of Some Random Matrix Ensembles

@article{Forrester2020DifferentialIF,
  title={Differential Identities for the Structure Function of Some Random Matrix Ensembles},
  author={Peter J. Forrester},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
  • P. Forrester
  • Published 1 June 2020
  • Mathematics
  • arXiv: Mathematical Physics
The structure function of a random matrix ensemble can be specified as the covariance of the linear statistics $\sum_{j=1}^N e^{i k_1 \lambda_j}$, $\sum_{j=1}^N e^{-i k_2 \lambda_j}$ for Hermitian matrices, and the same with the eigenvalues $\lambda_j$ replaced by the eigenangles $\theta_j$ for unitary matrices. As such it can be written in terms of the Fourier transform of the density-density correlation $\rho_{(2)}$. For the circular $\beta$-ensemble of unitary matrices, and with $\beta$ even… 
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  • P. Forrester
  • Physics
    Communications in Mathematical Physics
  • 2021
The ensemble average of $| \sum_{j=1}^N e^{i k \lambda_j} |^2$ is of interest as a probe of quantum chaos, as is its connected part, the structure function. Plotting this average for model systems of
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