Numerical Simulation of GUE Two-Point Correlation and Cluster Functions
arXiv:2010.03500 · doi:10.1007/s13538-020-00802-6
Abstract
Numerical simulations of the two-point eigenvalue correlation and cluster functions of the Gaussian unitary ensemble (GUE) are carried out directly from their definitions in terms of deltas functions. The simulations are compared with analytical results which follow from three analytical formulas for the two-point GUE cluster function: (i) Wigner's exact formula in terms of Hermite polynomials, (ii) Brezin and Zee's approximate formula which is valid for points with small enough separations and (iii) French, Mello and Pandey's approximate formula which is valid on average for points with large enough separations. It is found that the oscillations present in formulas (i) and (ii) are reproduced by the numerical simulations if the width of the function used to represent the delta function is small enough and that the non-oscillating behaviour of formula (iii) is approached as the width is increased.
arXiv comment8 pages, 8 figures
References in corpus (12)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Random Matrices and Chaos in Nuclear Physics
- Random Matrices and Chaos in Nuclear Physics: Nuclear Reactions
- On Asymptotic Properties of Large Random Matrices with Independent Entries
- Introduction to Random Matrices - Theory and Practice
- Misleading signatures of quantum chaos
- Universality of Brezin and Zee's Spectral Correlator
- Will a physicist prove the Riemann Hypothesis?
- Level density for deformations of the Gaussian orthogonal ensemble
- Universal Behavior of Correlations between Eigenvalues of Random Matrices
- Statistical features of the thermal neutron capture cross sections
- Saturation of the width of the strength function