Numerical simulation of GUE two-point correlation and cluster functions.

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dc.contributor.authorSargeant, Adam James
dc.date.accessioned2022-09-15T17:23:33Z
dc.date.available2022-09-15T17:23:33Z
dc.date.issued2021pt_BR
dc.description.abstractNumerical 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.pt_BR
dc.identifier.citationSARGEANT, A. J. Numerical simulation of GUE two-point correlation and cluster functions. Brazilian Journal of Physics, v. 51, p. 308-315, 2021. Disponível em: <https://link.springer.com/article/10.1007/s13538-020-00802-6>. Acesso em: 29 abr. 2022.pt_BR
dc.identifier.doihttps://doi.org/10.1007/s13538-020-00802-6pt_BR
dc.identifier.issn1678-4448
dc.identifier.urihttp://www.repositorio.ufop.br/jspui/handle/123456789/15292
dc.identifier.uri2https://link.springer.com/article/10.1007/s13538-020-00802-6pt_BR
dc.language.isoen_USpt_BR
dc.rightsrestritopt_BR
dc.subjectRandom matrix theorypt_BR
dc.subjectGaussian unitary ensemblept_BR
dc.subjectCorrelation functionspt_BR
dc.titleNumerical simulation of GUE two-point correlation and cluster functions.pt_BR
dc.typeArtigo publicado em periodicopt_BR
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