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• W4288434037 abstract "A random matrix representation is proposed for the two-dimensional (2D) Coulomb gas at inverse temperature $ensuremath{beta}$. For $2ifmmodetimeselsetexttimesfi{}2$ matrices with Gaussian distribution we analytically compute the nearest-neighbor spacing distribution of complex eigenvalues in radial distance. Because it does not provide such a good approximation as the Wigner surmise in 1D, we introduce an effective ${ensuremath{beta}}_{mathrm{eff}}(ensuremath{beta})$ in our analytic formula that describes the spacing obtained numerically from the 2D Coulomb gas well for small values of $ensuremath{beta}$. It reproduces the 2D Poisson distribution at $ensuremath{beta}=0$ exactly, that is valid for a large particle number. The surmise is used to fit data in two examples, from open quantum spin chains and ecology. The spacing distributions of complex symmetric and complex quaternion self-dual ensembles of non-Hermitian random matrices, that are only known numerically, are very well fitted by noninteger values $ensuremath{beta}=1.4$ and $ensuremath{beta}=2.6$ from a 2D Coulomb gas, respectively. These two ensembles have been suggested as the only two symmetry classes, where the 2D bulk statistics is different from the Ginibre ensemble." @default.
• W4288434037 created "2022-07-29" @default.
• W4288434037 creator A5018741680 @default.
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• W4288434037 date "2022-07-28" @default.
• W4288434037 modified "2023-10-14" @default.
• W4288434037 title "Spacing distribution in the two-dimensional Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at noninteger<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>β</mml:mi></mml:math>" @default.
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• W4288434037 doi "https://doi.org/10.1103/physreve.106.014146" @default.
• W4288434037 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/35974587" @default.
• W4288434037 hasPublicationYear "2022" @default.
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