Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $β$

Akemann G, Mielke A, Päßler P (2021)
arXiv:2112.12624.

Preprint | Englisch
 
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Abstract / Bemerkung
A random matrix representation is proposed for the two-dimensional (2D) Coulomb gas at inverse temperature $\beta$. For $2\times 2$ matrices with Gaussian distribution this yields a surmise for the nearest neighbour spacing distribution of complex eigenvalues in radial distance. It reproduces the 2D Poisson distribution at $\beta=0$ and approximates the complex Ginibre ensemble at $\beta=2$. The surmise is used to fit data from open quantum spin chains and ecology. The spacing distributions of complex symmetric and complex quaternion self-dual ensembles are fitted by non-integer values $\beta=1.4$ and $\beta=2.6$, respectively. They have been suggested as the only two symmetry classes with 2D bulk statistics different from the Ginibre ensemble.
Erscheinungsjahr
2021
Zeitschriftentitel
arXiv:2112.12624
Page URI
https://pub.uni-bielefeld.de/record/2963771

Zitieren

Akemann G, Mielke A, Päßler P. Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $β$. arXiv:2112.12624. 2021.
Akemann, G., Mielke, A., & Päßler, P. (2021). Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $β$. arXiv:2112.12624
Akemann, G., Mielke, A., and Päßler, P. (2021). Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $β$. arXiv:2112.12624.
Akemann, G., Mielke, A., & Päßler, P., 2021. Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $β$. arXiv:2112.12624.
G. Akemann, A. Mielke, and P. Päßler, “Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $β$”, arXiv:2112.12624, 2021.
Akemann, G., Mielke, A., Päßler, P.: Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $β$. arXiv:2112.12624. (2021).
Akemann, Gernot, Mielke, Adam, and Päßler, Patricia. “Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $β$”. arXiv:2112.12624 (2021).

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