### The high temperature crossover for general 2D Coulomb gases

Akemann G, Byun S-S (2018)
arXiv:1808.00319.

Preprint| Englisch

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Autor/in
Akemann, GernotUniBi; Byun, Sung-Soo
Abstract / Bemerkung
We consider $N$ particles in the plane influenced by a general external potential that are subject to the Coulomb interaction in two dimensions at inverse temperature $\beta$. At large temperature, when scaling $\beta=2c/N$ with some fixed constant $c>0$, in the large-$N$ limit we observe a crossover from Ginibre's circular law or its generalization to the density of non-interacting particles at $\beta=0$. Using several different methods we derive a partial differential equation of generalized Liouville type for the crossover density. For radially symmetric potentials we present some asymptotic results and give examples for the numerical solution of the crossover density. These findings generalise previous results when the interacting particles are confined to the real line. In that situation we derive an integral equation for the resolvent valid for a general potential and present the analytic solution for the density in case of a Gaussian plus logarithmic potential.
Erscheinungsjahr
2018
Zeitschriftentitel
arXiv:1808.00319
Page URI
https://pub.uni-bielefeld.de/record/2932616

### Zitieren

Akemann G, Byun S-S. The high temperature crossover for general 2D Coulomb gases. arXiv:1808.00319. 2018.
Akemann, G., & Byun, S. - S. (2018). The high temperature crossover for general 2D Coulomb gases. arXiv:1808.00319
Akemann, G., and Byun, S. - S. (2018). The high temperature crossover for general 2D Coulomb gases. arXiv:1808.00319.
Akemann, G., & Byun, S.-S., 2018. The high temperature crossover for general 2D Coulomb gases. arXiv:1808.00319.
G. Akemann and S.-S. Byun, “The high temperature crossover for general 2D Coulomb gases”, arXiv:1808.00319, 2018.
Akemann, G., Byun, S.-S.: The high temperature crossover for general 2D Coulomb gases. arXiv:1808.00319. (2018).
Akemann, Gernot, and Byun, Sung-Soo. “The high temperature crossover for general 2D Coulomb gases”. arXiv:1808.00319 (2018).

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