Macroscopic and edge behavior of a planar jellium

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We consider a planar Coulomb gas in which the external potential is generated by a smeared uniform background of opposite-sign charge on a disk. This model can be seen as a two-dimensional Wigner jellium, not necessarily charge-neutral, and with particles allowed to exist beyond the support of the smeared charge. The full space integrability condition requires a low enough temperature or high enough total smeared charge. This condition does not allow, at the same time, total charge-neutrality and determinantal structure. The model shares similarities with both the complex Ginibre ensemble and the Forrester-Krishnapur spherical ensemble of random matrix theory. In particular, for a certain regime of temperature and total charge, the equilibrium measure is uniform on a disk as in the Ginibre ensemble, while the modulus of the farthest particle has heavy-tailed fluctuations as in the Forrester-Krishnapur spherical ensemble. We also touch upon a higher temperature regime producing a crossover equilibrium measure, as well as a transition to Gumbel edge fluctuations. More results in the same spirit on edge fluctuations are explored by the second author together with Raphael Butez.
Publisher
AMER INST PHYSICS
Issue Date
2020-03
Language
English
Article Type
Article
Citation

JOURNAL OF MATHEMATICAL PHYSICS, v.61, no.3

ISSN
0022-2488
DOI
10.1063/1.5126724
URI
http://hdl.handle.net/10203/273930
Appears in Collection
MA-Journal Papers(저널논문)
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