---
res:
bibo_abstract:
- "We investigate a one-parameter family of Coulomb gases in two dimensions,\r\nwhich
are confined to an ellipse, due to a hard wall constraint, and are\r\nsubject
to an additional external potential. At inverse temperature $\\beta=2$\r\nwe can
use the technique of planar orthogonal polynomials, borrowed from random\r\nmatrix
theory, to explicitly determine all $k$-point correlation functions for\r\na fixed
number of particles $N$. These are given by the determinant of the\r\nkernel of
the corresponding orthogonal polynomials, which in our case are the\r\nGegenbauer
polynomials, or a subset of the asymmetric Jacobi polynomials,\r\ndepending on
the choice of external potential. In the rotationally invariant\r\ncase, when
the ellipse becomes the unit disc, our findings agree with that of\r\nthe ensemble
of truncated unitary random matrices. The thermodynamical\r\nlarge-$N$ limit is
investigated in the local scaling regime in the bulk and at\r\nthe edge of the
spectrum at weak and strong non-Hermiticity. We find new\r\nuniversality classes
in these limits and recover the sine- and Bessel-kernel in\r\nthe Hermitian limit.
The limiting global correlation functions of particles in\r\nthe interior of the
ellipse are more difficult to obtain but found in the\r\nspecial cases corresponding
to the Chebyshev polynomials.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Taro
foaf_name: Nagao, Taro
foaf_surname: Nagao
- foaf_Person:
foaf_givenName: Gernot
foaf_name: Akemann, Gernot
foaf_surname: Akemann
foaf_workInfoHomepage: http://www.librecat.org/personId=23134650
- foaf_Person:
foaf_givenName: Mario
foaf_name: Kieburg, Mario
foaf_surname: Kieburg
foaf_workInfoHomepage: http://www.librecat.org/personId=39774202
- foaf_Person:
foaf_givenName: Iván
foaf_name: Parra, Iván
foaf_surname: Parra
dct_date: 2019^xs_gYear
dct_language: eng
dct_title: 'Families of two-dimensional Coulomb gases on an ellipse: correlation functions
and universality@'
...