[{"external_id":{"arxiv":["1905.07977"]},"type":"preprint","publication":"arXiv:1905.07977","language":[{"iso":"eng"}],"date_updated":"2019-07-15T11:18:41Z","title":"Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality","abstract":[{"text":"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.","lang":"eng"}],"year":"2019","author":[{"full_name":"Nagao, Taro","last_name":"Nagao","first_name":"Taro"},{"id":"23134650","full_name":"Akemann, Gernot","last_name":"Akemann","first_name":"Gernot"},{"last_name":"Kieburg","first_name":"Mario","full_name":"Kieburg, Mario","id":"39774202"},{"full_name":"Parra, Iván","first_name":"Iván","last_name":"Parra"}],"status":"public","_id":"2936503","date_created":"2019-07-15T11:18:41Z","department":[{"_id":"29104678"}],"citation":{"harvard1":"Nagao, T., et al., 2019. Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality. *arXiv:1905.07977*.","mla":"Nagao, Taro, Akemann, Gernot, Kieburg, Mario, and Parra, Iván. “Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality”. *arXiv:1905.07977* (2019).","lncs":" Nagao, T., Akemann, G., Kieburg, M., Parra, I.: Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality. arXiv:1905.07977. (2019).","apa":"Nagao, T., Akemann, G., Kieburg, M., & Parra, I. (2019). Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality. *arXiv:1905.07977*","ieee":" T. Nagao, et al., “Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality”, *arXiv:1905.07977*, 2019.","chicago":"Nagao, Taro, Akemann, Gernot, Kieburg, Mario, and Parra, Iván. 2019. “Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality”. *arXiv:1905.07977*.

","apa_indent":"Nagao, T., Akemann, G., Kieburg, M., & Parra, I. (2019). Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality. *arXiv:1905.07977*

","dgps":"Nagao, T., Akemann, G., Kieburg, M. & Parra, I. (2019). Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality. *arXiv:1905.07977*.

","wels":"Nagao, T.; Akemann, G.; Kieburg, M.; Parra, I. (2019): Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality *arXiv:1905.07977*","ama":"Nagao T, Akemann G, Kieburg M, Parra I. Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality. *arXiv:1905.07977*. 2019.","bio1":"Nagao T, Akemann G, Kieburg M, Parra I (2019)

Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality.

arXiv:1905.07977.","angewandte-chemie":"T. Nagao, G. Akemann, M. Kieburg, and I. Parra, “Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality”, *arXiv:1905.07977*, **2019**.","default":"Nagao T, Akemann G, Kieburg M, Parra I (2019)

*arXiv:1905.07977*.","frontiers":"Nagao, T., Akemann, G., Kieburg, M., and Parra, I. (2019). Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality. *arXiv:1905.07977*."},"user_id":"67994"}]