Exact solution for mean energy of 2d Dyson gas at beta = 1

Details Exact solution for mean energy of 2d Dyson gas at beta = 1 Exact solution for mean energy of 2d Dyson gas at beta = 1

2009-12-30

arxiv.org/abs/0912.5520v2

Phys.Lett.A375:984-989,2011

Physics

Mathematical Physics

10 pages, 1 figure

Scientific paper

10.1016/j.physleta.2011.01.004

Mean Coulomb energy of 2d Dyson gas in quadratic potential is examined from combinatorial viewpoint. For beta = 1, we find a recursive relation on mean energy and obtain its exact (finite N) solution in closed form in terms of the hypergeometric function 3F2. Using this exact solution, we derive the large-N asymptotic expansion of mean energy and show, that this expansion contains half-integer powers of N.

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