ЖЭТФ, Том 144,
Вып. 3,
стр. 595 (Сентябрь 2013)
(Английский перевод - JETP,
Vol. 117, No 3,
p. 517,
September 2013
доступен on-line на www.springer.com
)
STATISTICAL MECHANICS OF COULOMB GASES AS QUANTUM THEORY ON RIEMANN SURFACES
Gulden T., Janas M., Koroteev P., Kamenev A.
Поступила в редакцию: 26 Марта 2013
DOI: 10.7868/S0044451013090125
Dedicated to the memory of Professor Anatoly Larkin} Statistical mechanics of a 1D multivalent Coulomb gas can be mapped onto non-Hermitian quantum mechanics. We use this example to develop the instanton calculus on Riemann surfaces. Borrowing from the formalism developed in the context of the Seiberg-Witten duality, we treat momentum and coordinate as complex variables. Constant-energy manifolds are given by Riemann surfaces of genus . The actions along principal cycles on these surfaces obey the ordinary differential equation in the moduli space of the Riemann surface known as the Picard-Fuchs equation. We derive and solve the Picard-Fuchs equations for Coulomb gases of various charge content. Analysis of monodromies of these solutions around their singular points yields semiclassical spectra as well as instanton effects such as the Bloch bandwidth. Both are shown to be in perfect agreement with numerical simulations.
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