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Title: Statistical mechanics of Coulomb gases as quantum theory on Riemann surfaces

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 g {>=} 1. 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.
Authors:
; ; ;  [1]
  1. University of Minnesota, Department of Physics (United States)
Publication Date:
OSTI Identifier:
22210470
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Experimental and Theoretical Physics; Journal Volume: 117; Journal Issue: 3; Other Information: Copyright (c) 2013 Pleiades Publishing, Inc.; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHEMICAL ANALYSIS; COMPUTERIZED SIMULATION; COULOMB FIELD; DIFFERENTIAL EQUATIONS; GASES; QUANTUM MECHANICS; RIEMANN SHEET; SEMICLASSICAL APPROXIMATION; STATISTICAL MECHANICS; SURFACES