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We argue that flows of the quantum electronic liquid in the Fractional Quantum Hall state are comprehensively described by the hydrodynamics of vortices in the quantum incompressible rotating liquid.
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The transformation ( 14
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Hydrodynamics of a non-chiral version of the same model and with β = 1 \beta=1 has been studied in relation to normal matrices by J. Feinberg, Nucl. Phys. B 705:403 (2005)
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Eq. ( 17
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V. V. Kozlov, General Theory of Vortices, Springer 2003
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For developments on this subject see Avron ; ReadHV ; Tokatly ; Son ; Abanov
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Our approach is a close analog of the hydrodynamics description of Calogero model of Refs. Calogero
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A.G. Abanov, On the effective hydrodynamics of FQHE, to be published
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Coulomb forces always emerge in flows of electronic liquids. They are essential factor in the bulk, less essential on the edge. In this paper we neglect Coulomb forces in order to unmask laws of quantum hydrodynamics
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C. Hoyos, D. T. Son, Phys. Rev. Lett. 108, 066805 (2012)
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Y. Greenberg, V. Zelevinsky, J.Phys.A 45, 035001 (2012)
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