Self-Dual Vortices in Chern-Simons Hydrodynamics

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dc.creatorPashaev, Oktay K.
dc.creatorLee, and Jyh-Hao
dc.date2001-04-30
dc.date.accessioned2026-07-25T20:59:30Z
dc.descriptionThe classical theory of non-relativistic charged particle interacting with U(1) gauge field is reformulated as the Schrödinger wave equation modified by the de-Broglie-Bohm quantum potential nonlinearity. For, (1 - $\hbar^2$) deformed strength of quantum potential the model is gauge equivalent to the standard Schrödinger equation with Planck constant $\hbar$, while for the strength (1 + $\hbar^2$), to the pair of diffusion-anti-diffusion equations. Specifying the gauge field as Abelian Chern-Simons (CS) one in 2+1 dimensions interacting with the Nonlinear Schrödinger field (the Jackiw-Pi model), we represent the theory as a planar Madelung fluid, where the Chern-Simons Gauss law has simple physical meaning of creation the local vorticity for the fluid flow. For the static flow, when velocity of the center-of-mass motion (the classical velocity) is equal to the quantum one (generated by quantum potential velocity of the internal motion), the fluid admits N-vortex solution. Applying the Auberson-Sabatier type gauge transform to phase of the vortex wave function we show that deformation parameter $\hbar$, the CS coupling constant and the quantum potential strength are quantized. Reductions of the model to 1+1 dimensions, leading to modified NLS and DNLS equations with resonance soliton interactions are discussed.
dc.description12 pages, Tex, to be published in Proc. "NEEDS'2000", Gokova, Turkey, 2000; Theor. and Math.Physics
dc.identifierhttps://arxiv.org/abs/hep-th/0104258
dc.identifierhttp://arxiv.org/abs/hep-th/0104258
dc.identifierTheor.Math.Phys. 127 (2001) 779-788; Teor.Mat.Fiz. 127 (2001) 432-443
dc.identifier.urihttps://dspace.dare.co.zw/handle/123456789/75120
dc.subjectHigh Energy Physics - Theory
dc.titleSelf-Dual Vortices in Chern-Simons Hydrodynamics
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