Geodesic
Static Vortex Solutions in a Planar Particle System Obeying a Generalized Exclusion Principle
Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 3, pp. 411-417

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We consider a planar particle system obeying a generalized Pauli exclusion principle. In the mean field approximation, this system is described by a Schrödinger equation we recently introduced, containing a complex nonlinearity. The particle number, the total energy, and the angular momentum are conserved in such a system. We consider vortexlike stationary solutions of the form $\psi(\mathbf r)= \rho(r)^{1/2}e^{in\theta}$ and write the differential equation for the vortex shape. We find an analytic solution of this equation and obtain a closed expression for the vortex profile. We investigate some mean properties and, in particular, calculate the energy spectrum and angular momentum of the vortex. 
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     author = {G. Kaniadakis and P. Quarati and A. M. Scarfone},
     title = {Static {Vortex} {Solutions} in a {Planar} {Particle} {System} {Obeying} a {Generalized} {Exclusion} {Principle}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {411--417},
     publisher = {mathdoc},
     volume = {127},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_127_3_a7/}
}
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G. Kaniadakis; P. Quarati; A. M. Scarfone. Static Vortex Solutions in a Planar Particle System Obeying a Generalized Exclusion Principle. Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 3, pp. 411-417. http://geodesic.mathdoc.fr/item/TMF_2001_127_3_a7/