Chern-Simons vortices in particle systems obeying an exclusion-inclusion principle

In this paper, we study the stationary solutions of a canonical system, the matter "eld obeying an exclusion}inclusion principle (EIP) which is minimally coupled to a gauge "eld whose dynamics are described within the frame of the Chern}Simons picture. We show that with a suitably selected non-linear algebraic potential ;(o), we can obtain the stationary states through the solution of a "rst-order di!erential equation aH la Bogomol'nyi. The model admits non-topological vortex solutions whose properties are studied in detail. We derive the expressions of the main physical quantities associated to these solutions, like the electric charge and the angular momentum and derive the vortex shape numerically integrating proper equations. As a consequence, we obtain that the introduction of the EIP in our model transforms in continuous quantities the electric charge and the angular momentum of the system, which are discrete in the absence of the EIP. Finally we show that when the EIP is reduced to an exclusion principle, the value of the above physical quantities have an upper limit.