Hidrodinâmica de Chern-Simons.

Abstract

In this Dissertation we consider the influence of the quantum potential on the planar vortex in a 2 + 1-dimensional problem for the non-linear Schr¨odinger equation (Jackiw-Pi model) that interacts with the Chern-Simons gauge field. This interaction will be studied using the Auberson-Sabatier gauge transform, which affects the phase of the wave function and this causes a considerable change in the parameters of the vortex configurations. In this work, the fluid considered has the characteristics of the Madelung fluid. Thus, the possibility for a simple physical interpretation is created, since the Gaussian law of Chern-Simons generates local vortices for liquid fluids and with this, to give equality conditions between the ”classical velocity”, which is the velocity of the center of mass and the velocity of the quantum movement, that generated by the velocity of the quantum potential of the internal motion, thus the fluid admits the solution of N vortex.