Analytical Solution for Gross-Pitaevskii Equation in Phase Space and Wigner Function
Mathematical Physics
2020-01-30 v1 High Energy Physics - Theory
math.MP
Abstract
In this work we study symplectic unitary representations for the Galilei group. As a consequence a Non-Linear Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using the group theory approach as a guide a physically consistent theory is constructed in phase space. The state is described by a quasi-probability amplitude that is in association with the Wigner function. With these results, we solve the Gross-Pitaevskii equation in phase space and obtained the Wigner function for the system considered.
Cite
@article{arxiv.2001.10925,
title = {Analytical Solution for Gross-Pitaevskii Equation in Phase Space and Wigner Function},
author = {A. X. Martins and R. A. S. Paiva and G. Petronilo and R. R. Luz and S. C. Ulhoa and R. G. G. Amorim and T. M. R. Filho},
journal= {arXiv preprint arXiv:2001.10925},
year = {2020}
}
Comments
12 pages, 3 figures