Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function. (30th April 2020)

• Record Type: Journal Article
• Authors: Martins, A. X.; Paiva, R. A. S.; Petronilo, G.; Luz, R. R.; Amorim, R. G. G.; Ulhoa, S. C.; Filho, T. M. R.
• Other Names: Mignemi Salvatore Academic Editor.
• Is Part Of: Advances in high energy physics. Volume 2020(2020)
• Publication Date: 2020-04-30
• Subjects: Particles (Nuclear physics) -- Periodicals; Particles (Nuclear physics); Periodicals; 539.76
• DOI: 10.1155/2020/7010957
• Languages: English
• ISSNs: 1687-7357

Abstract

Abstract : In this work, we study symplectic unitary representations for the Galilei group. As a consequence a nonlinear Schrödinger equation is derived in phase space. The formalism is based on the noncommutative 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.