2020/01/29 by A. X. Martins, R. A. S. Paiva, Martins, A. X. +13
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum optics and atomic interactions #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.2001.10925
12 pages, 3 figures
arxiv created 2020/01/29 · openalex publication_date 2020/01/29 · arxiv updated 2020/01/30 · openalex created_date 2020/02/07 · openalex updated_date 2026/07/28
In this work we study symplectic unitary representations for the Galilei group. As a consequence a Non-Linear Schrödinger 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.