Analytical Solution for Gross-Pitaevskii Equation in Phase Space and Wigner Function
Autor: | Martins, A. X., Paiva, R. A. S., Petronilo, G., Luz, R. R., Ulhoa, S. C., Amorim, R. G. G., Filho, T. M. R. |
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Rok vydání: | 2020 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | 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. Comment: 12 pages, 3 figures |
Databáze: | arXiv |
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