Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function
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 consis...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/7010957 |
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| author | A. X. Martins R. A. S. Paiva G. Petronilo R. R. Luz R. G. G. Amorim S. C. Ulhoa T. M. R. Filho |
| author_facet | A. X. Martins R. A. S. Paiva G. Petronilo R. R. Luz R. G. G. Amorim S. C. Ulhoa T. M. R. Filho |
| author_sort | A. X. Martins |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-bea52d7321df40428ee314d05ba7e87a |
| institution | Kabale University |
| issn | 1687-7357 1687-7365 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in High Energy Physics |
| spelling | doaj-art-bea52d7321df40428ee314d05ba7e87a2025-02-03T01:27:25ZengWileyAdvances in High Energy Physics1687-73571687-73652020-01-01202010.1155/2020/70109577010957Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner FunctionA. X. Martins0R. A. S. Paiva1G. Petronilo2R. R. Luz3R. G. G. Amorim4S. C. Ulhoa5T. M. R. Filho6International Center of Physics, Instituto de Física, Universidade de Brasília, 70910-900 Brasília, DF, BrazilInternational Center of Physics, Instituto de Física, Universidade de Brasília, 70910-900 Brasília, DF, BrazilInternational Center of Physics, Instituto de Física, Universidade de Brasília, 70910-900 Brasília, DF, BrazilInternational Center of Physics, Instituto de Física, Universidade de Brasília, 70910-900 Brasília, DF, BrazilInternational Center of Physics, Instituto de Física, Universidade de Brasília, 70910-900 Brasília, DF, BrazilInternational Center of Physics, Instituto de Física, Universidade de Brasília, 70910-900 Brasília, DF, BrazilInternational Center of Physics, Instituto de Física, Universidade de Brasília, 70910-900 Brasília, DF, BrazilIn 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.http://dx.doi.org/10.1155/2020/7010957 |
| spellingShingle | A. X. Martins R. A. S. Paiva G. Petronilo R. R. Luz R. G. G. Amorim S. C. Ulhoa T. M. R. Filho Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function Advances in High Energy Physics |
| title | Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function |
| title_full | Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function |
| title_fullStr | Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function |
| title_full_unstemmed | Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function |
| title_short | Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function |
| title_sort | analytical solution for the gross pitaevskii equation in phase space and wigner function |
| url | http://dx.doi.org/10.1155/2020/7010957 |
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