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arXiv · 2001.10925

Analytical Solution for Gross-Pitaevskii Equation in Phase Space and Wigner Function

A. X. Martins·R. A. S. Paiva·G. Petronilo·R. R. Luz·S. C. Ulhoa·R. G. G. Amorim·T. M. R. Filho
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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.

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A. X. Martins, R. A. S. Paiva, G. Petronilo, R. R. Luz, S. C. Ulhoa, R. G. G. Amorim, T. M. R. Filho. 2020-01-29. Analytical Solution for Gross-Pitaevskii Equation in Phase Space and Wigner Function. https://arxiv.org/abs/2001.10925

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