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• W2024454324 abstract "Unitary representations of the Galilei group are studied in phase space, in order to describe classical and quantum systems. Conditions to write in general form the generator of time translation and Lagrangians in phase space are then established. In the classical case, Galilean invariance provides conditions for writing the Liouville operator and Lagrangian for non-linear systems. We analyze, as an example, a generalized kinetic equation where the collision term is local and non-linear. The quantum counter-part of such unitary representations are developed by using the Moyal (or star) product. Then a non-linear Schrodinger equation in phase space is derived and analyzed. In this case, an association with the Wigner formalism is established, which provides a physical interpretation for the formalism." @default.
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• W2024454324 date "2010-09-01" @default.
• W2024454324 modified "2023-10-12" @default.
• W2024454324 title "Non-linear Liouville and Shrödinger equations in phase space" @default.
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• W2024454324 doi "https://doi.org/10.1016/j.physa.2010.04.030" @default.
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