Wigner Measures in Noncommutative Quantum Mechanics |
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Authors: | C Bastos N C Dias J N Prata |
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Institution: | 1. Departamento de Física and Instituto de Plasmas e Fus?o Nuclear, Instituto Superior Técnico, Avenida Rovisco Pais 1, 1049-001, Lisboa, Portugal 2. Departamento de Matemática, Universidade Lusófona de Humanidades e Tecnologias, Av. Campo Grande 376, 1749-024, Lisboa, Portugal 3. Grupo de Física Matemática, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal
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Abstract: | We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner measure, for a Gaussian to be a noncommutative Wigner measure, and derive certain properties of the marginal distributions which are not shared by ordinary Wigner measures. Moreover, we derive the Robertson-Schrödinger uncertainty principle. Finally, we show explicitly how the set of noncommutative Wigner measures relates to the sets of Liouville and (commutative) Wigner measures. |
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