Phase-Space Noncommutativity: from Gravity to Quantum Mechanics

Orador: Catarina Bastos (Instituto Superior Técnico, Universidade de Lisboa). Data, hora e local: 24 de Novembro de 2015, às 11h30m na sala de reuniões do Departamento de Matemática.

Resumo: A phase-space noncommutativity (NC) is considered in the context of a Kantowski-Sachs cosmological model. Then, the interior of a Schwarzschild black hole is analyzed. One deduces the thermodynamics and show that the Hawking temperature and entropy exhibit an explicit dependence on the momentum noncommutativity parameter. Furthermore, the t = r = 0 singularity is analysed in the noncommutative regime and it is shown that the wave function vanishes in this limit. Quantumness and separability criteria for continuous variable systems are discussed for the case of a NC phase-space quantum mechanics. In particular, the quantum nature and the entanglement configuration of NC two-mode Gaussian states are examined. Finally, a more general measurement disturbance uncertainty principle is presented in a Robertson-Schrdinger formulation. It is shown that it is stronger and having nicer properties than Ozawas uncertainty relations. In particular is invariant under symplectic transformations. One shows also that there are states of the probe (measuring device) that saturate the matrix formulation of measurement disturbance uncertainty principle.

Funded by the Portuguese Government through the FCT – Fundação para a Ciência e a Tecnologia under the project UID/MAT/00212/2013


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