Quantum Computation and Information Seminar 

07/10/2011, 15:00 — 16:00 — Room P4.35, Mathematics Building
João Nuno Prata, U Lusófona

Noncommutative Quantum Mechanics

I consider quantum systems based on a canonical extension of Heisenberg's algebra. Such systems can be regarded as the non-relativistic limit of a one-particle sector of some noncommutative quantum field theory, or alternatively, as the quantization of systems coupled to external fields. I advocate that the Weyl-Wigner formulation is better suited to deal with such system in comparison with the usual Schrodinger formulation. The corresponding Weyl calculus for observables is developped and the representatives of states are defined. These are called noncommutative Wigner functions. As an application, I consider a Brownian particle interacting with a noncommutative gas at thermal equilibrium. I estimate the time for the transition from noncommutative to ordinary quantum mechanics and compare it with the typical time scale of the quantum-classical transition.