Heidelberg 2015 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 50: Quantum Information: Concepts and Methods VII
Q 50.2: Talk
Thursday, March 26, 2015, 11:15–11:30, K/HS1
Wigner function for curved configuration spaces — •Clemens Gneiting1, Timo Fischer2, and Klaus Hornberger2 — 1Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg — 2Universität Duisburg-Essen, Lotharstraße 1-21, 47057 Duisburg
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The resulting Wigner function displays the axioms of a quasiprobability distribution, and any Weyl-ordered operator gets associated with the corresponding phase-space function. Moreover, the corresponding quantum Liouville equation reduces to the classical curved space Liouville equation in the semiclassical limit. We demonstrate the formalism for a point particle moving on two-dimensional manifolds, such as a paraboloid or the surface of a sphere.