Heidelberg 2015 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 50: Quantum Information: Concepts and Methods VII

Q 50.2: Vortrag

Donnerstag, 26. März 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.