Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

When dealing with the classical limit of two quantum mechanical oscillators on a non-commutative configuration space, the limits corresponding to the removal of configuration-space non-commutativity and position-momentum non-commutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits