Partially coherent matter wave and its evolution

The evolution and propagation of a partially coherent matter wave (PCMW) is investigated theoretically by the correlation function method. The ABCD matrix formalism previously used for a fully coherent matter wave is extended to make it applicable for the PCMW. A new tensor ABCD law is derived, which makes the propagation and evolution of a PCMW very simple and clear. As an example, the evolution of the coherence of a PCMW in a gravitational field is calculated.