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 the PCMW domain. A new ABCD law is derived, using a tensor method to describe the evolution of a PCMW. An analytical solution of the first-order correlation function is obtained that makes the propagation and evolution of a PCMW very simple and clear. As an example, the propagation of a PCMW in a gravitational field is calculated numerically.