Extended time-dependent mean-field approximation

The time-dependent mean-field approximation for two dynamically coupled subsystems is extended to include correlation effects between the subsystems, allowing for decorrelation processes to develop in the reduced density matrices. The extended scheme is formulated in terms of the truncation to M terms of the Schmidt decomposition of the full density matrix. This M natural orbitals truncation scheme is compared to the exact numerical solution for a system of two coupled anharmonic oscillators in a factorized initial state. It is found that the approximation M=3 gives a good approximation to the exact results over several characteristic times of the system.