Once the system Hamiltonian is known, one can use the Heisenberg equation of motion to generate the dynamics of a given N -particle operator. However, the many-body as well as quantum-optical interactions couple the N -particle quantities to ( N + 1 ) -particle expectation values, which is known as the Bogolyubov–Born–Green–Kirkwood–Yvon (BBGKY) hierarchy problem. More mathematically, all particles interact with each other leading to an equation structure