UNITARY INTEGRATION - A NUMERICAL TECHNIQUE PRESERVING THE STRUCTURE OF THE QUANTUM LIOUVILLE EQUATION

The quantum Liouville equation for an n-level atomic system driven by external fields has a nontrivial kinematic structure; the quantities t r rho(j), j = 1,2,...,n remain constant in time, independent of the Ha miltonian. These invariants are physically significant; the qualitativ e character of the solution depends on their existence. A generic nume rical method will not, in general, preserve these invariants. We prese nt a numerical technique which evolves the density matrix via unitary transformations thus exactly preserving these invariants to all orders in the time step. [S0031-9007(97)04662-0].