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 tr {rho}{sup j}, j=1,2,{hor_ellipsis},n remain constant in time, independent of the Hamiltonian. These invariants are physically significant; the qualitative character of the solution depends on their existence. A generic numerical method will not, in general, preserve these invariants. We present a numerical technique which evolves the density matrix {ital via} unitary transformations thus {ital exactly} preserving these invariants to {ital all orders} in the time step. {copyright} {ital 1997} {ital The American Physical Society}