EFFECTIVE-HAMILTONIANS FROM 1ST PRINCIPLES

The equations of motion for a quantum system of the electromagnetic fi eld interacting with matter are derived from the ''first principle'' H amiltonian (two-level atomic systems are assumed) and from the effecti ve Hamiltonian. The derivation is based on the memory-function theory of Mori and on the theory of random frequency modulation of Tokuyama a nd Mori. On the ground of comparison of the equations of motion from t he ''first principle' Hamiltonian with those from the effective Hamilt onian a justification of the use of effective Hamiltonians is discusse d.