The collisional decay of a Fermi system interacting with a many-mode electromagnetic field

We consider a system of Z fermions coupled to a dissipative environment thr ough a two-body potential. We represent the system in a basis of single-par ticle, two-particle,... Z-particle excitated states. Using a procedure for averaging the rapid oscillations of the reduced density matrix in the inter action picture, the master equation of the system takes the form of a serie s expansion of powers of the dissipative potential matrix elements. The ter m of the second-order describes single-particle transitions, while the high er-order terms correspond to correlated transitions of the system particles . For the second- and the third-order terms, we derive microscopic expressi ons of the dissipative coefficients. For dissipative systems, when the stat e collectivity is broken into pieces through quantum diffusion, we use the quantum master equation of the second-order approximation. This equation sa tisfies basic physical conditions: particle conservation, Fermi-Dirac or Bo se-Einstein distributions as asymptotic solutions of the populations, and e ntropy increase. On this basis, the decay of a Fermi system interacting wit h a many-mode electromagnetic field is described in terms of microscopic qu antities: the matrix elements of the dissipative potential, the densities o f the environment states, and the occupation probabilities of these states. A near-dipode-dipode interaction of the system with other neighbouring sys tems is taken into account. In addition to the coupling of the polarization with the population, included in the usual equations for two-level systems as a non-linear detuning, in equations for N-level systems two new couplin gs of the polarizations appear: a coupling due to the proximity potential, and a coupling due to the local field corrections, as a renormalization of the Rabi frequencies.