Coherent dynamics of a system of coupled Bose and Fermi oscillators

A quantum model of single-mode radiation interacting nonlinearly with an $N$-site lattice of Bose or Fermi oscillators is investigated. In the approximation of “equivalent sites” for resonant and nonresonant interactions, the dynamics of the model generated by the asymptotic behavior of the matrix elements of its evolution operator as $N\to\infty$ is investigated. It is shown that in the case of a Bose lattice (infinite-level system) the nature of the solutions of the equations of motion depends on the boundary values of the variables and the parameters and that in the case of a Fermi lattice (two-level system) there is no such dependence. The collective effect of condensation of the radiation field is investigated in a Bose lattice with resonant interaction.