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In this paper we give fully analytical description of the dynamics of acollection of $N$-Frenkel excitons in high density regime dispersively coupledto a single mode cavity field, in the presence of both exciton and cavity-fielddissipations. By using excitonic operators as q-deformed bosonic operators forthe system, we solve analytically the Liouville equation for the densityoperator at zero temperature and investigate the influence of the number ofexcitons and the effect of both dissipations on dynamical behavior of thesystem. We use the solution of master equation to explore the dissipativedynamics of non-classical properties such as, molecule-field entanglement,quadrature squeezing of the field, and molecular dipole squeezing. We find thatthe non-classical properties are strongly affected by the number of excitonsand also by the existence of both dissipations.

Dissipative dynamics of the semiconductor-cavity QED with q-deformed bosons in the dispersive approximation