The 1/N-expansion, quantum-classical correspondence and nonclassical states generation in dissipative higher-order anharmonic oscillators

We develop a method for the determination of the dynamics of dissipative qu antum systems in the limit of large number of quanta N, based on the 1/N-ex pansion of Heidmann et al. [Opt. Commun. 54, 189 (1985)] and the quantum-cl assical correspondence. Using this method, we End analytically the dynamics of nonclassical states generation in the higher-order anharmonic dissipati ve oscillators for an arbitrary temperature of a reservoir. We show that th e quantum correction to the classical motion increases with time quadratica lly up to some maximal value, which is dependent on the degree of nonlinear ity and a damping constant, and then it decreases. Similarities and differe nces with the corresponding behavior of the quantum corrections to the clas sical motion in the Hamiltonian chaotic systems are discussed. We also comp are our results obtained for some limiting cases with the results obtained by using other semiclassical tools and discuss the conditions for validity of our approach.