Classical Limit of Quantum Dissipative Systems

K. N. Alekseev, Jan Peřina

Summary form only given. The situation when nonlinear interactions involve a large number of photons, N, is quite typical of many of the problems of quantum and nonlinear optics. To describe the dynamics of such quantum systems a classical approach is often used. In this theoretical work we compare classical and quantum dynamics of several dissipative quantum optical systems, which have a limit cycle in the classical limit N/spl rarr//spl infin/. In particular, we consider the dynamics of intracavity second harmonic generation (SHG) described by the Hamiltonian.

Dong‐In Lee, Jun-Ho LEE*, Woon Hak Baek +1 more

Joseph V. Pulé, André F. Verbeure

For finite quantum systems the classical limit of the general dissipative generator of a semigroup of completely positive maps is obtained, yielding a generalized Fokker–Planck generator.

M. Fannes

Gaspar Gonzalez, Angelo Plastino, A.M. Kowalski

We analyze the nonlinear dynamics of a quartic semiclassical system able to describe the interaction of matter with a field. We do it in both dissipative and conservative scenarios. In particular, we study the classical limit of both frameworks and compare the associated features. In the two environments, we heavily use a system's invariant, related to the Uncertainty Principle, that helps to determine how the dynamics tends to the pertinent classical limit. We exhibit the convergence to the classical limit and also verify that the Uncertainty Principle is complied with during the entire process, even in the presence of dissipation.