Dynamical classic limit: Dissipative vs conservative systems

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.

Automated summary

We investigate the nonlinear dynamics of a quartic semiclassical system, which provides a description of the interaction between matter and a field. Our analysis covers both dissipative and conservative scenarios, and focuses on the classical limit of these frameworks. Utilizing a system's invariant associated with the Uncertainty Principle, we determine the dynamics towards the classical regime. We demonstrate the convergence to the classical limit and confirm the fulfillment of the Uncertainty Principle throughout the entire process, including cases with dissipation.