A Simple Testbed for Stability Analysis of Quantum Dissipative Systems

We study a two-state quantum system with a nonlinearity intended to describe interactions with a complex environment, arising through a nonlocal coupling term. We study the stability of particular solutions, obtained as constrained extrema of the energy functional of the system. The simplicity of the model allows us to justify a complete stability analysis. This is the opportunity to review in detail the techniques to investigate the stability issue. We also bring out the limitations of perturbative approaches based on simpler asymptotic models.