On quantum dissipative systems: ground states and orbital stability

We investigate the existence and stability of ground states for a model coupling the Schr8dinger equation to the wave equation in transverse directions. The model is intended to describe complex interactions between quantum particles and their environment. The re-sult can be interpreted as a dissipation statement, induced by the energy exchanges with the environment. The proofs use either concentration-compactness arguments or spectral analysis of the linearized energy. Difficulties arise related to the fact the model does not satisfy scale invariance properties.