Dressed States Approach to Quantum Systems

Using the non-perturbative method of {\it dressed} states previously introduced in JPhysA, we study effects of the environment on a quantum mechanical system, in the case the environment is modeled by an ensemble of non interacting harmonic oscillators. This method allows to separate the whole system into the {\it dressed} mechanical system and the {\it dressed} environment, in terms of which an exact, non-perturbative approach is possible. When applied to the Brownian motion, we give explicit non-perturbative formulas for the classical path of the particle in the weak and strong coupling regimes. When applied to study atomic behaviours in cavities, the method accounts very precisely for experimentally observed inhibition of atomic decay in small cavities PhysLA, physics0111042.