By constructing the Riemann surface controlling the resonance structure of Winter model, we determine the limitations of perturbation theory. We then derive explicit non-perturbative results for various observables in the weak-coupling regime, in whi
ch the model has an infinite tower of long-lived resonant states. The problem of constructing proper initial wavefunctions coupled to single excitations of the model is also treated within perturbative and non-perturbative methods.
We present a detailed non-perturbative analysis of the time-evolution of a well-known quantum-mechanical system - a particle between potential walls - describing the decay of unstable states. For sufficiently high barriers, corresponding to unstable
particles with large lifetimes, we find an exponential decay for intermediate times, turning into an asymptotic power decay. We explicitly compute such power terms in time as a function of the coupling in the model. The same behavior is obtained with a repulsive as well as with an attractive potential, the latter case not being related to any tunnelling effect.
