On the relation between the singular and the weak coupling limits

Luigi Accardi, A. Frigerio, Yun Gang Lu

P. F. Palmer

We show that the analysis of the motion of a system coupled to an infinite reservoir in the singular coupling limit and the weak coupling limit can be performed in the same mathematical framework. This enables us to clarify the way in which the motion of the system in the singular coupling limit depends on the temperature of the reservoir.

Deok Kyo Lee

Ground states of two typical many-boson model systems are studied: (i) a weakly interacting boson system at low density, and (ii) a low-density hard-sphere boson gas in the low-energy limit. For both of these systems it is shown explicitly that the uniform-limit formalism based on the method of correlated basis functions can be used to obtain, in a relatively simple way, exact results for the ground-state energy per particle and other related properties in the weak-coupling limit. In the problem of the hard-sphere boson gas the $T$-matrix method is found to be particularly useful in dealing with the singular interaction potential.

R. Dümcke

For a system coupled to a thermal bath we prove the convergence of the multitime correlation functions of system observables in the weak and singular coupling limits. The limiting correlation functions are given by the quantum regression law. Therefore, our result implies that in the limit the dynamics of the system are governed by a quantum stochastic process in the sense of Lindblad.

F. Benatti, Roberto Floreanini B