The low-density limit of quantum systems
Luigi Accardi, Yun Gang Lu · Journal of Physics A Mathematical and General · 1991
The authors conclude a research programme developed by various authors in several papers. The basic idea of this programme is to explain the irreversible behaviour of quantum systems as a limiting case (in a sense to be made precise) of usual quantum dynamics. One starts with a system interacting with a reservoir and, in the first attempts to deal with this problem, only limits of observables of the system and deduced master equations were considered. In their approach they study the limits of quantities related to the whole compound system. As a corollary they obtain an explanation of the physical origins of the quantum Brownian motion. They study the low-density limit of a system coupled to a quasi-free boson reservoir in the equilibrium state at inverse temperature beta and fugacity z, through an interaction of the scattering type, i.e. one which preserves the total number of particles of the reservoir.