The decoherence criterion

The decoherence mechanism signals the limits beyond which the system dynamics approaches the classical behavior. We show that in some cases decoherence may also signal the limits beyond which the system dynamics has to be described by quantum field theory, rather than by quantum mechanics. The problem of the range of applicability of quantum mechanics (QM) has been the object of much attention and studies since the early days of its foundation. However, only at a later time it has been fully recognized and appreciated the purely quantum phenomenon of decoherence [1, 2, 3, 4, 5], which in many cases signals the appearance of a classical world in quantum theory [5]. Decoherence is normally triggered by the interaction of the system with the environment and formally consists in suppressing the off-diagonal elements of the reduced density matrix. Its effect is such that quantum superposition in the system wave function is destroyed and thus, provided the time-scale τdyn characteristic of the dynamics is much greater than the decoherence time-scale τdec, τdyn ≫ τdec, the classical behavior may be approached. It should be noted that sometimes the system under consideration, assumed to be a closed system, is viewed as composed of two subsystems and we are actually interested only in one of them. The other subsystem is then regarded to be the environment in which the former one is embedded. The reduced density matrix is the one obtained by tracing over the degrees of freedom of the environment (the rest of the Universe, whatever it is). 1 [email protected] 2 [email protected] 3 [email protected]