The problem of decoherence in closed quantum systems is one of the hottest unsolved problems in condensed matter physics. It is important conceptually, as it addresses the basic issue of the nature and decay of many-body states in quantum physics. It also has important implications, as it governs the low temperature noise that makes quantum computing with solid-state devices so difficult.
Usually, in atoms or molecules, one thinks of decoherence as being imposed by the classical environment, evil external agent. However, in some condensed matter systems like strongly disordered superconductors, the interaction with the environment is negligible at very low temperatures: the main source of decoherence comes from the system itself, through its many degrees of freedom. In this paper we predict that the disorder-driven quantum phase transition from superconductor to insulator occurs in two steps. One first finds an insulating phase where the system is able to self-generate its decoherence, leading to a significant dynamics, heat transport and noise. Upon further increase of disorder a second transition occurs, to a completely coherent insulating phase that does not support any transport or noise. A key ingredient driving this physics is the very strong heterogeneity of the electronic states of the system, already present in the superconducting phase, despite the homogeneity of the samples. This prediction has been confirmed by recent experiments by B. Sacepe et al (to be published in Nature Physics).