On the basis of a lemma designed to decide whether a discrete system decoheres or not with no need of computer simulations, in this paper we analyze the well-known spin-bath model. The lemma allows us to predict the decoherence of the system by analytical means.
In this paper we propose a closed-system perspective to study decoherence. From this perspective we analyze the spin-bath model as presented in the literature, and a natural generalization of that model. On the basis of the results obtained from that analysis, we argue that decoherence may be understood as a phenomenon relative to the partition of a closed system, selected in each particular case. This viewpoint frees the decoherence program from certain conceptual difficulties derived from its open-system perspective. We also argue that the usual picture of decoherence in terms of energy dissipation is misguided.
In this review we discuss approaches to numerical modelling of decoherence by a spin bath. We consider several popular simulation methods, briefly discussing their implementation, and analyse their advantages and drawbacks. Furthermore, we consider application of these methods to several different physical systems, demonstrating how the numerical simulations can help in understanding the details of the decoherence process in quantum spin systems. The discussion of possible interesting directions for further research concludes the review.
We develop a mathematical description of the decoherence caused by "spin baths", such as nuclear spins or magnetic impurities. In contrast to the usual oscillator bath models of quantum environments, decoherence in the spin bath can occur without any dissipation. Given the almost ubiquitous presence of nuclear spins in nature, our results have important consequences for quantum measurement theory, particularly as the decoherence mechanisms in spin baths work very differently from those in oscillator baths.