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The report presents an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of nonlinear and stochastic modifications of the Schrödinger equation. The proposed new dynamics is characterized by the feature of not contradicting any known fact about microsystems and of accounting, on the basis of a unique, universal dynamical principle, for wavepacket reduction and for the classical behavior of macroscopic systems. We recall the motivations for the new approach and we briefly review the other proposals to circumvent the above mentioned difficulties which appeared in the literature. In this way we make clear the conceptual and historical context characterizing the new approach. After having reviewed the mathematical techniques (stochastic differential calculus) which are essential for the rigorous and precise formulation of the new dynamics, we discuss in great detail its implications and we stress its relevant conceptual achievements. The new proposal requires also to work out an appropriate interpretation; a procedure which leads us to a reconsideration of many important issues about the conceptual status of theories based on a genuinely Hilbert space description of natural processes. Attention is also paid to many problems which are naturally raised by the dynamical reduction program. In particular we discuss the possibility and the problems one meets in trying to develop an analogous formalism for the relativistic case. Finally we discuss the experimental implications of the new dynamics for various physical processes which should allow, in principle, to test it against quantum mechanics. The review covers the work which has been done in the last 15 years by various scientists and the lively debate which has accompanied the elaboration of the new proposal

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The quantum description of unstable systems has been the subject of many investigations since the early days of quantum mechanics. As is well known such a description gives rise to several conceptual problems, arising from the difficulty of finding a satisfactory general characterisation of these systems, and from the unavoidable difference which exists between the quantum and the classical predictions about the decay. For these reasons interest in this subject has increased recently and some contributions which have provided a new insight into the problem have appeared.The present review article is aimed at a clear formulation of the basic problematics of the decay and at a description of the various recent attempts to solve this delicate problem, illustrating both their successes and limitations. From this review should emerge a clear view of the present theoretical situation. The organisation of the article is as follows. After a short summary of the classical description of the decay, a detailed study of the quantum non-decay probability is given. Then the peculiar dynamical situation leading to the formation of an unstable system is identified and the formal and physical aspects of the process are discussed. A detailed analysis is then made of the preparation procedure of an unstable system which is shown to amount to a localisation of the decay fragments within a distance of the order of the range of the forces acting between them. After this the discussion on the general properties of the non-decay probability at all times is completed.I n the first part of the review the basic elements for a theoretical description of decay processes are formulated and all mathematical aspects as well as conceptual implications are clarified. It is then possible to undertake a discussion on the crucial points of the theory. First, the various attempts to characterise unstable systems are reviewed, in particular those based on the association of unstable particles with poles of the S matrix and those based on the consideration of the time-translation semigroup. Finally, the most recent contributions to the problem are reviewed. They take more properly into account the actual physical situation, i.e. the fact that an unstable system unavoidably interacts with its environment. As a consequence one is led to the formulation of a better dynamical description which allows one to overcome, in a very natural way, all the relevant difficulties of the previous approaches. The problem raised by the new description, such as the possible dependence of the lifetime on the measuring apparatus, are discussed. I n conclusion it is shown how the new approach makes it possible to associate the unfolding of the decay process with a semi-group law of evolution with time.

We relate the notion of entanglement for quantum systems composed of two identical constituents to the impossibility of attributing a complete set of properties to both particles. This implies definite constraints on the mathematical form of the state vector associated with the whole system. We then analyze separately the cases of fermion and boson systems, and we show how the consideration of both the Slater-Schmidt number of the fermionic and bosonic analog of the Schmidt decomposition of the global state vector and the von Neumann entropy of the one-particle reduced density operators can supply us with a consistent criterion for detecting entanglement. In particular, the consideration of the von Neumann entropy is particularly useful in deciding whether the correlations of the considered states are simply due to the indistinguishability of the particles involved or are a genuine manifestation of the entanglement. The treatment leads to a full clarification of the subtle aspects of entanglement of two identical constituents which have been a source of embarrassment and of serious misunderstandings in the recent literature.

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