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Classical behavior in quantum systems: the case of straight tracks in a cloud chamber

The aim of this review is to discuss in a pedagogical way the problem of the emergence of a classical behavior in certain physical systems which, in principle, are correctly described by quantum mechanics. It is stressed that the limit $\hbar \to 0$ is not sufficient and the crucial role played by the environment must be taken into account. In particular it is recalled the old problem raised by Mott in 1929 (\cite{m}) concerning the straight tracks observed in a cloud chamber, produced by an $α$-particle emitted by a source in the form of a spherical wave. The conceptual relevance of the problem for a clearer understanding of the classical limit is discussed in a historical perspective. Moreover a simple mathematical model is proposed, where the result of Mott is obtained in a rigorous mathematical way.