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arXiv:quant-ph/0503118 · Brazilian Journal of Physics

Classical limit of non-integrable systems

Mario Castagnino

Published Jun 1, 2005• 7 citations
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Abstract

Self-induced decoherence formalism and the corresponding classical limit are extended from quantum integrable systems to non-integrable ones.
DOI
10.1590/s0103-97332005000300002

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Our account of the problem of the classical limit of quantum mechanics involves two elements. The first one is self-induced decoherence, conceived as a process that depends on the own dynamics of a closed quantum system governed by a Hamiltonian with continuous spectrum; the study of decoherence is addressed by means of a formalism used to give meaning to the van Hove states with diagonal singularities. The second element is macroscopicity: when the macroscopic limit is applied to the Wigner transformation of the diagonal state resulting from decoherence, the description of the quantum system becomes equivalent to the description of an ensemble of classical trajectories on phase space weighted by their corresponding probabilities.