Decoherence in the thermodynamic limit: A general result

We prove a very general theorem on decoherence in the thermodynamic limit, widely extending the scope of our preceding results [Phys. Lett. A 308, 135 (2003)]. The concept of a singular limit in time is used in the proof. Recent experimental findings [1, 2, 3, 4, 5] in NMR with organic molecular crystals have shown that an intrinsic decoherence effect is present in a many-body system in the thermodynamic limit. These experiments, that are known just in the NMR community, give a strong support to our understanding of decoherence as an effect arising from the thermodynamic limit applied to unitary evolution [6, 7, 8, 9, 10, 11, 12]. These theoretical results are based on a concept of singular limit in time. This concept seems to have been pioneered by Bohm [13, 14]. Indeed, the existence of such an effect would give a relevant answer both to the measurement problem and the question of the irreversibility: both are essential to the understanding of a classical world emerging from quantum mechanics. Besides, recent experiments with cavities realized by Haroche’s group [15, 16] have produced asymptotic states with a large number of photons as foreseen by Gea-Banacloche [17, 18] and further analyzed by Knight and Phoenix [19, 20]. As firstly pointed out by Gea-Banacloche, these states support a view of quantum measurement described by decoherence in the thermodynamic limit, in agreement with our view. In this case one has that ∗ e-mail:[email protected]