General theorems on decoherence in the thermodynamic limit

Marco Frasca

Marco Frasca

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

Marco Frasca

Time evolution operator in quantum mechanics can be changed into a statistical operator by a Wick rotation. This strict relation between statistical mechanics and quantum evolution can reveal deep results when the thermodynamic limit is considered. These results translate in a set of theorems proving that these effects can be effectively at work producing an emerging classical world without recurring to any external entity that in some cases cannot be properly defined. For a many-body system it has been recently shown that Gaussian decay of the coherence is the rule with a duration of recurrence more and more small as the number of particles increases. This effect has been observed experimentally. More generally, a theorem about coherence of bulk matter can be proved. All this takes us to the conclusion that a well defined boundary for the quantum to classical world does exist and that can be drawn by the thermodynamic limit, extending in this way the deep link between statistical mechanics and quantum evolution to a high degree.

Frasca, M

Time evolution operator in quantum mechanics can be changed into a statistical operator by a Wick rotation. This strict relation between statistical mechanics and quantum evolution can reveal deep results when the thermodynamic limit is considered. These results translate in a set of theorems proving that these effects can be effectively at work producing an emerging classical world without recurring to any external entity that in some cases cannot be properly defined. In a many-body system has been recently shown that Gaussian decay of the coherence is the rule with a duration of recurrence more and more small as the number of particles increases. This effect has been observed experimentally. More generally, a theorem about coherence of bulk matter can be proved. All this takes us to the conclusion that a well definite boundary for the quantum to classical world does exist and that can be drawn by the thermodynamic limit, extending in this way the deep link between statistical mechanics and quantum evolution to a high degree.

Meir Hemmo, Orly Shenker