Thermodynamic Limit and Decoherence: Rigorous Results

Abstract

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.

5 pages, no figures. Contribution to proceedings of DICE 2006 (Piombino, Italy, September 11-15, 2006)

References in corpus (16)

• Theory of Bose-Einstein condensation in trapped gases
• Chaos and the Quantum Phase Transition in the Dicke Model
• Dynamical Reduction Models
• Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The Dicke Model
• The wave nature of biomolecules and fluorofullerenes
• Entanglement of a Mesoscopic Field with an Atom induced by Photon Graininess in a Cavity
• Decoherence, chaos, quantum-classical correspondence, and the algorithmic arrow of time
• Attenuation of polarization echoes in NMR: A study of the emergence of dynamical irreversibility in many-body quantum systems
• A model independent approach to non dissipative decoherence
• Decoherence time in self-induced decoherence
• The Quantum Mechanics of Hyperion
• Gaussian quantum fluctuations in interacting many particle systems
• A modern review of the two-level approximation
• Self-induced decoherence approach: Strong limitations on its validity in a simple spin bath model and on its general physical relevance
• 1/N-expansion for the Dicke model and the decoherence program
• A Quantum Many-Body Instability in the Thermodynamic Limit