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arXiv:quant-ph/0007020 · Modern Physics Letters B

THE DECOHERENCE CRITERION

Eleonora Alfinito, Rosario Gaetano Viglione, Giuseppe Vitiello

Published Feb 28, 2001• 19 citations
arXivHTMLPDF

Abstract

The decoherence mechanism signals the limits beyond which the system dynamics approaches the classical behavior. We show that in some cases decoherence may also signal the limits beyond which the system dynamics has to be described by quantum field theory, rather than by quantum mechanics.
DOI
10.1142/s0217984901001410

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•Aug 28, 2026•0 citations
The quite different behaviors exhibited by microscopic and macroscopic systems with respect to quantum interferences suggest the existence of a borderline beyond which quantum systems loose their coherences and can be described classically. Gravitational waves, generated within our galaxy or during the cosmic expansion, constitute a universal environment susceptible to lead to such a quantum decoherence mechanism. We assess this idea by studying the quantum decoherence due to gravitational waves on typical microscopic and macoscopic systems, namely an atom interferometer (HYPER) and the Earth-Moon system. We show that quantum interferences remain unaffected in the former case and that they disappear extremely rapidly in the latter case. We obtain the relevant parameters which, besides the ratio of the system's mass to Planck mass, characterize the loss of quantum coherences.
The decoherence of the quantum bit is studied in the approximation of weak coupling in the Liouville space. The dynamic equation of N quantum bits is given in the weakly coupling limits and under the non-Markovian approximation. The rate of decoherence is given in the approximation of different time order. Based on the above results, the general form of criterion for decoherence-free states is proposed. Also a new method for quantum correction is proposed from the non-Markovian dynamic equation in the weak coupling limit.
This paper explores the application of quantum decoherence theory to the control of complex classical systems. We propose a novel framework leveraging the probabilistic nature of decoherence to achieve precise control and prediction of complex system dynamics. The core mechanism involves stochastic control, where noise injection and coupling strength are optimized to steer the system towards a desired evolution path. Unlike traditional approaches to complex system analysis and control, this work introduces a fundamentally new perspective by translating core quantum concepts – specifically decoherence – into the domain of classical complexity. The theoretical development presents a method for managing and manipulating complex systems by understanding and mitigating the effects analogous to decoherence, offering potential advancements in fields ranging from chaos control to network dynamics. The central aim is to provide a robust and adaptable strategy for influencing the behavior of intricate systems, moving beyond purely deterministic models. ---