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arXiv:1702.03835 · Networks and Heterogeneous Media

The Wigner-Lohe model for quantum synchronization and its emergent dynamics

Paolo Antonelli, Seung‐Yeal Ha, Dohyun Kim, Pierangelo Marcati

Published Jan 1, 2017• 9 citations
arXivHTMLPDF

Abstract

We present the Wigner-Lohe model for quantum synchronization which can be derived from the Schrödinger-Lohe model using the Wigner formalism. For identical one-body potentials, we provide a priori sufficient framework leading the complete synchronization, in which L2-distances between all wave functions tend to zero asymptotically.
DOI
10.3934/nhm.2017018

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Abstract We investigate a non-Abelian generalization of the Kuramoto model proposed by Lohe and given by N quantum oscillators (‘nodes’) connected by a quantum network where the wavefunction at each node is distributed over quantum channels to all other connected nodes. It leads to a system of Schrödinger equations coupled by nonlinear self-interacting potentials given by their correlations. We give a complete picture of synchronization results, given on the relative size of the natural frequency and the coupling constant, for two non-identical oscillators and show complete phase synchronization for arbitrary N > 2 identical oscillators. Our results are mainly based on the analysis of the ODE system satisfied by the correlations and on the introduction of a quantum order parameter, which is analogous to the one defined by Kuramoto in the classical model. As a consequence of the previous results, we obtain the synchronization of the probability and the current densities defined via the Madelung transformations.
Can synchronization -- the widespread spontaneous emergence of coordinated dynamics in classical nonlinear systems -- also occur in the quantum regime? This question has recently sparked intense research into collective behavior and temporal self-organization in quantum systems. Typical quantum features such as the linearity of time evolution and the presence of quantum noise seem to hinder the appearance of synchrony at the microscopic level. At the same time, quantum coherence and quantum correlations may provide novel mechanisms for enhancing synchronization beyond its classical counterpart. We here survey recent theoretical and experimental advances in quantum synchronization, ranging from the characterization of synchronous oscillations and genuinely nonclassical forms of synchrony to many-body synchronization on quantum networks.
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The observer problem remains one of the central unresolved questions in the foundations of quantum mechanics. This paper derives the logical structure of observation without assuming an observer, consciousness, measurement, or information as primitive concepts. Starting from the primitive notion of Meaning, the following logical sequence is derived: Meaning → Being → Closure → I₄ → Update → Time → 0 < δ < ∞ → Self-Reference → Observer → Observation → Record → Synchronization → Information. Within this framework, an observer is shown to emerge necessarily from persistent self-referential closure possessing finite residual relation. Observation is interpreted as the generation of persistent internal representations, while measurement is reformulated as synchronization between independent closures. Information is derived as synchronized records supported by an information medium. This logical structure provides a unified reinterpretation of Schrödinger's cat and Wigner's friend. The apparent paradoxes are shown to originate from synchronization between independent observers rather than from consciousness, observer-dependent reality, or wave-function collapse. The paper establishes an ontological hierarchy connecting Meaning, Being, observation, synchronization, and information within the MBC (Meaning-Based Constraint) framework.