网络上的意见动力学量子模型
A quantum model of opinion dynamics on networks
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中文总结 AI 辅助
提出基于密度矩阵的量子意见动力学模型，通过非对易算符解释认知矛盾与顺序效应，并识别量子相干性等非经典量，在乘积态近似下退化为经典Friedkin-Johnsen模型。
中文摘要 AI 辅助
经典的意见动力学模型将个体意见表示为标量或向量值，受经典概率论支配，要么是确定性量，要么是随机变量。该框架无法解释经验观察到的现象，如认知矛盾（个体同时持有相互冲突的观点）和顺序效应（调查回答取决于问题提问的顺序）。我们提出了一种意见动力学的量子模型，其中每个智能体的认知状态由一个密度矩阵表示，该矩阵编码了表达的意见和认知矛盾。调查问题成为非对易的自伴算子，这为顺序效应提供了原则性解释。我们的模型还识别了没有经典对应物的量，包括量子相干性和成对意见协方差。在乘积态近似下，量子模型退化为经典的Friedkin-Johnsen意见模型。我们在合成和真实网络上测试了该框架，观察到成对相关性遵循网络依赖的瞬态动力学，但无论网络如何都收敛到相同的稳态，并且量子相干性以与网络无关的速率指数衰减。
英文摘要
Classical models of opinion dynamics represent individual opinions as scalar or vector values governed by the classical probability theory, either as deterministic quantities or random variables. This framework does not account for empirically observed phenomena such as cognitive ambivalence (where an individual simultaneously holds conflicting views) and order effects (where survey responses depend on the order in which questions are asked). We propose a quantum model of opinion dynamics in which each agent's cognitive state is represented by a density matrix that encodes both the expressed opinion and cognitive ambivalence. Survey questions become non-commuting self-adjoint operators, which provides a principled explanation for order effects. Our model also identifies quantities without classical counterparts, including quantum coherence and pairwise opinion covariances. Under a product state approximation, the quantum model reduces to the classical Friedkin--Johnsen opinion model. We test the framework on synthetic and real-world networks and observe that pairwise correlations follow network-dependent transient dynamics but converge to the same steady state regardless of the network, and that quantum coherence decays exponentially at a rate independent of the network.
