论文标题
在量子旋转和种群动态观点中，与同一状态的独特关键行为不同
Distinct Critical Behaviors from the Same State in Quantum Spin and Population Dynamics Perspectives
论文作者
论文摘要
横向场自旋系统的基态与不断发展的病毒群体的延迟分布之间存在深厚的联系 - 在简单模型中，两者均从同一基质的主要特征向量获得。但是，该矢量是量子自旋模型中的波函数振幅，而这是人口模型中的概率本身。我们表明，这种看似较小的差异具有重大的后果：从人口观点看时，在自旋系统中不连续的相位变得连续，并且连续的过渡受到新的关键指数的控制。我们引入了更一般的模型类别，该模型涵盖了这两个情况，并且可以在平均范围限制中精确解决。还为许多具有幂律相互作用的一维链提供了数值结果。我们看到，当被视为人群动力学模型及以后时，量子统计力学的磨损旋转模型可能包含意外的新物理和见解，从而激发进一步的研究。
There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations -- within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wavefunction amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: phase transitions which are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions which are continuous become governed by new critical exponents. We introduce a more general class of models which encompasses both cases, and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.
