Mean field equation and relativistic Abelian Chern-Simons model on finite graphs
Mean field equation and relativistic Abelian Chern-Simons model on finite graphs
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有限图上的平均场方程和相对论阿贝尔陈-西蒙斯模型
DOI：
10.1016/j.jfa.2021.109218
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发表时间：
2021-08
期刊：
影响因子：
--
通讯作者：
Wen Yang
中科院分区：
文献类型：
--
作者：
Hsin-Yuan Huang;Jun Wang;Wen Yang
在本文中，我们在有限的图形上研究了平均场方程和。对于以前的方程式，我们建立了存在结果和一些独特性结果。特别是，我们发现有限图和存在上的均值字段方程没有一组关键参数。另外，我们给出了最佳常数，这是有限完整图上的方程式的阈值。一个关键的观察结果是，该解决方案可以采用。大多数值两个值。在第二个问题中，我们研究了最大冷凝水的存在，还建立了多种解决方案的存在，包括用于局部的最小化器
In this paper, we study the Mean field equation and the.relativistic Abelian Chern-Simons equations (involving two.Higgs particles and any two gauge fields) on the finite.connected graphs. For the former equation, we establish the.existence results and some uniqueness result. In particular,.we find that there is no set of critical parameters for the.Mean field equation on the finite graphs and the existence.is ensured for any non-negative parameters, which is in.contrast to the continuous case. In addition, we give the.optimal constant which is the threshold for the uniqueness.of the equation on the finite complete graphs with simple.weight. A key observation is that the solution can take at.most two values. While for the second problem, we study.the existence of maximal condensates, and also establish the.existence of multiple solutions, including a local minimizer for