Lohe张量模型二次可分态的存在性和突现动力学
Existence and emergent dynamics of quadratically separable states to the Lohe tensor model
摘要：
张量是复数的多维数组，Lohe张量模型是具有相同秩和大小的张量空间上的聚合模型。它结合了以前研究的聚集模型的空间低秩张量，如仓本模型，Lohe球和矩阵模型的特殊情况。由于Lohe张量模型在立方相互作用中的结构复杂性，具有特定结构的解决方案的显式构造看起来令人生畏。最近，我们通过关联秩1张量得到了完全可分的态。在本文中，我们进一步研究了另一种类型的解决方案，即“{ \it二次可分状态}”组成的张量积的矩阵和他们的分量秩2张量是解决方案的双矩阵模型的涌现动力学可以使用相同的方法来研究Lohe矩阵模型。
英文摘要：
A tensor is a multi-dimensional array of complex numbers, and the Lohe tensor model is an aggregation model on the space of tensors with the same rank and size. It incorporates previously well-studied aggregation models on the space of low-rank tensors such as the Kuramoto model, Lohe sphere and matrix models as special cases. Due to its structural complexities in cubic interactions for the Lohe tensor model, explicit construction of solutions with specific structures looks daunting. Recently, we obtained completely separable states by associating rank-1 tensors. In this paper, we further investigate another type of solutions, namely "{\it quadratically separable states}" consisting of tensor products of matrices and their component rank-2 tensors are solutions to the double matrix model whose emergent dynamics can be studied using the same methodology of the Lohe matrix model.
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