We study completely separable states of the Lohe tensor model and their asymptotic collective dynamics. Here, the completely separable state means that it is a tensor product of rank-1 tensors. For the generalized Lohe matrix model corresponding to the Lohe tensor model for rank-2 tensors with the same size, we observe that the component rank-1 tensors of the completely separable states satisfy the swarm double sphere model introduced in [Lohe in Physica D 412, 2020]. We also show that the swarm double sphere model can be represented as a gradient system with an analytic potential. Using this gradient flow formulation, we provide the swarm multisphere model on the product of multiple unit spheres with possibly different dimensions, and then we construct a completely separable state of the swarm multisphere model as a tensor product of rank-1 tensors which is a solution of the proposed swarm multisphere model. This concept of separability has been introduced in the theory of quantum information. Finally, we also provide a sufficient framework leading to the complete aggregation of completely separable states.

我们研究了Lohe张量模型的完全可分离状态及其渐近的集体动力学。在这里，完全可分离状态意味着它是等级1张量的张量积。对于与相同大小的秩2张量的Lohe张量模型相对应的广义Lohe矩阵模型，我们观察到完全可分离状态的分量rank-1张量满足Physica D 412中的Lohe引入的群双球模型。 ，2020]。我们还表明，群体双球体模型可以表示为具有分析潜力的梯度系统。使用此梯度流公式，我们提供了可能具有不同尺寸的多个单位球的乘积的群体多球模型，然后构造一个完全可分离的群体多球模型作为1级张量的张量积，这是所提出的群体多球模型的一种解决方案。这种可分离性的概念已被引入量子信息理论中。最后，我们还提供了一个足以导致完全可分离状态的完全聚合的框架。