具有高次多项式耦合的Lohe矩阵模型的梯度流公式
A gradient flow formulation of the Lohe matrix model with a high-order polynomial coupling
摘要：
本文利用梯度流方法对具有高阶耦合的均匀系综提出了一个广义Lohe矩阵模型。对于具有相同哈密顿量的均匀自由流，具有立方耦合的Lohe矩阵模型可以转化为具有平均状态的平方Frobenius范数势的梯度系统。在本文中，我们进一步推导出一个广义Lohe矩阵模型与高阶耦合的梯度流方法的多项式势。对于所提出的模型，我们还提供了一个充分的框架，耦合强度和初始数据，这导致涌现的均匀系综的动力学。
英文摘要：
We present a generalized Lohe matrix model for a homogeneous ensemble with higher order couplings via the gradient flow approach. For the homogeneous free flow with the same hamiltonian, it is well known that the Lohe matrix model with cubic couplings can recast as a gradient system with a potential which is a squared Frobenius norm of of averaged state. In this paper, we further derive a generalized Lohe matrix model with higher-order couplings via gradient flow approach for a polynomial potential. For the proposed model, we also provide a sufficient framework in terms of coupling strengths and initial data, which leads to the emergent dynamics of the homogeneous ensemble.
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