标题： 两个非互惠耦合场的动态模型：零、一和两个守恒定律的微观推导 显示英文标题

标题： Dynamic Models for Two Nonreciprocally Coupled Fields: A Microscopic Derivation for Zero, One, and Two Conservation Laws

摘要： 我们构建了描述两种非互惠耦合场的动力学模型，适用于零、一和两个守恒定律的情况。 从两个微观的非互惠耦合的伊辛模型出发，并使用平均场近似，我们得到了每个晶格中空间分辨磁化的显式演化方程。 对于单自旋翻转动力学，在热力学极限下的宏观方程与非互惠的阿伦-卡恩方程密切相关，即： 没有守恒定律。 同样地，对于每个晶格内的自旋交换动力学，热力学极限得到类似于非互惠的卡恩-希利亚德模型的方程，即： 具有两个守恒定律。 在两个晶格内部和之间的自旋交换动力学情况下，我们得到了两个非互惠耦合的方程，它们相加得到一个守恒定律。 对于每种情况，我们系统地描绘了可能出现的线性不稳定性。 我们的结果为一大类非互惠场理论提供了微观基础，建立了非平衡统计力学与宏观连续描述之间的直接联系。 显示英文摘要

摘要： We construct the dynamic models governing two nonreciprocally coupled fields for cases with zero, one, and two conservation laws. Starting from two microscopic nonreciprocally coupled Ising models, and using the mean-field approximation, we obtain closed-form evolution equations for the spatially resolved magnetization in each lattice. For single spin-flip dynamics, the macroscopic equations in the thermodynamic limit are closely related to the nonreciprocal Allen-Cahn equations, i.e. conservation laws are absent. Likewise, for spin-exchange dynamics within each lattice, the thermodynamic limit yields equations similar to the nonreciprocal Cahn-Hilliard model, i.e. with two conservation laws. In the case of spin-exchange dynamics within and between the two lattices, we obtain two nonreciprocally coupled equations that add up to one conservation law. For each of these cases, we systematically map out the linear instabilities that can arise. Our results provide a microscopic foundation for a broad class of nonreciprocal field theories, establishing a direct link between non-equilibrium statistical mechanics and macroscopic continuum descriptions.