中文摘要：

对具有反铁磁相互作用的一维双铁链的非线性激发,采用双子格模型,考虑外加势能的影响,从薛定谔微分方程推导出非线性激发的二模矩阵形式和对应的哈密顿量,并进一步得到系统的二次量子化形式及纯量子哈密顿量在Fock态下的矩阵形式。鉴于此系统含有非厄米项和复共轭项,利用非线性平方根代数对该系统进行重新描述。重新描述的哈密顿量和角动量都出现了非线性平方根代数的生成元。重新描述的系统角动量不再保持封闭性,角动量随时间演化的方程也不再封闭。

英文摘要：

Employing the double sublattice model and considering the effects of external potential,we study the properties of nonlinear excitation in one-dimensional two ferromagnetic chains with antiferromagnetic interaction by the Schrdinger equation,and obtain the matrix form of the two-level non-linear excitation.We get the Hamilton of the system and its second quantized form,and further obtain the matrix form of pure quantum Hamilton in Fock states.As this system contains a non-hermite Gaussian item and complex conjugate items,so we describe the model of the system by square root algebra.The Hamilton of nonlinear algebra and the angular momentum both contain the generated units of square root algebra.We obtain a model of angular momentum which is changing over time.These equations are no longer closed.