论文标题
Davydov Dimer的确切分析多Quanta状态
Exact analytic multi-quanta states of the Davydov Dimer
论文作者
论文摘要
Davydov模型描述了蛋白质中的酰胺I能量转移，而无需分散或耗散。尽管有五十年的研究，但几乎没有确切的分析结果，尤其是对于该模型的离散版本。在这里，我们开发了两种方法来确定Davydov二聚体的确切的正顺序，多Quanta，特征状态。第一种方法涉及整合普通微分方程的系统，第二种方法将纯粹的代数方法应用于此问题。我们为任何数量的量子获得了特征值的一般表达，并且作为示例，将方法应用于特征向量的详细推导，以量一到四个量子，以及在$ n = 5 $和$ n = 6 $的情况下的简短示例。
The Davydov model describes amide I energy transfer in proteins without dispersion or dissipation. In spite of five decades of study, there are few exact analytical results, especially for the discrete version of this model. Here we develop two methods to determine the exact orthonormal, multi-quanta, eigenstates of the Davydov dimer. The first method involves the integration of a system of ordinary differential equations and the second method applies purely algebraic methods to this problem. We obtain the general expression of the eigenvalues for any number of quanta and also, as examples, apply the methods to the detailed derivation of the eigenvectors for one to four quanta, plus a brief example in the case of $n=5$ and $n=6$.
