标题： 伽莫夫-乔丹矢量和从高阶S矩阵极点得到的不可约化密度算子 显示英文标题

标题： Gamow-Jordan Vectors and Non-Reducible Density Operators from Higher Order S-Matrix Poles

摘要： 类似于从S矩阵的一阶共振极点得到的Gamow向量，也可以定义高阶Gamow向量，这些向量是从S矩阵的高阶极点导出的。 S矩阵在z_R=E_R-i\Gamma /2处的r阶极点会导致r个广义特征向量，其阶数k= 0, 1, ..., r-1，这些向量也是度为(k+1)的Jordan向量，具有广义特征值(E_R-i\Gamma /2)。 Gamow-Jordan向量是广义复特征向量展开的一部分，其形式暗示了为此高阶极点的微观物理衰变态定义一个状态算符（密度矩阵）。 这个微观物理态是由不可约成分组成的混合态。 尽管第k阶Gamow-Jordan向量具有通常与高阶极点相关的多项式时间依赖性，但微观物理态遵循纯粹的指数衰减定律。 显示英文摘要

摘要： In analogy to Gamow vectors that are obtained from first order resonance poles of the S-matrix, one can also define higher order Gamow vectors which are derived from higher order poles of the S-matrix. An S-matrix pole of r-th order at z_R=E_R-i\Gamma/2 leads to r generalized eigenvectors of order k= 0, 1, ... , r-1, which are also Jordan vectors of degree (k+1) with generalized eigenvalue (E_R-i\Gamma/2). The Gamow-Jordan vectors are elements of a generalized complex eigenvector expansion, whose form suggests the definition of a state operator (density matrix) for the microphysical decaying state of this higher order pole. This microphysical state is a mixture of non-reducible components. In spite of the fact that the k-th order Gamow-Jordan vectors has the polynomial time-dependence which one always associates with higher order poles, the microphysical state obeys a purely exponential decay law.