高阶S-矩阵极点的Gamow-Jordan向量和不可约密度算子
Gamow-Jordan Vectors and Non-Reducible Density Operators from Higher Order S-Matrix Poles
摘要：
类似于从S矩阵的一阶谐振极点获得的伽莫夫向量，也可以定义从S矩阵的高阶极点导出的高阶伽莫夫向量。r阶S-矩阵在z_R=E_R-iΓ/2处的极点导致r阶k= 0，1，…的广义特征向量。，r-1，它们也是具有广义特征值（E_R-iΓ/2）的（k+1）次Jordan向量。伽莫夫-约当矢量是广义复本征矢量展开式的元素，其形式表明该高阶极点的微物理衰减状态的状态算子（密度矩阵）的定义。这种微观物理状态是不可还原成分的混合物。尽管k阶Gamow-Jordan矢量具有多项式时间依赖性，人们总是将其与高阶极点相关联，但微物理状态服从纯指数衰减定律。
英文摘要：
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-iΓ/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-iΓ/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.
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