论文标题
量子与经典的出生和死亡过程；确切可解决的示例
Quantum vs Classical Birth and Death Processes; Exactly Solvable Examples
论文作者
论文摘要
提出了连续和离散时间出生和死亡（BD）过程的无金定量程序。量子Hamiltonian H是通过相似性来得出的，该相似性以固定（可逆）分布的平方根来转换矩阵L。量子系统和经典系统共享整个特征值，而特征向量与一个相关。当选择B（X）和死亡率D（X）作为管理ASKEY方案正交多项式的差异方程的系数时，量子系统是可以解决的。特征向量是正交多项式本身，并且特征值可以通过分析。许多示例是周期性的，因为它们的特征值都是整数，或所有用于整数参数的整数。这种情况与确切的一维量子机械系统非常相似。这些确切的可解决的马尔可夫连锁店包含许多可调节的免费参数，这可能有助于各种模拟。
A coinless quantisation procedure of continuous and discrete time Birth and Death (BD) processes is presented. The quantum Hamiltonian H is derived by similarity transforming the matrix L describing the BD equation in terms of the square root of the stationary (reversible) distribution. The quantum and classical systems share the entire eigenvalues and the eigenvectors are related one to one. When the birth rate B(x) and the death rate D(x) are chosen to be the coefficients of the difference equation governing the orthogonal polynomials of Askey scheme, the quantum system is exactly solvable. The eigenvectors are the orthogonal polynomials themselves and the eigenvalues are given analytically. Many examples are periodic since their eigenvalues are all integers, or all integers for integer parameters. The situation is very similar to the exactly solvable one dimensional quantum mechanical systems. These exactly solvable Markov chains contain many adjustable free parameters which could be helpful for various simulation purposes.
