标题： 迪森级数中的常数项到微扰的所有阶次 显示英文标题

标题： Secular Terms in Dyson Series to All-Orders of Perturbation

摘要： 在经典和量子系统中，演化方程的摄动通常会被发散项破坏，这些发散项会在晚时间趋于无穷大。 可以通过重整化群或多重尺度分析等多种重求和技术来修复演化的发散行为。 本文证明了，在一般的量子力学系统中，可以通过改进（重整化）摄动方法，系统地消除戴森级数中所有阶次的发散项。 给出了一个递归关系以提供显式的方法来消除发散项。 作为副产品，我们给出了一种简单的方法，可以得到任意阶摄动的能量本征值和衰减率。 显示英文摘要

摘要： In classical and quantum systems, perturbation of an evolution equation is often invalidated by secular terms which diverge at late times. The diverging behavior of evolution can be remedied by various techniques of resumma- tion such as renormalization group or multi-scale analysis. In this paper, we prove that, in a generic quantum mechanical system, secular terms can be systematically removed to all orders in the Dyson series by the method of improved (renormalized) perturbation. A recurrence relation to provide an explicit method to remove the secular terms is given. As a byproduct, we give a simple method to obtain energy eigenvalues and decay rates to all orders of perturbation.