含时微扰理论应用于laser诱导分子跃迁的发散性：简单算法的解析计算
On the divergence of time-dependent perturbation theory applied to laser-induced molecular transitions: Analytical calculations for the simple algorithm
摘要：
整形激光脉冲是诱导电子分子态间布居转移的有力工具，含时微扰理论适用于描述弱外场下的这种转移。微扰理论在场-物质相互作用的数值模拟中的应用会导致发散。在最近的一篇论文[K。伦齐豪森等例如，J. Phys. B：At.摩尔光学物理，42：195402，2009]我们解释了在波函数的范数中出现的误差可以被分成两部分。第一部分是有关的数值误差所造成的离散化的时间，这是在模拟中所需的，可以抑制一个足够小的时间步长或取消一个足够的数值实施扰动理论。第二部分可能导致发散，并与微扰展开阶有关。我们提出了数字证据，但没有任何分析证明。在这里，我们专注于推导分析表达式来解释我们在上面提到的论文中所说的“简单算法”的行为。在另一篇文章[K]中给出了解释我们在上述文章中所称的“改进算法”的解析表达式的推导。伦齐豪森arXiv，in preparation，2012].此外，我们还介绍了一个格丹肯实验来说明不同阶数对光场-分子相互作用的影响。
英文摘要：
Shaped laser pulses are a powerful tool to induce population transfer between electronic molecular states, and time-dependent perturbation theory is suitable for a description of such a transfer in weak external fields. The application of perturbation theory in numerical simulations of field matter interactions can lead to divergences. In a recent paper [K. Renziehausen et. al., J. Phys. B: At. Mol. Opt. Phys., 42:195402, 2009] we explained that the arising error in the norm of the wave function can be split into two parts. The first part is related to numerical errors caused by the discretisation of time that is required in the simulation and can be suppressed for a sufficiently small time step or abolished for an adequate numerical implementation of perturbation theory. The second part may cause divergences and is associated with the perturbative expansion order. We presented numerical evidence without any analytical proof. Here we are focussing on the derivation of analytical expressions to interpret the behavior of what we have called in the above mentioned paper 'simple algorithm'. The derivation of analytical expressions for the interpretation of what we have called in the above mentioned paper 'improved algorithm' are given in another paper [K. Renziehausen. arXiv, in preparation, 2012]. Moreover, we introduce here a gedankenexperiment to illustrate the influence of the different orders on the field-molecule interaction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
