高阶含时微扰对跃迁速率的修正

Modification of transition rate by higher order time-dependent perturbation

费米黄金规则被广泛用于物理、化学、生物等学科理论研究,尤其是量化计算领域.在传统量子力学书籍中,往往忽略微扰高阶修正项,给出低阶微扰近似的跃迁几率或者跃迁速率.对于多态系统,若一阶微扰为零,或费米黄金规则不再适用,面对这种复杂情况,需要超越费米黄金规则,考虑高阶含时微扰对跃迁速率的影响是非常必要的.本文基于含时微扰理论,考虑常微扰与周期性含时微扰两种情况下推导高阶修正项对于跃迁速率的影响.结果发现当考虑高阶微扰近似时,初末态之间满足一定条件的中间态会对跃迁速率产生影响,这样的结果将更全面地体现实际的量子跃迁过程.

Quantum mechanics is a physical theory which describes the behavior of microscopic matter.Moreover,it is the foundation of many physical branches.In fact,under the influence of external time-dependent perturbation,microscopic particles can undergo quantum transitions between different stationary states,which has attracted great research interest.According to time-dependent perturbation theory,the probability of microscopic particles transitioning from one stationary state to another per unit time is called the transition rate.For the constant perturbation,transition rate formula derived by the first-order perturbation approximation is time independent,which is the so-called Fermi s golden rule and is widely used in theoretical research in physics,chemistry,biology,and other disciplines,especially in the field of quantitative computing.In traditional quantum mechanics text books,the high-order perturbation corrections are often ignored,and the transition probability or transition rate is derived by the low-order perturbation approximation.In the multi-levels systems,if the first-order perturbation is zero,or the Fermi golden rule is no longer applicable.For this complex situation,it is necessary to go beyond the Fermi's golden rule and consider the impact of high-order time-dependent perturbation on the transition rate.On the basis of the time-dependent perturbation theory,both constant perturbation and periodic time-dependent perturbation are considered in this paper and the influence of high-order correction terms on the transition rate is attained.Furthermore,it is shown that intermediate states which satisfy certain conditions between the initial and final states can have an impact on the transition rate when the high-order perturbation approximation are considered.Therefore,the results can reflect the actual quantum transition process more comprehensively.