论文标题
Pauli-Fierz操作员的时间演变（Markov近似和RABI循环）
Time evolution for the Pauli-Fierz operator (Markov approximation and Rabi cycle)
论文作者
论文摘要
本文与非相对论量子电动力学（QED）框架中的量化电磁场（光子）相互作用的颗粒系统有关，并由Pauli-Fierz Hamiltonian控制。我们不仅有兴趣在耦合常数较小时得出几个数量的近似值，而且还有兴趣获得误差项的不同对照。首先，我们研究了两种情况下的时间动力学近似，马尔可夫（定理1.4由定理1.16完成）和非马尔可夫（定理1.6）案例。这两个上下文在近似领先术语，误差控制和初始状态方面有所不同。其次，我们检查了两个应用程序。第一个应用是对\ cite {b-s}在\ cite {b-s}中分析的边际过渡概率的研究，例如在马尔可夫案例中证明了指数衰减，假设费米黄金法则（FMEREM 1.17或THEOREM 1.17或THEOREM 1.15）或fGR类型1.在Fermi Golden rules（FGR）假设（Fermi Golden）中进行了衰减。在非马尔可夫情况下，第二个应用程序包括QED的狂犬循环（定理1.7）。所有结果均在以下假设下在证据的某些步骤下建立：施加了紫外线和红外正规化，删除了Pauli-Fierz Hamiltonian的二次术语，并假定偶极子近似值，但仅用于获得最佳误差控制。
This article is concerned with a system of particles interacting with the quantized electromagnetic field (photons) in the non relativistic Quantum Electrodynamics (QED) framework and governed by the Pauli-Fierz Hamiltonian. We are interested not only in deriving approximations of several quantities when the coupling constant is small but also in obtaining different controls of the error terms. First, we investigate the time dynamics approximation in two situations, the Markovian (Theorem 1.4 completed by Theorem 1.16) and non Markovian (Theorem 1.6) cases. These two contexts differ in particular regarding the approximation leading terms, the error control and the initial states. Second, we examine two applications. The first application is the study of marginal transition probabilities related to those analyzed by Bethe and Salpeter in \cite{B-S}, such as proving the exponential decay in the Markovian case assuming the Fermi Golden Rule (FGR) hypothesis (Theorem 1.17 or Theorem 1.15) and obtaining a FGR type approximation in the non Markovian case (Theorem 1.5). The second application, in the non Markovian case, includes the derivation of Rabi cycles from QED (Theorem 1.7). All the results are established under the following assumptions at some steps of the proofs: an ultraviolet and an infrared regularization are imposed, the quadratic terms of the Pauli-Fierz Hamiltonian are dropped, and the dipole approximation is assumed but only to obtain optimal error controls.
