arXiv 2212.095482022-12math-phmath.MP

Pauli-Fierz 算子的时间演化（Markov 近似与 Rabi 周期）

Time evolution for the Pauli-Fierz operator (Markov approximation and Rabi cycle)

Laurent Amour, Jean Nourrigat

备注：: This version improves some results such as Theorem 1.4, which now includes an estimate without the dipolar approximation, and some proofs are then reorganized

AI总结：

本文研究 Pauli-Fierz Hamiltonian 支配的非相对论 QED 系统在 Markov 与非 Markov 情形下的时间演化近似，给出误差控制，并在此基础上证明 Markov 情形下边缘跃迁概率的指数衰减以及非 Markov 情形下的 Rabi 周期。

摘要：

本文研究非相对论量子电动力学（QED）框架中粒子与量子化电磁场（光子）相互作用的系统，该系统由 Pauli-Fierz Hamiltonian 支配。我们不仅关注在耦合常数较小时对若干量的近似推导，还关注对误差项的不同控制。首先，我们研究两种情形下的时间动力学近似：Markov 情形（定理 1.4，由定理 1.16 补充）和非 Markov 情形（定理 1.6）。这两种情形尤其在近似主导项、误差控制和初始状态方面存在差异。其次，我们考察两个应用。第一个应用是研究与 Bethe 和 Salpeter 在 \cite{B-S} 中分析过的边缘跃迁概率相关的问题，例如在假定 Fermi Golden Rule（FGR）假设成立的 Markov 情形下证明指数衰减（定理 1.17 或定理 1.15），以及在非 Markov 情形下获得 FGR 型近似（定理 1.5）。第二个应用是在非 Markov 情形下从 QED 推导 Rabi 周期（定理 1.7）。所有结果在证明的某些步骤中均基于以下假设：施加紫外和红外正则化，略去 Pauli-Fierz Hamiltonian 的二次项，并假定偶极近似，但偶极近似仅用于获得最优误差控制。

英文摘要：

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.

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。

AI总结：

摘要：

英文摘要：

相关论文