Space-time formulation of quantum transitions
Space-time formulation of quantum transitions
复制标题
量子跃迁的时空表述
DOI：
10.1103/physreva.64.062101
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发表时间：
2001
影响因子：
2.9
通讯作者：
I. Prigogine
中科院分区：
文献类型：
--
作者：
T. Petrosky;G. Ordonez;I. Prigogine
在之前的一篇论文中，我们研究了弗里德里希模型中的装饰激发态，该模型描述了一个二能级原子与辐射的相互作用。在我们的方法中，激发态是Liouville空间中的分布(或广义函数)。这些态以严格的指数方式衰变。相反，人们可以在波函数的希尔伯特空间中构造的状态总是呈现出与指数衰减的偏差。我们考虑了适用于全局量(迹线、能量转移)的动量表象。在这里，我们研究了与修饰不稳定态相关的局域量的时空描述，例如光子场的强度。在这种情况下，激发态在Gamow态中被分解。要从局部数量到全球数量，我们必须进行空间上的积分，这绝不是微不足道的。在该系统的时空演化中出现了各种元素：围绕裸原子的不稳定云，发射的真实光子，以及与指数衰减偏差有关的“零点光子”。我们考虑一个希尔伯特空间近似我们修饰的激发态。这种近似已经导致原子周围的场以指数形式衰减，并形成不同于洛伦兹线形的线形。我们的结果与数值模拟结果进行了比较。我们证明了不稳定态的时间演化满足一个类似玻尔兹曼的数学式的{H}定理。这适用于发射和吸收以及散射。一个微观的数学{H}定理的存在并不令人惊讶。激发态是“非平衡态”，它们的时间演化导致光子的发射，从而在场模之间分配不稳定态的能量。
In a previous paper we have studied dressed excited states in the Friedrichs model, which describes a two-level atom interacting with radiation. In our approach, excited states are distributions (or generalized functions) in the Liouville space. These states decay in a strictly exponential way. In contrast, the states one may construct in the Hilbert space of wave functions always present deviations from exponential decay. We have considered the momentum representation, which is applicable to global quantities (trace, energy transfer). Here we study the space-time description of local quantities associated with dressed unstable states, such as, the intensity of the photon field. In this situation the excited states become factorized in Gamow states. To go from local quantities to global quantities, we have to proceed to an integration over space, which is far from trivial. There are various elements that appear in the space-time evolution of the system: the unstable cloud that surrounds the bare atom, the emitted real photons and the ``Zeno photons,'' which are associated with deviations from exponential decay. We consider a Hilbert space approximation to our dressed excited state. This approximation leads already to decay close to exponential in the field surrounding the atom, and to a line shape different from the Lorentzian line shape. Our results are compared with numerical simulations. We show that the time evolution of an unstable state satisfies a Boltzmann-like $\mathcal{H}$ theorem. This is applied to emission and absorption as well as scattering. The existence of a microscopic $\mathcal{H}$ theorem is not astonishing. The excited states are ``nonequilibrium'' states and their time evolution leads to the emission of photons, which distributes the energy of the unstable state among the field modes.