Exact diagonalization of two quantum models for the damped harmonic oscillator
Exact diagonalization of two quantum models for the damped harmonic oscillator
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DOI：
10.1103/physreva.61.022107
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发表时间：
1999-03
影响因子：
2.9
通讯作者：
M. Costa;A. Caldeira;S. M. Dutra;H. Westfahl
中科院分区：
文献类型：
--
作者：
M. Costa;A. Caldeira;S. M. Dutra;H. Westfahl
阻尼谐振子是量子力学中耗散研究的主力。然而，尽管该系统很简单，但它产生了一些近似值，其有效性以及与更精确的描述的关系值得彻底研究。在这项工作中，我们应用了一种方法，使我们能够精确对角化文献中经常采用的耗散哈密顿量。使用这种方法，我们推导了旋转波近似（RWA）的有效性条件，并展示了这种近似描述如何与更一般的描述相关。我们还表明，耗散相干态的存在与 RWA 密切相关。最后，通过对阻尼振荡器动力学的评估，我们注意到耗散模型的一个重要属性在以前的工作中没有得到适当的考虑，即对可分解初始条件的应用施加新的约束的必要性。
The damped harmonic oscillator is a workhorse for the study of dissipation in quantum mechanics. However, despite its simplicity, this system has given rise to some approximations whose validity and relation to more refined descriptions deserve a thorough investigation. In this work, we apply a method that allows us to diagonalize exactly the dissipative Hamiltonians that are frequently adopted in the literature. Using this method, we derive the conditions of validity of the rotating-wave approximation (RWA) and show how this approximate description relates to more general ones. We also show that the existence of dissipative coherent states is intimately related to the RWA. Finally, through the evaluation of the dynamics of the damped oscillator, we notice an important property of the dissipative model that has not been properly accounted for in previous works, namely the necessity of new constraints to the application of the factorizable initial conditions.