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arXiv 1209.1401quant-phcond-mat.mes-hall
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自发发射过程中的记忆效应

Memory Effects in Spontaneous Emission Processes

Arne L. Grimsmo, Asle H. Vaskinn, Per K. Rekdal, Bo-Sture K. Skagerstam

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13 pages, 5 figures and 46 references
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摘要：

考虑了真空衰减率为$Γ_0$，跃迁角频率为$ω_A$的有效二能级系统的自发发射的量子力学分析.我们的分析是在原则上准确的，即使作为一个数值解的时间演化，包括记忆效应。这样得到的结果与文献中以前的讨论。根据自发发射的{ \it无量纲}寿命$τ= tΓ_0$，我们得到了衰减幅度与${\cal O} (1/τ)$形式的指数衰减的偏差，以及以前得到的$τ\gg 1 $的${\cal O} (1/τ^2)$或${\cal O} (1/τ\ln^2τ)$形式的渐近行为.实际的渐近行为取决于所采用的正则化过程以及手头的物理参数。我们表明，对于任何合理的范围内的$τ$和足够大的值所需的角频率截止$ω_c$的电磁波动，即$ω_c \gg ω_A$，一个获得${\cal O} (1/τ)$或${\cal O} (1/τ^2)$的依赖性。在物理边界的存在下，这可以改变许多数量级的衰减率，结论保持不变后，适当的参数重新缩放。

英文摘要：

We consider a quantum-mechanical analysis of spontaneous emission in terms of an effective two-level system with a vacuum decay rate $Γ_0$ and transition angular frequency $ω_A$. Our analysis is in principle exact, even though presented as a numerical solution of the time-evolution including memory effects. The results so obtained are confronted with previous discussions in the literature. In terms of the {\it dimensionless} lifetime $τ= tΓ_0$ of spontaneous emission, we obtain deviations from exponential decay of the form ${\cal O} (1/τ)$ for the decay amplitude as well as the previously obtained asymptotic behaviors of the form ${\cal O} (1/τ^2)$ or ${\cal O} (1/τ\ln^2τ)$ for $τ\gg 1 $. The actual asymptotic behavior depends on the adopted regularization procedure as well as on the physical parameters at hand. We show that for any reasonable range of $τ$ and for a sufficiently large value of the required angular frequency cut-off $ω_c$ of the electro-magnetic fluctuations, i.e. $ω_c \gg ω_A$, one obtains either a ${\cal O} (1/τ)$ or a ${\cal O} (1/τ^2)$ dependence. In the presence of physical boundaries, which can change the decay rate with many orders of magnitude, the conclusions remains the same after a suitable rescaling of parameters.

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