arXiv quant-ph/06040332006-04-05quant-ph

基于密度矩阵的Casimir-Polder力

Casimir-Polder forces from density matrix formalism

T. N. C. Mendes, C. Farina

备注：: 11 pages, 3 figures
DOI：: 10.1088/0305-4470/39/21/S51

摘要：

本文用密度矩阵方法计算了偶极近似下，在理想导电壁存在下，原子在相互作用下的二阶能级位移。本文还研究了当$\hbar ω_0/k_B T = k_0 λ_T \gg 1$，其中${$ ω_0=k_0 c $}$是原子的主跃迁频率，$λ_T$是热长度时的热修正。当原子与壁面的距离$z$大于$λ_T$时，我们发现由Lifshitz公式得到的著名结果，其首项与温度成正比，且与$c$，$\hbar$和$k_0$无关.在短距离极限中，当$z\llλ_T$时，仅对主导真空项进行非常小的修正。我们还表明，对于所有的距离制度，主要的热修正是独立的$k_0$（分散是不重要的）和依赖的$c$，这意味着没有一个非延迟制度的热贡献。

英文摘要：

We use the density matrix formalism in order to calculate the energy level shifts, in second order on interaction, of an atom in the presence of a perfectly conducting wall in the dipole approximation. The thermal corrections are also examined when $\hbar ω_0/k_B T = k_0 λ_T \gg 1$, where ${$ω_0=k_0 c$}$ is the dominant transition frequency of the atom and $λ_T$ is the thermal length. When the distance $z$ between the atom and the wall is larger than $λ_T$ we find the well known result obtained from Lifshitz's formula, whose leading term is proportional to temperature and is independent of $c$, $\hbar$ and $k_0$. In the short distance limit, when $z\llλ_T$, only very small corrections to the leading vacuum term occur. We also show, for all distance regimes, that the main thermal corrections are independent of $k_0$ (dispersion is not important) and dependent of $c$, which means that there is not a non-retarded regime for the thermal contributions.

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英文摘要：

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