Quantum reflection by Casimir-van der Waals potential tails
Quantum reflection by Casimir-van der Waals potential tails
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DOI：
10.1103/physreva.65.032902
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发表时间：
2002-02
影响因子：
2.9
通讯作者：
H. Friedrich;G. Jacoby;Carlo G. Meister
中科院分区：
文献类型：
--
作者：
H. Friedrich;G. Jacoby;Carlo G. Meister
我们研究了卡西米尔-范德华势的反射率，其在大距离处表现为 -C 4 /r 4 ，在小距离处表现为 -C 3 /r 3 。反射幅度R的总体行为主要取决于参数ρ= √2MC 3 /( ∞√C 4 )，该参数决定了电势的-1/r 3 和- 1/r 4 部分的相对重要性。接近阈值，E=∞ 2 k 2 /(2M)→0，反射率由 ‖R‖∼exp(-2bk) 给出，其中 b 取决于 p 和中间距离处势的形状。在大能量的极限下，In‖R‖与-k 1 / 3 成比例，已知比例常数仅取决于C 3 。对于较小的ρ值，反射率在整个能量范围内表现为均匀的- 1/r 3 势，并且不依赖于C 4 或超出- 1/r 3 区域的势的形状。对于中等和较大的 ρ 值，反射率取决于 C 4 和潜在形状。对于在现实系统中普遍存在的足够大的 ρ 值，存在超出近阈值区域的能量范围，其中反射率显示适合均匀 -l/r 4 势的高能量行为，即，In‖R‖与 - √k 成正比，比例常数仅取决于 C 4 。卡西米尔效应的这种显着且与模型无关的特征通过硅表面散射的氖原子的反射率得到了说明，清水最近测量了这种反射率。
We study the reflectivity of Casimir-van der Waals potentials, which behave as -C 4 /r 4 at large distances and as -C 3 /r 3 at small distances. The overall behavior of the reflection amplitude R depends crucially on the parameter ρ= √2MC 3 /( ∞√C 4 ) which determines the relative importance of the -1/r 3 and the - 1/r 4 parts of the potential. Near threshold, E=∞ 2 k 2 /(2M)→0, the reflectivity is given by ‖R‖∼exp(-2bk), with b depend-ing on p and the shape of the potential at intermediate distances. In the limit of large energies, In‖R‖ is proportional to -k 1 / 3 with a known constant of proportionality depending only on C 3 . For small values of ρ, the reflectivity behaves as for a homogeneous - 1/r 3 potential in the whole range of energies and does not depend on C 4 or the shape of the potential beyond the - 1/r 3 region. For moderate and large values of ρ, the reflectivity depends on C 4 and on the potential shape. For sufficiently large values of ρ, which are ubiquitous in realistic systems, there is a range of energies beyond the near-threshold region, where the reflectivity shows the high-energy behavior appropriate for a homogeneous -l/r 4 potential, i.e., In‖R‖ is proportional to - √k with a proportionality constant depending only on C 4 . This conspicuous and model-independent signature of the Casimir effect is illustrated for the reflectivities of neon atoms scattered off a silicon surface, which were recently measured by Shimizu.