评“量子临界顺电体与卡西米尔时间效应”
Comment on "Quantum critical paraelectrics and the Casimir effect in time"
摘要：
与作者的声明[L. Pálová，P. Chandra和P. Coleman，Phys.Rev.B79，075101（2009）]，我们证明了声子色散关系中的隙函数的普适标度振幅的行为作为维度$d$的函数，在自洽单圈方法内获得，与以前在$ε$ -展开和场论重整化群方法框架下得到的一些分析结果一致[S. Sachdev，Phys.Rev.B55，142（1997）]和对应于球面极限的精确计算，即序参量的分量的无穷多个$N$ [H.查马蒂和N. S. Tonchev，J.Phys.A：Math.Gen.33，873（2000）]。此外，我们确定数值的行为的“时间”Casimir振幅作为一个函数的维数$d$之间的下限和上限的临界尺寸，并发现在$d=2.9144$的最大值。这通过在上维度$d=3$附近的展开来证实。
英文摘要：
At variance with the authors' statement [L. Pálová, P. Chandra and P. Coleman, Phys. Rev. B 79, 075101 (2009)], we show that the behavior of the universal scaling amplitude of the gap function in the phonon dispersion relation as a function of the dimensionality $d$, obtained within a self--consistent one--loop approach, is consistent with some previous analytical results obtained in the framework of the $ε$--expansion in conjunction with the field theoretic renormalization group method [S. Sachdev, Phys. Rev. B 55, 142 (1997)] and the exact calculations corresponding to the spherical limit i.e. infinite number $N$ of the components of the order parameter [H. Chamati. and N. S. Tonchev, J. Phys. A: Math. Gen. 33, 873 (2000)]. Furthermore we determine numerically the behavior of the "temporal" Casimir amplitude as a function of the dimensionality $d$ between the lower and upper critical dimension and found a maximum at $d=2.9144$. This is confirmed via an expansion near the upper dimension $d=3$.
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