论文标题
理想玻色气体中卡西米尔力的方差
Variance of the Casimir force in an ideal Bose gas
论文作者
论文摘要
我们认为理想的bose气体包含在$ d $维的厚度$ d $中的理想情况。使用大规范合奏，我们计算出作用在平板壁上的热Casimir力的方差。显示每单位墙面积评估的差异显示出大于$ d $的$δ_{var}/d $的衰减。振幅$δ_{var} $是两个缩放变量$λ/ξ$和$ d/ξ$的非宇宙函数，其中$λ$是Thermal de Broglie波长，而$ξ$是大量相关长度。它可以通过散装压力，每单位壁面积的Casimir力以及相对于化学势而表达。对于热力学状态，对应于玻璃体的存在，将振幅$δ_{var} $凝结为非全球性特征，而平均标准偏差和Casimir力的比例则取扩展表格$（d/l）墙的线性大小。
We consider an ideal Bose gas enclosed in a $d$-dimensional slab of thickness $D$. Using the grand canonical ensemble we calculate the variance of the thermal Casimir force acting on the slab's walls. The variance evaluated per unit wall area is shown to decay like $ Δ_{var}/D$ for large $D$. The amplitude $ Δ_{var}$ is a non-universal function of two scaling variables $λ/ ξ$ and $D/ ξ$, where $λ$ is the thermal de Broglie wavelength and $ξ$ is the bulk correlation length. It can be expressed via the bulk pressure, the Casimir force per unit wall area, and its derivative with respect to chemical potential. For thermodynamic states corresponding to the presence of the Bose-Einstein condensate the amplitude $ Δ_{var}$ retains its non-universal character while the ratio of the mean standard deviation and the Casimir force takes the scaling form $(D/L)^{\frac{d-1}{2}}\, (D/λ)^{d/2}$, where $L$ is the linear size of the wall.
