论文标题
在爱因斯坦宇宙中的热casimir效应具有球形边界
Thermal Casimir effect in the Einstein Universe with a spherical boundary
论文作者
论文摘要
在本文中，我们调查了在零温度下对真空能的热波动校正的质量，其模式在爱因斯坦宇宙中以球形边界传播，其特征在于Dirichlet和Neumann边界条件。因此，我们在这种情况下概括了文献中发现的结果，后者仅考虑了在零温度下的真空能量。为此，我们使用广义Zeta函数方法加上ABEL-PLANA公式，并计算重新归一化的Casimir自由能以及其他热力学数量，即内部能量和熵。对于每个人，我们还研究了高温和低温的限制。在高温下，我们发现重新归一化的Casimir自由能提供了经典的贡献以及对数项。同样在此限制下，内部能量还提出了经典的贡献和熵，除了经典的贡献外，还具有对数项。相反，在低温下，这表明重新归一化的Casimir自由能和内部能量在零温度下的真空能均由真空能支配。还表明熵遵守热力学的第三定律。
In the present paper we investigate thermal fluctuation corrections to the vacuum energy at zero temperature of a conformally coupled massless scalar field whose modes propagate in the Einstein universe with a spherical boundary, characterized by both Dirichlet and Neumann boundary conditions. Thus, we generalize the results found in literature in this scenario, which has considered only the vacuum energy at zero temperature. To do this, we use the generalized zeta function method plus Abel-Plana formula and calculate the renormalized Casimir free energy as well as other thermodynamics quantities, namely, internal energy and entropy. For each one of them we also investigate the limits of high and low temperatures. At high temperatures we found that the renormalized Casimir free energy presents classical contributions, along with a logarithmic term. Also in this limit, the internal energy presents a classical contribution and the entropy a logarithmic term in addition to a classical contribution as well. Conversely, at low temperatures, it is shown that both the renormalized Casimir free energy and internal energy are dominated by the vacuum energy at zero temperature. It is also shown that the entropy obeys the third law of thermodynamics.
