Finite Temperature Casimir Effect of Scalar Field: Revisit and New Results

• URL: http://arxiv.org/abs/2410.19275v2
• Date: Fri, 08 Nov 2024 04:50:38 GMT
• Title: Finite Temperature Casimir Effect of Scalar Field: Revisit and New Results
• Authors: Liang Chen, Sheng-Yan Li,
• Abstract summary: We find the analytic expressions of Gibbs free energy, Casimir force, and Casimir entropy for one-dimensional and three-dimensional fields at finite temperature. Results show that the widely used low-temperature approximation of thermal correction of Casimir force, $piTe-pivhbar/aT/2a3$, have large errors with the exact solution.
• Score: 6.110491566305613
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• Abstract: For both the one-dimensional and three-dimensional scalar fields at finite temperature, we find the analytic expressions of Gibbs free energy, Casimir force, and Casimir entropy. These results show that the widely used low-temperature approximation of thermal correction of Casimir force, $\pi{T}e^{-\pi{v}\hbar/aT}/2a^3$, have large errors with the exact solution. Here $T$, $v$ and $a$ represent the finite temperature, the velocity of scalar field, and the distance between the two boundaries of the fields, respectively. $\hbar$ is the reduced Planck's constant. For three-dimensional scalar field, we find the leading order thermal correction of Gibbs free energy density, $F(a,T)=3\zeta(7/2)aT^4/8\pi^{3/2}(v\hbar)^3$, where $\zeta(.)$ represents the Riemann $\zeta$ function. This thermal correction can not be cancelled by the blackbody radiation density, $\pi^2{a}T^4/90(v\hbar)^3$.

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