Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on a zeta function technique
We derive rigorously explicit formulae of the Casimir free energy at finite temperature for massless scalar field and electromagnetic field confined in a closed rectangular cavity with different boundary conditions by a zeta regularization method. We study both the low and high temperature expansion...
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IOP PUBLISHING LTD
2007
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| Online Access: | http://shdl.mmu.edu.my/3007/ |
| _version_ | 1848790208372277248 |
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| author | Lim, S C Teo, L P |
| author_facet | Lim, S C Teo, L P |
| author_sort | Lim, S C |
| building | MMU Institutional Repository |
| collection | Online Access |
| description | We derive rigorously explicit formulae of the Casimir free energy at finite temperature for massless scalar field and electromagnetic field confined in a closed rectangular cavity with different boundary conditions by a zeta regularization method. We study both the low and high temperature expansions of the free energy. In each case, we write the free energy as a sum of a polynomial in temperature plus exponentially decay terms. We show that the free energy is always a decreasing function of temperature. In the cases of massless scalar field with the Dirichlet boundary condition and electromagnetic field, the zero temperature Casimir free energy might be positive. In each of these cases, there is a unique transition temperature (as a function of the side lengths of the cavity) where the Casimir energy changes from positive to negative. When the space dimension is equal to two and three, we show graphically the dependence of this transition temperature on the side lengths of the cavity. Finally we also show that we can obtain the results for a non-closed rectangular cavity by letting the size of some directions of a closed cavity go to infinity, and we find that these results agree with the usual integration prescription adopted by other authors. |
| first_indexed | 2025-11-14T18:08:58Z |
| format | Article |
| id | mmu-3007 |
| institution | Multimedia University |
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| last_indexed | 2025-11-14T18:08:58Z |
| publishDate | 2007 |
| publisher | IOP PUBLISHING LTD |
| recordtype | eprints |
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| spelling | mmu-30072011-09-29T06:59:03Z http://shdl.mmu.edu.my/3007/ Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on a zeta function technique Lim, S C Teo, L P T Technology (General) QC Physics We derive rigorously explicit formulae of the Casimir free energy at finite temperature for massless scalar field and electromagnetic field confined in a closed rectangular cavity with different boundary conditions by a zeta regularization method. We study both the low and high temperature expansions of the free energy. In each case, we write the free energy as a sum of a polynomial in temperature plus exponentially decay terms. We show that the free energy is always a decreasing function of temperature. In the cases of massless scalar field with the Dirichlet boundary condition and electromagnetic field, the zero temperature Casimir free energy might be positive. In each of these cases, there is a unique transition temperature (as a function of the side lengths of the cavity) where the Casimir energy changes from positive to negative. When the space dimension is equal to two and three, we show graphically the dependence of this transition temperature on the side lengths of the cavity. Finally we also show that we can obtain the results for a non-closed rectangular cavity by letting the size of some directions of a closed cavity go to infinity, and we find that these results agree with the usual integration prescription adopted by other authors. IOP PUBLISHING LTD 2007-09 Article NonPeerReviewed Lim, S C and Teo, L P (2007) Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on a zeta function technique. Journal of Physics A: Mathematical and Theoretical, 40 (38). pp. 11645-11674. ISSN 1751-8113 http://dx.doi.org/10.1088/1751-8113/40/38/014 doi:10.1088/1751-8113/40/38/014 doi:10.1088/1751-8113/40/38/014 |
| spellingShingle | T Technology (General) QC Physics Lim, S C Teo, L P Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on a zeta function technique |
| title | Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on a zeta function technique |
| title_full | Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on a zeta function technique |
| title_fullStr | Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on a zeta function technique |
| title_full_unstemmed | Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on a zeta function technique |
| title_short | Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on a zeta function technique |
| title_sort | finite temperature casimir energy in closed rectangular cavities: a rigorous derivation based on a zeta function technique |
| topic | T Technology (General) QC Physics |
| url | http://shdl.mmu.edu.my/3007/ http://shdl.mmu.edu.my/3007/ http://shdl.mmu.edu.my/3007/ |