Finite-temperature Casimir effect in piston geometry and its classical limit

European Physical Journal C

Volumn 60, Issue 2, 2009, Pages 323-344

  Lim, S C ^a   Teo, L P ^a  

^a MULTIMEDIA UNIVERSITY   (Malaysia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 68349107030     PISSN: 14346044     EISSN: 14346052     Source Type: Journal    
DOI: 10.1140/epjc/s10052-009-0867-8     Document Type: Article

References (44)

1. H.B.G. Casimir, On the attraction between two perfectly conducting plates. Proc. K. Ned. Akad. Wet. B 51, 793-795 (1948)
2. H.B.G. Casimir, D. Polder, The influence of retardation on the London-van der Waals forces. Phys. Rev. 73(4), 360-372 (1948)
3. U. Mohideen, A. Roy, Precision measurement of the Casimir force from 0.1 to 0.9 μm. Phys. Rev. Lett. 81, 4549-4552 (1998)
4. A. Roy, C.Y. Lin, U. Mohideen, Improved precision measurement of the Casimir force. Phys. Rev. D 60, 111101 (1999)
5. D. Deutsch, P. Candelas, Boundary effects in quantum field theory. Phys. Rev. D 20, 3063-3080 (1979)
6. J. Baacke, G. Krüsemann, Perturbative analysis of the divergent contributions to the Casimir energy. Z. Phys. C 30, 413-420 (1986)
7. N. Graham, R.L. Jaffe, V. Khemani, M. Quandt, M. Scandurra, H. Weigel, Calculating vacuum energies in renormalizable quantum field theories:-A new approach to the Casimir problem. Nucl. Phys. B 645, 49-84 (2002)
8. N. Graham, R.L. Jaffe, V. Khemani, M. Quandt, M. Scandurra, H. Weigel, Casimir energies in light of quantum field theory. Phys. Lett. B 572, 196-201 (2003)
9. R.L. Jaffe, Unnatural acts: unphysical consequences of imposing boundary conditions on quantum fields, in Quantum Field Theory Under the Influence of External Conditions, ed. by K. Milton (Rinton Press, Paramus, 2004)
10. N. Graham, R.L. Jaffe, V. Khemani, M. Quandt, O. Schröder, H. Weigel, The Dirichlet Casimir problem. Nucl. Phys. B 677, 379-404 (2004)
11. R.M. Cavalcanti, Casimir force on a piston. Phys. Rev. D 69, 065015 (2004)
12. M.P. Hertzberg, R.L. Jaffe, M. Kardar, A. Scardicchio, Attractive Casimir forces in a closed geometry. Phys. Rev. Lett. 95, 250402 (2005)
13. M.P. Hertzberg, R.L. Jaffe, M. Kardar, A. Scardicchio, Casimir forces in a piston geometry at zero and finite temperatures. Phys. Rev. D 76, 045016 (2007)
14. V.N. Marachevsky, One loop boundary effects: techniques and applications. arXiv:hep-th/0512221 (2005)
15. V.N. Marachevsky, Casimir energy of two plates inside a cylinder. arXiv:hep-th/0609116 (2006). Published in QUARKS-2006 Proceedings
16. V.N. Marachevsky, Casimir interaction: pistons and cavity. J. Phys. A Math. Theor. 41, 164007 (2008)
17. A. Edery, Casimir piston for a massless scalar fields in three dimensions. Phys. Rev. D 75, 105012 (2007)
18. A. Edery, I. Macdonald, Cancellation of nonrenormalizable hyper-surface divergences and the d-dimensional Casimir piston. J. High Energy Phys. 9, 0709005 (2007)
19. A. Edery, V.N. Marachevsky, The perfect magnetic conductor (PMC) Casimir piston in d + 1 dimensions. Phys. Rev. D 78, 025021 (2008)
20. H. Cheng, The Casimir force on a piston in the spacetime with extra compactified dimensions. arXiv:0801.2810 (2008)
21. O. Kenneth, I. Klich, Opposites attract: A theorem about the Casimir force. Phys. Rev. Lett. 97, 160401 (2006)
22. C.P. Bachas, Comment on the sign of the Casimir force. J. Phys. A 40, 409089 (2007)
23. F.M. Serry, D. Walliser, G.J. Maclay, The anharmonic Casimir oscillator (ACO)-the Casimir effect in amodel microelectromechan-ical system. J. Microelectromech. Syst. 4, 193-205 (1995)
24. F.M. Serry, D. Walliser, G.J. Maclay, The role of the Casimir effect in the static deflection and stiction of membrane strips in mi-croelectromechanical systems (MEMS). J. Appl. Phys. 84, 2501-2506 (1998)
25. G. Barton, Casimir piston and cylinder, perturbatively. Phys. Rev. D 73, 065018 (2006)
26. X.H. Zhai, X.Z. Li, Casimir pistons with hybrid boundary conditions. Phys. Rev. D 76, 047704 (2007)
27. S.A. Fulling, L. Kaplan, J.H. Wilson, Vacuum energy and repulsive Casimir forces in quantum star graphs. Phys. Rev. A 76, 012118(2007)
28. M. Reuter, W Dittrich, Regularization schemes for the Casimir effect. Eur. J. Phys. 6, 33-40 (1985)
29. 4 theory in (3 + 1) dimensions: A new renormalization approach. J. High Energy Phys. 9, 0709029 (2007)
30. S.C. Lim, L.P Teo, Finite-temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on zeta function technique. J. Phys. A Math. Theor. 40, 11645-11674 (2007)
31. J. Ambjørn, S. Wolfram, Properties of the vacuum. I. Mechanical and thermodynamic. Ann. Phys. 147, 1-32 (1983)
32. P. Epstein, Zur Theorie allgemeiner Zetafunktionen. Math. Ann. 56, 615-644 (1903)
33. P. Epstein, Zur Theorie allgemeiner Zetafunktionen II. Math. Ann. 65, 205-216 (1907)
34. E. Elizalde, S.D. Odintsov, A. Romeo, A.A. Bytsenko, S. Zerbini, Zeta Regularization Techniques with Applications (World Scientific, Singapore, 1994)
35. E. Elizalde, Ten Physical Applications of Spectral Zeta Functions. Lecture Notes in Physics. New Series m: Monographs, vol. 35 (Springer, Berlin, 1995)
36. K. Kirsten, Spectral Functions in Mathematics and Physics (Chapman & Hall, London, 2002)
37. S.A. Fulling, L. Kaplan, K. Kirsten, Z.H. Liu, K.A. Milton, Vacuum stress and closed paths in rectangles, pistons, and pistols. arXiv:0806.2468
38. S. Chowla, A. Selberg, On Epstein's zeta function. I. Proc. Nat. Acad. Sci. USA 35, 371-374 (1949)
39. A. Selberg, S. Chowla, On Epstein's zeta-function. J. Reine Angew. Math. 227, 86-110 (1967)
40. B. Geyer, G.L. Klimchitskaya, V.M. Mostepanenko, Thermal Casimir effect in ideal metal rectangular boxes. arXiv:0808.3754
41. S.C. Lim, L.P. Teo, Casimir piston at zero and finite temperature. arXiv:0808.0047
42. K.A. Milton, The Casimir Effect: Physical Manifestation of Zero-Po in t E n e rg y (World Scientific, Singapore, 2001)
43. K. Scharnhorst, D. Robaschik, E. Wieczorek, Quantum field theoretic treatment of the Casimir effect at T > 0. Real time formalism-free field approximation. Ann. Phys. (Leipz.) 499, 351-360 (1987)
44. D. Robaschik, E. Wieczorek, Fluctuations of the Casimir pressure at finite temperature. Phys. Rev. D 52, 2341-2354 (1995)