On Casimir forces for media with arbitrary dielectric properties
W. L. Mochán1, C. Villarreal2 and R. Esquivel-Sirvent2
1 Centro de Ciencias Físicas, Universidad Nacional Autónoma de México Av. Universidad S/N, Cuernavaca, Morelos 62210, México.
2 Instituto de Física, Universidad Nacional Autónoma de México Ciudad Universitaria, D.F. 04510, México.
]]> Recibido el 19 de febrero de 2002.
Abstract
We derive an expression for the Casimir force between slabs with arbitrary dielectric properties characterized by their reflection coefficients. The formalism presented here is applicable to media with a local or a non-local dielectric response, an infinite or a finite width, inhomoge-neous dissipative, etc. Óur results reduce to the Lifshitz formula for the force between semi-infinite dielectric slabs by replacing the reflection coefficients by the Fresnel amplitudes.
Keywords: Casimir forces; dielectrics; Lifshitz formula.
Resumen
Se presenta una deducción para la expresión de la fuerza de Casimir entre placas con propiedades dieléctricas arbitrarias caracterizadas por sus coeficientes de reflección. El formalismo que presentamos es válido para medios con una respuesta dieléctrica local, no local, placas de ancho finito o semi-infinito, inhomogéneos, disipativos, etc. Nuestros resultados se reducen a la fórmula de Lifshitz para la fuerza entre placas dieléctricas semi-infinitas substituyendo los coeficientes de reflección por las amplitudes de Fresnel.
Descriptores: Fuerzas de Casimir; dieléctricos; fórmula de Lifshitz.
]]>PACS: 12.20.D.s; 03.70.+k; 77.55.+f; 78.67.-n
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Acknowledgments
This work was partially supported by NASA Breakthrough Propulsion Physics Project, and by DGAPA-UNAM Project IN-110999.
References
1. H. B. G. Casimir, Proc. Kon. Ned. Akad. Wet. 51 (1948) 793. [ Links ]
2. B. V. Derjaguin, I. I. Abrikosova, Vestnik Akad. Nauk. SSSR 6 (1951) 125. [ Links ]
3. P. W. Milonni and Mei-Li Shih, Contemporary Physics 33 (1992)313. [ Links ]
4. S. K. Lamoreaux, Phys. Rev. Lett. 78 (1997) 5. [ Links ]
5. H. B. Chan, V. A. Aksyuk, R. N. Kliman, D. J. Bishop and F. Capasso, Science 291 (2001) 1942. [ Links ]
6. U. Mohideen and Anushree Roy, Phys. Rev. Lett. 81 (1998) 4549. [ Links ]
7. B. W. Harris, F. Chen, and U. Mohideen, Phys. Rev. A 62 (2000) 052109. [ Links ]
8. H. B. Chan, V. A. Aksyuk, R. N. Kliman, D. J. Bishop and F. Capasso, Science 291 (2001) 1942. [ Links ]
9. F. M. Serry, D. Walliser and G. J. Maclay, J. Appl. Phys. 84 (1998)2501. [ Links ]
10. R. Esquivel-Sirvent, C. Villarreal y G. H. Cocoletzi, Phys. Rev. A 64 (2001)052108 . [ Links ]
11. C. Villarreal, R. Esquivel-Sirvent and G. H. Cocoletzi, Int. J. Mod. Phys. A (in press).
]]> 12. R. Esquivel-Sirvent, C. Villarreal, G. H Cocoletzi and W. L. Mochan, Phys. Stat. Sol. (in press).13. M. Bordag, B.Geyer, G.L. Klimchitskaya, and V.M. Mostepa-nenko, Phys. Rev. Lett. 85 (2000) 503; [ Links ] G.L. Klimchitskaya, and V.M. Mostepanenko, Phys. Rev. 63 (2001) 062108. [ Links ]
14. E. M. Lifshitz, Sov. Phys. JETP 2 (1956) 73. [ Links ]
15. Yu. S. Barash and V.L. Ginzburg, Sov. Phys.-Usp., 18 (1975) 305. [ Links ]
16. N. G. Van Kampen, B. R. A. Nijboer, and K. Schram, Phys. Lett. 26a (1968)307. [ Links ]
]]>17. P. Candelas, Ann. Phys. (N.Y.) 143 (1982) 241. [ Links ]
18. R. Matloob, Phys. Rev. A 60 (1999) 50. [ Links ]
19. D. Kupiszewska and J. Mostowski, Phys. Rev. A 41 (1990) 4636. [ Links ]
20. D. Kupiszewska, Phys. Rev. A 46 (1992) 2286. [ Links ]
21. R. Matloob, A. Keshavaraz, and D. Sedighi, Phys. Rev. A, 60 (1999) 3410. [ Links ]
]]>22. E. I. Kats, Sov. Phys. JETP 46 (1977) 109. [ Links ]
23. V. M. Mostepanenko and N. N. Trunov, Sov. J. Nucl. Physics 42 (1985)818. [ Links ]
24. V. B. Bezerra, G. L. Klimchitskaya and C. Romero, Phys. Rev. A 65 (2001)012111. [ Links ]
25. See the review books Photonic Probes of Surfaces, edited by P. Halevi (Elsevier, Amsterdam, 1995) and Spatial Dispersion in Solids and Plasmas, [ Links ] Electromagnetic Waves, Vol. 1, ed. by P. Halevi (North-Holland, Amsterdam, 1992). [ Links ] For an example of a nontrivial application of the surface impedance to non-local excitonic semiconductor superlattices see G. H. Cocoletzi and W. Luis Mochan, Phys. Rev. B 39 (1989) 8403. [ Links ]
]]>26. M. T. Jaekel and S. Reynaud, J. Phys. I France 1 (1991) 1395; [ Links ] R. Matloob, A. Keshavaraz, and D. Sedighi, Phys. Rev. A 60 (1999) 3410. [ Links ]
27. G. Plunien, B. Müller and W. Greiner, Phys. Rep. 134 (1986) 87. [ Links ]
28. A. E. González, Physica A 131 (1985) 228. [ Links ]
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