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Repulsive Casimir–Lifshitz pressure in closed cavities

Abstract

We consider the interaction pressure acting on the surface of a dielectric sphere enclosed within a magnetodielectric cavity. We determine the sign of this quantity regardless of the geometry of the cavity for systems at thermal equilibrium, extending the Dzyaloshinskii–Lifshitz–Pitaevskii result for homogeneous slabs. As in previous theorems regarding Casimir–Lifshitz forces, the result is based on the scattering formalism. In this case, the proof follows from the variable phase approach of electromagnetic scattering. With this, we present configurations in which both the interaction and the self-energy contribution to the pressure tend to expand the sphere.

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References

  1. M. Bordag, G.L. Klimchitskaya, U. Mohideen, V.M. Mostepanenko, Advances in the Casimir Effect (Oxford University Press, Oxford, 2009)

    MATH  Book  Google Scholar 

  2. K.A. Milton, The Casimir Effect: Physical Manifestations of Zero-Point Energy (World Scientific, Singapore, 2001)

    MATH  Book  Google Scholar 

  3. O. Kenneth, I. Klich, Phys. Rev. Lett. 97, 160401 (2006)

    ADS  Article  Google Scholar 

  4. C.P. Bachas, J. Phys. A 40, 9089 (2007)

    ADS  MathSciNet  Article  Google Scholar 

  5. E. Buks, M.L. Roukes, Phys. Rev. B 63, 033402 (2001)

    ADS  Article  Google Scholar 

  6. J.N. Munday, F. Capasso, Int. J. Mod. Phys. A 25, 2252 (2010)

    ADS  Article  Google Scholar 

  7. T.H. Boyer, Phys. Rev. A 9, 2078 (1974)

    ADS  Article  Google Scholar 

  8. F.S.S. Rosa, D.A.R. Dalvit, P.W. Milonni, Phys. Rev. Lett. 100, 183602 (2008)

    ADS  Article  Google Scholar 

  9. R. Zhao, J. Zhou, Th. Koschny, E.N. Economou, C.M. Soukoulis, Phys. Rev. Lett. 103, 103602 (2009)

    ADS  Article  Google Scholar 

  10. A.G. Grushin, A. Cortijo, Phys. Rev. Lett. 106, 020403 (2011)

    ADS  Article  Google Scholar 

  11. P. Rodriguez-Lopez, A.G. Grushin, Phys. Rev. Lett. 112, 056804 (2014)

    ADS  Article  Google Scholar 

  12. M. Levin, A.P. McCauley, A.W. Rodriguez, M.T.H. Reid, S.G. Johnson, Phys. Rev. Lett. 105, 090403 (2010)

    ADS  Article  Google Scholar 

  13. P.P. Abrantes, Y. França, F.S.S. da Rosa, C. Farina, R. de Melo, Phys. Rev. A 98, 012511 (2018)

    ADS  Article  Google Scholar 

  14. I.E. Dzyaloshinskii, E.M. Lifshitz, L.P. Pitaevskii, Adv. Phys. 10, 165 (1961)

    ADS  Article  Google Scholar 

  15. J.N. Munday, F. Capasso, V.A. Parsegian, Nature 457, 170 (2009)

    ADS  Article  Google Scholar 

  16. P.S. Venkataram, S. Molesky, P. Chao, A.W. Rodriguez, Phys. Rev. A 101, 052115 (2020)

    ADS  MathSciNet  Article  Google Scholar 

  17. F. Capasso, J.N. Munday, D. Iannuzzi, H.B. Chan, IEEE J. Quantum Electron. 13, 400 (2007)

    Article  Google Scholar 

  18. S.J. Rahi, M. Kardar, T. Emig, Phys. Rev. Lett. 105, 070404 (2010)

    ADS  Article  Google Scholar 

  19. Q.D. Jiang, F. Wilczek, Phys. Rev. B 99, 125403 (2019)

    ADS  Article  Google Scholar 

  20. V.N. Marachevsky, Phys. Scr. 64, 205 (2001)

    ADS  Article  Google Scholar 

  21. J.S. Høye, I. Brevik, J.B. Aarseth, Phys. Rev. E 63, 051101 (2001)

    ADS  Article  Google Scholar 

  22. I. Brevik, J.B. Aarseth, J.S. Høye, Phys. Rev. E 66, 026119 (2002)

    ADS  Article  Google Scholar 

  23. I. Brevik, E.K. Dahl, G.O. Myhr, J. Phys. A Math. Gen. 38, L49 (2005)

    ADS  Article  Google Scholar 

  24. D.A.R. Dalvit, F.C. Lombardo, F.D. Mazzitelli, R. Onofrio, Phys. Rev. A 74, 020101(R) (2006)

    ADS  Article  Google Scholar 

  25. V.N. Marachevsky, Phys. Rev. D 75, 085019 (2007)

    ADS  Article  Google Scholar 

  26. S. Zaheer, S.J. Rahi, T. Emig, R.L. Jaffe, Phys. Rev. A 82, 052507 (2010)

    ADS  Article  Google Scholar 

  27. L.P. Teo, Phys. Rev. D 82, 085009 (2010)

    ADS  Article  Google Scholar 

  28. S.J. Rahi, S. Zaheer, Phys. Rev. Lett. 104, 070405 (2010)

    ADS  Article  Google Scholar 

  29. P. Parashar, K.A. Milton, K.V. Shajesh, I. Brevik, Phys. Rev. D 96, 085010 (2017)

    ADS  MathSciNet  Article  Google Scholar 

  30. O. Kenneth, I. Klich, Phys. Rev. B 78, 014103 (2008)

    ADS  Article  Google Scholar 

  31. S.J. Rahi, T. Emig, N. Graham, R.L. Jaffe, M. Kardar, Phys. Rev. D 80, 085021 (2009)

    ADS  Article  Google Scholar 

  32. R.G. Newton, Scattering Theory of Waves and Particles (Dover, Mineola, New York, 2002)

    MATH  Google Scholar 

  33. G.W. Hanson, A.B. Yakovlev, Operator Theory for Electromagnetics (Springer, New York, 2002)

    MATH  Book  Google Scholar 

  34. B. Sun, L. Bi, P. Yang, M. Kahnert, G. Kattawar, Invariant Imbedding T-Matrix Method for Light Scattering by Nonspherical and Inhomogeneous Particles (Elsevier, Amsterdam, 2019)

    Google Scholar 

  35. L.P. Teo, Int. J. Mod. Phys. A 27, 1230021 (2012)

    ADS  Article  Google Scholar 

  36. B. Simon, Adv. Math. 24, 244 (1977)

    Article  Google Scholar 

  37. G. Barton, J. Phys. A Math. Gen. 37, 3725 (2004)

    ADS  Article  Google Scholar 

  38. Y. Li, K.A. Milton, X. Guo, G. Kennedy, S.A. Fulling

  39. B.R. Johnson, Appl. Opt. 27, 4861 (1988)

    ADS  Article  Google Scholar 

  40. A. Forrow, N. Graham, Phys. Rev. A 86, 062715 (2012)

    ADS  Article  Google Scholar 

  41. F. Calogero, Variable Phase Approach to Potential Scattering (Academic, New York, 1967)

    MATH  Google Scholar 

  42. B.R. Johnson, J. Opt. Soc. Am. A 16, 845 (1999)

    ADS  Article  Google Scholar 

  43. B. Toni, Advances in Interdisciplinary Mathematical Research (Springer, New York, 2014). (Chapter 3)

  44. R.P. Feynman, Phys. Rev. 56, 340 (1939)

    ADS  Article  Google Scholar 

  45. J.L. Garrett, D.A.T. Somers, J.N. Munday, Phys. Rev. Lett. 120, 040401 (2018)

    ADS  MathSciNet  Article  Google Scholar 

  46. K.A. Milton, P. Parashar, I. Brevik, G. Kennedy, Ann. Phys. 412, 168008 (2020)

    Article  Google Scholar 

  47. I. Cavero -Peláez, J.M. Muñoz-Castañeda, C. Romaniega, Phys. Rev. D 103, 045005 (2021)

  48. M. Asorey, J.M. Munoz-Castaneda, Nucl. Phys. B 874, 852 (2013)

    ADS  Article  Google Scholar 

  49. G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. B 75(3), 036101 (2007)

    ADS  Article  Google Scholar 

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Acknowledgements

I am grateful to I. Cavero -Peláez, A. Romaniega, L. M. Nieto and J. M. Muñoz-Castañeda for the useful suggestions. This work was supported by the FPU fellowship program (FPU17/01475) and the Junta de Castilla y León and FEDER projects (BU229P18 and VA137G18).

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Romaniega, C. Repulsive Casimir–Lifshitz pressure in closed cavities. Eur. Phys. J. Plus 136, 327 (2021). https://doi.org/10.1140/epjp/s13360-021-01308-z

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  • DOI: https://doi.org/10.1140/epjp/s13360-021-01308-z