RT Journal Article T1 Casimir forces in granular and other non equilibrium systems A1 Brito, Ricardo A1 Soto, R. AB In this paper we present a method to calculate Casimir Forces for non equilibrium systems with long range correlations. The origin of the force are the fluctuating fields, and the modification that the external, macroscopic objects induce in the spectrum of the fluctuations. The method is first illustrated with a simple model: a reaction-diffusion non-equilibrium system with an structure factor that possesses a characteristic length. The second part of the paper deals with a granular fluid where correlations are long ranged at all scales. In the first case the hydrodynamic fluctuations are confined by two plates, while in the second one the confinement comes from two immobile large and heavy particles. In both cases Casimir forces are calculated, and their properties analyzed. SN 1434-7636 YR 2007 FD 2007-12 LK https://hdl.handle.net/20.500.14352/50635 UL https://hdl.handle.net/20.500.14352/50635 LA eng NO 1. Casimir, H.B.G.: Proc. K. Ned. Akad. Wet. 51, 793 (1948)2. Lamoreaux, S.K.: Phys. Rev. Lett. 78, 5 (1997)3. Lamoreaux, S.K.: Phys. Rev. Lett. 81, 5475 (1998)4. Mohideen, U., Roy, A.: Phys. Rev. Lett. 81, 4549 (1998)5. Roy, A., Lin,C.-Y., Mohideen,U.: Phys.Rev.D60, 111101 (1999)6. Milton, K.A.: J. Phys. A 37, R209 (2004)7. Kardar, M., Golestanian, R.: Rev. Mod. Phys. 71, 1233 (1999)8. Fisher, M., de Gennes, C.R.: C. R. Acad. Sci. Ser. B 287, 207 (1978)9. Stanley, H.G.: Introduction to Phase Transitions and Critical Phenomena. Oxford University Press, Oxford (1971)10. Krech, M.: The Casimir Effect in Critical Systems. World Scientific, Singapore (1994)11. Brankov, I., Danchev, D.M., Tonchev, N.S., Brankov, J.G.: Theory of Critical Phenomena in Finite-Size Systems: Scaling and Quantum Effects (Series in Modern Condensed Matter Physics, vol 9. World Scientific, Singapore (2000))12. Forster, D.: Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions. HarperCollins Canada, (1994)13. deGennes, P.G., Prost, J.: The Physics of Liquid Crystals. Oxford University Press, Oxford (1993)14. Ajdari, A., Peliti, L., Prost, J.: Phys. Rev. Lett. 66, 1481 (1991)15. Ueno, T. et al.: Phys. Rev. Lett. 90, 116102 (2003)16. Martín, A. et al.: Phys. Rev. E 58, 2151 (1998)17. Cardy, J.L.: Conformal invariance. In: Domb, C., Lebowitz, J.L. (eds.) Phase Transitions and Critical Phenomena, vol 11. Academic, New York (1987)18. Gambassi, A., Dietrich, S.: J. Stat. Phys. 123, 929 (2006)19. Dnatchev, D., Krech, M.: Phys. Rev. E 69, 046119 (2004)20. Dorfman, J.R., Kirkpatrick, T.R., Sengers, J.V.: Ann. Rev. Phys. Chem. 45, 213 (1994)21. Machta, J., Oppenheim, I., Procaccia, I.: Phys. Rev. Lett. 42, 1368 (1979)22. Lutsko, J.F., Dufty, J.W.: Phys. Rev. E 66, 041206 (2002)23. Procaccia, I., Ronis, D., Oppenheim, I.: Phys. Rev. Lett. 42, 287 (1979)24. Li, W.B. et al.: Phys. Rev. Lett. 81, 5580 (1998)25. Ortiz de Zárate, J.M., Sengers, J.V.: Hydrodynamic Fluctuations in Fluids and Fluid Mixtures. Elsevier, Amsterdam (2006)26. Spohn, H.: J. Phys. A 16, 4275 (1983)27. Garrido, P.L. et al.: Phys. Rev. A 42, 1954 (1990)28. Grinstein, G., Lee, D.H., Sachdev, S.: Phys. Rev. Lett. 64, 1927 (1990)29. Pagonabarraga, I., Rubí, M.: Phys. Rev. E 49, 267 (1994)30. Gardiner, C.W.: Handbook of Stochastic Methods. Springer, Heidelberg (2004)31. van Noije, T.P.C. et al.: Phys. Rev. Lett 79, 411 (1997)32. van Noije, T.P.C. et al.: Phys. Rev. E 59, 4326 (1999)33. Family, F., Vicsek, T. (eds.): Dynamics of Fractal Surfaces. World Scientific, Singapore (1991)34. Kardar,M., Parisi,G., Zhang,Y.C.: Phys. Rev. Lett. 56, 889 (1986)35. Roters, L., Lübeck, S., Usadel, K.D.: Phys. Rev. E 59, 2672 (1999)36. Martínez, F.C. et al.: Phys. Rev. E 51, 835 (1995)37. Beijeren, H. van : J. Stat. Phys. 60, 845 (1990)38. Ernst, M.H., Bussemaker, H.J.: J. Stat. Phys. 81, 515 (1995)39. Suárez, A., Boon, J.P., Grosfils, P.: Phys. Rev. E 54, 1208 (1996)40. Baldassarri,A., Marini Bettolo Marconi,U., Puglisi, A.: Europhys. Lett. 58, 14 (2002)41. Ernst, M.H., Brito, R.: Phys. Rev. E 65, 040301 (2002)42. van Wijland, F., Oerding, K., Hilhorst, H.J.: Physica A 251, 179 (1998)43. García-Ojalvo, J., Sancho, J.M.: Noise in Spatially Extended Systems. Springer, New York (1999)44. Ajdari, A. et al.: J. Phys. II France 2, 487 (1992)45. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products, 5th edn. Academic, New York (1994)46. Bordag, M., Mohideen, U., Mostepanenko, V.M.: Phys. Reports 353, 1 (2001)47. Reis, P., Mullin, T.: Phys. Rev. Lett. 89, 244301 (2002)48. Aumaitre, S., Kruelle, C.A., Rehberg, I.: Phys. Rev. E 64, 041305 (2001)49. Schnautz, T. et al.: Phys. Rev. Lett. 95, 028001 (2005)50. Zuriguel, I. et al.: Phys. Rev. Lett. 95, 258002 (2005)51. Cattuto, C., Marini Bettolo Marconi, U.: Phys. Rev. Lett. 92, 174502 (2004)52. Kudrolli, A.: Rep. Prog. Phys. 67, 209 (2004)53. Peng, G., Ohta, T.: Phys. Rev. E 58, 4737 (1998)54. Verlet, L., Levesque, D.: Mol. Phys. 46, 969 (1982)55. van Noije, T.P.C., Ernst, M.H., Brito, R.: Phys. Rev. E 57, 4891 (1998)56. Cattuto, C. et al.: Phys. Rev. Lett. 96, 178001 (2006)57. Gotzelmann, B., Evans, R., Dietrich, S.: Phys. Rev. E 57, 6785 (1998)58. Crocker, J.C. et al.: Phys. Rev. Lett. 82, 4352 (1999)59. Sanders, D.A. et al.: Phys. Rev. Lett. 93, 208002 (2004)60. Bose, M. et al.: Phys. Rev. E 72, 021305 (2005) NO © Springer-Verlag 2007. The authors want to thank C. Cattuto for performing the computer simulations in the granular case. R.B. is supported by the Projects MOSAICO, FIS2004-271 and and UCM PR27/05-13923-BSCH. U.M.B.M. acknowledges a grant COFIN-MIUR 2005, 2005027808. R.S. is supported by Fondecyt research grants 1030993 and 1061112 and Fondap grant 11980002. NO MOSAICO NO Fondecyt NO Fondap DS Docta Complutense RD 28 abr 2024