Abstract
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.
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Casimir H.B.G. (1948). Proc. K. Ned. Akad. Wet. 51: 793
Lamoreaux S.K. (1997). Phys. Rev. Lett. 78: 5
Lamoreaux S.K. (1998). Phys. Rev. Lett. 81: 5475
Mohideen U. and Roy A. (1998). Phys. Rev. Lett. 81: 4549
Roy A., Lin C.-Y. and Mohideen U. (1999). Phys. Rev. D 60: 111101
Milton K.A. (2004). J. Phys. A 37: R209
Kardar M. and Golestanian R. (1999). Rev. Mod. Phys. 71: 1233
Fisher M. and Gennes C.R. (1978). C. R. Acad. Sci. Ser. B 287: 207
Stanley H.G. (1971). Introduction to Phase Transitions and Critical Phenomena. Oxford University Press, Oxford
Krech M. (1994). The Casimir Effect in Critical Systems. World Scientific, Singapore
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))
Forster D. Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions. HarperCollins Canada, 1994
deGennes P.G. and Prost J. (1993). The Physics of Liquid Crystals. Oxford University Press, Oxford
Ajdari A., Peliti L. and Prost J. (1991). Phys. Rev. Lett. 66: 1481
Ueno T. (2003). Phys. Rev. Lett. 90: 116102
Martín A. (1998). Phys. Rev. E 58: 2151
Cardy J.L. (1987). Conformal invariance. In: Domb, C. and Lebowitz, J.L. (eds) Phase Transitions and Critical Phenomena, vol 11., pp. Academic, New York
Gambassi A. and Dietrich S. (2006). J. Stat. Phys. 123: 929
Dnatchev D. and Krech M. (2004). Phys. Rev. E 69: 046119
Dorfman J.R., Kirkpatrick T.R. and Sengers J.V. (1994). Ann. Rev. Phys. Chem. 45: 213
Machta J., Oppenheim I. and Procaccia I. (1979). Phys. Rev. Lett. 42: 1368
Lutsko J.F. and Dufty J.W. (2002). Phys. Rev. E 66: 041206
Procaccia I., Ronis D. and Oppenheim I. (1979). Phys. Rev. Lett. 42: 287
Li W.B. (1998). Phys. Rev. Lett. 81: 5580
Ortizde Zárate J.M. and Sengers J.V. (2006). Hydrodynamic Fluctuations in Fluids and Fluid Mixtures. Elsevier, Amsterdam
Spohn H. (1983). J. Phys. A 16: 4275
Garrido P.L. (1990). Phys. Rev. A 42: 1954
Grinstein G., Lee D.H. and Sachdev S. (1990). Phys. Rev. Lett. 64: 1927
Pagonabarraga I. and Rubí M. (1994). Phys. Rev. E 49: 267
Gardiner C.W. (2004). Handbook of Stochastic Methods. Springer, Heidelberg
Noije T.P.C. (1997). Phys. Rev. Lett 79: 411
Noije T.P.C. (1999). Phys. Rev. E 59: 4326
Family, F., Vicsek, T. (eds.) (1991). Dynamics of Fractal Surfaces. World Scientific, Singapore
Kardar M., Parisi G. and Zhang Y.C. (1986). Phys. Rev. Lett. 56: 889
Roters L., Lübeck S. and Usadel K.D. (1999). Phys. Rev. E 59: 2672
Martınez F.C. (1995). Phys. Rev. E 51: 835
Beijeren H. (1990). J. Stat. Phys. 60: 845
Ernst M.H. and Bussemaker H.J. (1995). J. Stat. Phys. 81: 515
Suárez A., Boon J.P. and Grosfils P. (1996). Phys. Rev. E 54: 1208
Baldassarri A., Marini Bettolo Marconi U. and Puglisi A. (2002). Europhys. Lett. 58: 14
Ernst M.H. and Brito R. (2002). Phys. Rev. E 65: 040301
van Wijland, F., Oerding, K., Hilhorst, H.J. (1998). Physica A 251: 179
García-Ojalvo J. and Sancho J.M. (1999). Noise in Spatially Extended Systems. Springer, New York
Ajdari A. (1992). J. Phys. II France 2: 487
Gradshteyn I.S. and Ryzhik I.M. (1994). Table of Integrals, Series and Products. Academic, New York
Bordag M., Mohideen U. and Mostepanenko V.M. (2001). Phys. Reports 353: 1
Reis P. and Mullin T. (2002). Phys. Rev. Lett. 89: 244301
Aumaitre S., Kruelle C.A. and Rehberg I. (2001). Phys. Rev. E 64: 041305
Schnautz T. (2005). Phys. Rev. Lett. 95: 028001
Zuriguel I. (2005). Phys. Rev. Lett. 95: 258002
Cattuto C. and Marini Bettolo Marconi U. (2004). Phys. Rev. Lett. 92: 174502
Kudrolli A. (2004). Rep. Prog. Phys. 67: 209
Peng G. and Ohta T. (1998). Phys. Rev. E 58: 4737
Verlet L. and Levesque D. (1982). Mol. Phys. 46: 969
Ernst M.H., Brito R. and Noije T.P.C. (1998). Phys. Rev. E 57: 4891
Cattuto C. (2006). Phys. Rev. Lett. 96: 178001
Gotzelmann B., Evans R. and Dietrich S. (1998). Phys. Rev. E 57: 6785
Crocker J.C. (1999). Phys. Rev. Lett. 82: 4352
Sanders D.A. (2004). Phys. Rev. Lett. 93: 208002
Bose M. (2005). Phys. Rev. E 72: 021305
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Brito, R., Soto, R. & Marconi, U.M.B. Casimir forces in granular and other non equilibrium systems. Granular Matter 10, 29–36 (2007). https://doi.org/10.1007/s10035-007-0056-0
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DOI: https://doi.org/10.1007/s10035-007-0056-0