SPECIAL ISSUE: Selected Papers from the Ninth Conference on Quantum Field Theory Under the Influence of External Conditions (QFEXT09); University of Oklahoma, 21–25 September 2009; Editors: K. Milton and M. BordagNo Access

THE SCATTERING APPROACH TO THE CASIMIR FORCE

S. REYNAUD

Laboratoire Kastler Brossel, ENS, UPMC, CNRS, Jussieu, 75252 Paris, France

Search for more papers by this author

A. CANAGUIER-DURAND

Laboratoire Kastler Brossel, ENS, UPMC, CNRS, Jussieu, 75252 Paris, France

Search for more papers by this author

R. MESSINA

Laboratoire Kastler Brossel, ENS, UPMC, CNRS, Jussieu, 75252 Paris, France

Search for more papers by this author

A. LAMBRECHT

Laboratoire Kastler Brossel, ENS, UPMC, CNRS, Jussieu, 75252 Paris, France

Search for more papers by this author

, and

P. A. MAIA NETO

Instituto de Física, UFRJ, CP 68528, Rio de Janeiro, RJ, 21941-972, Brazil

Search for more papers by this author

https://doi.org/10.1142/S0217751X10049475Cited by:7 (Source: Crossref)

Abstract

We present the scattering approach which is nowadays the best tool for describing the Casimir force in realistic experimental configurations. After reminders on the simple geometries of 1d space and specular scatterers in 3d space, we discuss the case of stationary arbitrarily shaped mirrors in electromagnetic vacuum. We then review specific calculations based on the scattering approach, dealing for example with the forces or torques between nanostructured surfaces and with the force between a plane and a sphere. In these various cases, we account for the material dependence of the forces, and show that the geometry dependence goes beyond the trivial Proximity Force Approximation often used for discussing experiments.

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948). Google Scholar
P. W. Milonni , The quantum vacuum ( Academic , 1994 ) . Google Scholar
S. K. Lamoreaux, Am. J. Phys. 67, 850 (1999), DOI: 10.1119/1.19138. Web of Science, ADS, Google Scholar
M. Bordag, U. Mohideen and V. M. Mostepanenko, Phys. Rep. 353, 1 (2001), DOI: 10.1016/S0370-1573(01)00015-1. Web of Science, ADS, Google Scholar
K. A. Milton, J. Phys. A 20, 4628 (2005). Google Scholar
R. S. Deccaet al., Annals Phys. 318, 37 (2005), DOI: 10.1016/j.aop.2005.03.007. Web of Science, ADS, Google Scholar
A. Lambrecht, P. A. Maia Neto and S. Reynaud, New J. Phys. 8, 243 (2006), DOI: 10.1088/1367-2630/8/10/243. Web of Science, Google Scholar
C. Genet , A. Lambrecht and S. Reynaud , On the Nature of Dark Energy 121 , eds. U. Brax , J. Martin and J. P. Uzan ( Frontier Group , 2002 ) , arXiv:quant-ph/0210173 . Google Scholar
M.-T. Jaekel and S. Reynaud, Proc. of the Orleans School on Mass (2009), arXiv:0812.3936. Google Scholar
M.-T. Jaekel and S. Reynaud, Reports on Progress in Physics 60, 863 (1997), DOI: 10.1088/0034-4885/60/9/001. Web of Science, ADS, Google Scholar
A. Lambrecht, Journal of Optics, B 7, 3 (2005). Web of Science, Google Scholar
C. Braggio et al, in the present volume (2009) . Google Scholar
E. Fischbach and C. Talmadge , The Search for Non Newtonian Gravity ( AIP Press/Springer Verlag , 1998 ) . Google Scholar
E. G. Adelberger, B. R. Heckel and A. E. Nelson, Ann. Rev. Nucl. Part. Sci. 53, 77 (2003), DOI: 10.1146/annurev.nucl.53.041002.110503. Web of Science, ADS, Google Scholar
D. J. Kapneret al., Phys. Rev. Lett. 98, 021101 (2007), DOI: 10.1103/PhysRevLett.98.021101. Web of Science, Google Scholar
A. Lambrecht and S. Reynaud, Poincaré Seminar on Vacuum Energy and Renormalization 1, 107 (2002), arXiv:quant-ph/0302073. Google Scholar
R. Onofrio, New J. Phys. 8, 237 (2006), DOI: 10.1088/1367-2630/8/10/237. Web of Science, Google Scholar
S. Lepoutre and et al, EPL 88, 20002 (2009), DOI: 10.1209/0295-5075/88/20002. Web of Science, Google Scholar
V. Nesvizhevsky and et al, Phys. Rev. D 77, 034020 (2008), DOI: 10.1103/PhysRevD.77.034020. Web of Science, Google Scholar
V. A. Parsegian , Van der Waals Forces : a Handbook for Biologists, Chemists, Engineers and Physicists ( Cambridge UP , 2006 ) . Google Scholar
A. Lambrecht and S. Reynaud, Euro. Phys. J. D 8, 309 (2000), DOI: 10.1007/s100530050041. Web of Science, ADS, Google Scholar
J. Mehra, Physica 37, 145 (1967), DOI: 10.1016/0031-8914(67)90115-2. Web of Science, ADS, Google Scholar
J. Schwinger, L. L. de Raad and K. A. Milton, Ann. Phys. 115, 1 (1978). Web of Science, ADS, Google Scholar
C. Genet, A. Lambrecht and S. Reynaud, Phys. Rev. A 62, 012110 (2000), DOI: 10.1103/PhysRevA.62.012110. Web of Science, Google Scholar
M. Bostrm and Bo E. Sernelius, Phys. Rev. Lett. 84, 4757 (2000). Web of Science, ADS, Google Scholar
S. Reynaud, A. Lambrecht and C. Genet, Quantum Field Theory Under the Influence of External Conditions, ed. K. A. Milton (Rinton Press, 2004) p. 36, arXiv:quant-ph/0312224. Google Scholar
I. Brevik, S. A. Ellingsen and K. Milton, New J. Phys. 8, 236 (2006), DOI: 10.1088/1367-2630/8/10/236. Web of Science, Google Scholar
G.-L. Ingold, A. Lambrecht and S. Reynaud, Phys. Rev. E 80, 041113 (2009), DOI: 10.1103/PhysRevE.80.041113. Web of Science, Google Scholar
R. Decca and et al, Phys. Rev. D 75, 077101 (2007), DOI: 10.1103/PhysRevD.75.077101. Web of Science, Google Scholar
B. Jancovici and L. Šamaj, Europhys. Lett. 72, 35 (2005), DOI: 10.1209/epl/i2005-10201-5. ADS, Google Scholar
P. R. Buenzli and Ph. A. Martin, Europhys. Lett. 72, 42 (2005), DOI: 10.1209/epl/i2005-10200-6. ADS, Google Scholar
G. Bimonte, Phys. Rev. A 79, 042107 (2009), DOI: 10.1103/PhysRevA.79.042107. Web of Science, Google Scholar
B. V. Deriagin, I. I. Abrikosova and E. M. Lifshitz, Quart. Rev. 10, 295 (1968). Google Scholar
E. M. Lifshitz, Sov. Phys. JETP 2, 73 (1956). Web of Science, Google Scholar
I. E. Dzyaloshinskii, E. M. Lifshitz and L. P. Pitaevskii, Sov. Phys. Uspekhi 4, 153 (1961), DOI: 10.1070/PU1961v004n02ABEH003330. ADS, Google Scholar
R. Balian and B. Duplantier, Ann. Phys. NY 104 300 (1977); 112 165 (1978); in 15th SIGRAV Conference on General Relativity and Gravitation , arXiv:quant-ph/0408124 . Google Scholar
R. L. Jaffe and A. Scardicchio, Phys. Rev. Lett. 92, 070402 (2004), DOI: 10.1103/PhysRevLett.92.070402. Web of Science, Google Scholar
S. Reynaud, P. A. Maia Neto and A. Lambrecht, J. Phys. A 41, 164004 (2008), DOI: 10.1088/1751-8113/41/16/164004. ADS, Google Scholar
T. Emig and R. L. Jaffe, J. Phys. A 41, 164001 (2008), DOI: 10.1088/1751-8113/41/16/164001. ADS, Google Scholar
M. Bordag and V. Nikolaev, J. Phys. A 41, 164002 (2008), DOI: 10.1088/1751-8113/41/16/164002. ADS, Google Scholar
A. Wirzba, J. Phys. A 41, 164003 (2008), DOI: 10.1088/1751-8113/41/16/164003. ADS, Google Scholar
K. Klingmller and H. Gies, J. Phys. A 41, 164042 (2008). ADS, Google Scholar
A. Canaguier-Durandet al., Phys. Rev. Lett. 102, 230404 (2009), DOI: 10.1103/PhysRevLett.102.230404. Web of Science, Google Scholar
D. E. Krauseet al., Phys. Rev. Lett. 98, 050403 (2007), DOI: 10.1103/PhysRevLett.98.050403. Web of Science, Google Scholar
F. Chen, U. Mohideen, G. L. Klimchitskaya and V. Mostepanenko, Phys. Rev. Lett. 88 101801 (2002); Phys. Rev. A66 032113 (2002) . Google Scholar
R. Bscher and T. Emig, Phys. Rev. Lett. 94, 133901 (2005). Web of Science, ADS, Google Scholar
P. A. Maia Neto, A. Lambrecht and S. Reynaud, Europhys. Lett. 69 924 (2005); Phys. Rev. A72 012115 (2005) . Google Scholar
R. B. Rodrigues, P. A. Maia Neto, A. Lambrecht and S. Reynaud, Phys. Rev. Lett. 96 100402 (2006); Phys. Rev. Lett. 98 068902 (2007) . Google Scholar
R. B. Rodrigueset al., Phys. Rev. A 75, 062108 (2007), DOI: 10.1103/PhysRevA.75.062108. Web of Science, Google Scholar
H. B. Chan and et al, Phys. Rev. Lett. 101, 030401 (2008), DOI: 10.1103/PhysRevLett.101.030401. Web of Science, Google Scholar
H. C. Chiu and et al, Phys. Rev. B 80, 121402 (2009), DOI: 10.1103/PhysRevB.80.121402. Web of Science, ADS, Google Scholar
A. Lambrecht and V. N. Marachevsky, Phys. Rev. Lett. 101 160403 (2008); A. Lambrecht Nature 454 836 (2008) . Google Scholar
M. T. Jaekel and S. Reynaud, J. Physique I 1, 1395 (1991), arXiv:quant-ph/0101067 DOI: 10.1051/jp1:1991216. Google Scholar
C. Genet, A. Lambrecht and S. Reynaud, Phys. Rev. A 67, 043811 (2003), DOI: 10.1103/PhysRevA.67.043811. Web of Science, Google Scholar
The question had been asked in [26] whether the regularity conditions needed to write the Matsubara sum were met for the Drude model; this question has been answered positively in [28] . Google Scholar
L. P. Pitaevskii, Phys. Rev. Lett. 101 163202 (2008); Phys. Rev. Lett. 102 189302 (2009); B. Geyer et al, Phys. Rev. Lett. 102 189301 (2009) . Google Scholar
D. A. R. Dalvit and S. K. Lamoreaux, Phys. Rev. Lett. 101 163203 (2008); Phys. Rev. Lett. 102 189304 (2009); R. S. Decca et al, Phys. Rev. Lett. 102 189303 (2009) . Google Scholar
V. B. Svetovoy, Phys. Rev. Lett. 101 163603 (2008); Phys. Rev. Lett. 102 219903 (E) (2009) . Google Scholar
T. Emig, J. Stat. Mech.: Theory Exp. P04007 (2008), DOI: 10.1088/1742-5468/2008/04/P04007. Google Scholar
O. Kenneth and I. Klich, Phys. Rev. B 78, 014103 (2008), DOI: 10.1103/PhysRevB.78.014103. Web of Science, Google Scholar
K. A. Milton and J. Wagner, J. Phys. A 41, 155402 (2008), DOI: 10.1088/1751-8113/41/15/155402. ADS, Google Scholar
R. B. Rodrigueset al., Europhys. Lett. 76, 822 (2006), DOI: 10.1209/epl/i2006-10340-1. ADS, Google Scholar
J. Mundayet al., Phys. Rev. A 71, 042102 (2005), DOI: 10.1103/PhysRevA.71.042102. Web of Science, Google Scholar
D. A. R. Dalvitet al., Phys. Rev. Lett. 100, 040405 (2008), DOI: 10.1103/PhysRevLett.100.040405. Web of Science, Google Scholar
R. Messinaet al., Phys. Rev. A 80, 022119 (2009), DOI: 10.1103/PhysRevA.80.022119. Web of Science, Google Scholar
P. A. Maia Neto, A. Lambrecht and S. Reynaud, Phys. Rev. A 78, 012115 (2008), DOI: 10.1103/PhysRevA.78.012115. Web of Science, Google Scholar
M. Bordag and V. Nikolaev , arXiv:0911.0146 . Google Scholar
A. Canaguier-Durandet al., Phys. Rev. Lett. (2010), arXiv:0911.0913. Google Scholar

Vol. 25, No. 11

Metrics

Downloaded 50 times

History

PDF download

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

THE SCATTERING APPROACH TO THE CASIMIR FORCE

Abstract

Recommended