Abstract
The theory of the Casimir effect for diffraction gratings is considered; symmetry breaking in geometric transitions is discussed.
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REFERENCES
H. B. G. Casimir and D. Polder, “The influence of retardation on the London–van der Waals forces,” Phys. Rev. 73, 360–372 (1948).
H. B. G. Casimir, “On the attraction between two perfectly conducting plates,” Proc. Kon. Ned. Akad. Wetensch. B 51, 793–795 (1948).
E. M. Lifshitz, “The theory of molecular attractive forces between solids,” Zh. Eksp. Teor. Fiz. 29, 94–110 (1955).
V. V. Nesterenko and I. G. Pirozhenko, “Lifshitz formula by a spectral summation method,” Phys. Rev. D 86, 052503 (2012).
V. N. Marachevsky and A. A. Sidelnikov, “Green functions scattering in the Casimir effect,” Universe 7, 195 (2021).
A. Rodriguez, F. Capasso, and S. Johnson, “The Casimir effect in microstructured geometries,” Nat. Photon 5, 211–221 (2011).
L. M. Woods, M. Krüger, and V. V. Dodonov, “Perspective on some recent and future developments in Casimir Interactions,” Appl. Sci. 11, 293 (2021).
V. N. Marachevsky and Y. M. Pis’mak, “Casimir–Polder Effect for a plane with Chern–Simons interaction,” Phys. Rev. D 81, 065005 (2010).
V. N. Marachevsky, “Casimir effect for Chern–Simons layers in the vacuum,” Theor. Math. Phys. 190, 315–320 (2017).
I. V. Fialkovsky, V. N. Marachevsky, and D. V. Vassilevich, “Finite-temperature Casimir effect for graphene,” Phys. Rev. B 84, 035446 (2011).
D. Fursaev and D. Vassilevich, Operators, Geometry and Quanta: Methods of Spectral Geometry in Quantum Field Theory (Springer, Dordrecht, 2011).
M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, Advances in the Casimir Effect (Oxford University Press, 2015).
A. Lambrecht and V. N. Marachevsky, “Casimir Interaction of dielectric gratings,” Phys. Rev. Lett. 101, 160403 (2008).
A. Lambrecht and V. N. Marachevsky, “Theory of the Casimir effect in one-dimensional periodic dielectric systems,” Int. J. Mod. Phys. A 24, 1789–1795 (2009).
T. Emig, R. L. Jaffe, M. Kardar, and A. Scardicchio, “Casimir interaction between a plate and a cylinder,” Phys. Rev. Lett. 96, 080403 (2006).
S. J. Rahi, T. Emig, N. Graham, R. L. Jaffe, and M. Kardar, “Scattering theory approach to electromagnetic Casimir forces,” Phys. Rev. D 80, 085021 (2009).
A. Canaguier-Durand, P. A. Maia Neto, I. Cavero-Pelaez, A. Lambrecht, and S. Reynaud, “Casimir interaction between plane and spherical metallic surfaces,” Phys. Rev. Lett. 102, 230404 (2009).
M. Bordag and I. Pirozhenko, “Vacuum energy between a sphere and a plane at finite temperature,” Phys. Rev. D 81, 085023 (2010).
O. M. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London, Ser. A 79, 399–415 (1907).
H. B. Chan, Y. Bao, J. Zou, R. A. Cirelli, F. Klemens, W. Mansfield, and C. Pai, “Measurement of the Casimir force between a gold sphere and a silicon surface with nanoscale trench arrays,” Phys. Rev. Lett. 101, 030401 (2008).
H.-C. Chiu, G. L. Klimchitskaya, V. N. Marachevsky, V. M. Mostepanenko, and U. Mohideen, “Demonstration of the asymmetric lateral Casimir force between corrugated surfaces in the nonadditive regime,” Phys. Rev. B 80, 121402 (2009).
H.-C. Chiu, G. L. Klimchitskaya, V. N. Marachevsky, V. M. Mostepanenko, and U. Mohideen, “Lateral Casimir force between sinusoidally corrugated surfaces: asymmetric profiles, deviations from the proximity force approximation, and comparison with exact theory,” Phys. Rev. B 81, 115417 (2010).
B. V. Derjaguin, I. I. Abrikosova, and E. M. Lifshitz, “Direct measurement of molecular attraction between solids separated by a narrow gap,” Q. Rev. 10, 295–329 (1956).
F. Intravaia, S. Koev, I. W. Jung, A. A. Talin, P. S. Davids, R. S. Decca, V. A. Aksyuk, D. A. R. Dalvit, and D. López, “Strong Casimir force reduction through metallic surface nanostructuring,” Nat. Commun. 4, 2515 (2013).
Y. Bao, R. Guérout, J. Lussange, A. Lambrecht, R. A. Cirelli, F. Klemens, W. M. Mansfield, C. S. Pai, and H. B. Chan, “Casimir force on a surface with shallow nanoscale corrugations: geometry and finite conductivity effects,” Phys. Rev. Lett. 105, 250402 (2010).
L. Tang, M. Wang, C. Y. Ng, M. Nikolic, C. T. Chan, A. W. Rodriguez, and H. B. Chan, “Measurement of non-monotonic Casimir forces between silicon nanostructures,” Nat. Photon. 11, 97–101 (2017).
M. Wang, L. Tang, C. Y. Ng, R. Messina, B. Guizal, J. A. Crosse, M. Antezza, C. T. Chan, and H. B. Chan, “Strong geometry dependence of the Casimir force between interpenetrated rectangular gratings,” Nat. Commun. 12, 600 (2021).
S. Y. Buhmann, Dispersion Forces (Springer, Berlin, 2012), Vols. 1–2.
H. Bender, C. Stehle, C. Zimmermann, S. Slama, J. Fiedler, S. Scheel, S. Y. Buhmann, and V. N. Marachevsky, “Probing atom-surface interactions by diffraction of Bose–Einstein condensates,” Phys. Rev. X 4, 011029 (2014).
S. Y. Buhmann, V. N. Marachevsky, and S. Scheel, “Impact of anisotropy on the interaction of an atom with a one-dimensional nano-grating,” Int. J. Mod. Phys. A 31, 1641029 (2016).
M. Antezza, H. B. Chan, B. Guizal, V. N. Marachevsky, R. Messina, and M. Wang, “Giant Casimir Torque between rotated gratings and the θ = 0 anomaly,” Phys. Rev. Lett. 124, 013903 (2020).
R. Guérout, C. Genet, A. Lambrecht, and S. Reynaud, “Casimir torque between nanostructured plates,” Europhys. Lett. 111, 44001 (2015).
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This work was supported by a grant from the Russian Science Foundation, project no. 22-13-00151.
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Marachevsky, V.N. The Casimir Effect for Diffraction Gratings, Symmetry Breaking, and Geometric Transitions. Phys. Part. Nuclei Lett. 20, 255–258 (2023). https://doi.org/10.1134/S1547477123030457
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DOI: https://doi.org/10.1134/S1547477123030457