Geodesic
Casimir effect for Chern–Simons layers in the vacuum
Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 2, pp. 366-372 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We solve the diffraction problem for electromagnetic waves on a planar $(2{+}1)$-dimensional layer with a given Chern–Simons action. The Casimir energy of a system of two parallel planar Chern–Simons layers is expressed in terms of the coefficients of reflection from separate layers.
Keywords: Chern–Simons interaction, Casimir energy.
Mots-clés : diffraction problem 
@article{TMF_2017_190_2_a11,
     author = {V. N. Marachevsky},
     title = {Casimir effect for {Chern{\textendash}Simons} layers in the~vacuum},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {366--372},
     year = {2017},
     volume = {190},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_190_2_a11/}
}
TY  - JOUR
AU  - V. N. Marachevsky
TI  - Casimir effect for Chern–Simons layers in the vacuum
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2017
SP  - 366
EP  - 372
VL  - 190
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2017_190_2_a11/
LA  - ru
ID  - TMF_2017_190_2_a11
ER  - 
%0 Journal Article
%A V. N. Marachevsky
%T Casimir effect for Chern–Simons layers in the vacuum
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2017
%P 366-372
%V 190
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2017_190_2_a11/
%G ru
%F TMF_2017_190_2_a11
V. N. Marachevsky. Casimir effect for Chern–Simons layers in the vacuum. Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 2, pp. 366-372. http://geodesic.mathdoc.fr/item/TMF_2017_190_2_a11/

[1] H. B. G. Casimir, “On the attraction between two perfectly conducting plates”, Proc. Akad. Wet. Amsterdam, 51 (1948), 793–795 | Zbl

[2] Yu. S. Barash, V. L. Ginzburg, “Elektromagnitnye fluktuatsii v veschestve i molekulyarnye (van-der-vaalsovy) sily mezhdu telami”, UFN, 116:1 (1975), 5–40 ; “Некоторые вопросы теории сил Ван-дер-Ваальса”, 143:3 (1984), 345–389 | DOI | DOI | DOI | DOI

[3] G. Plunien, B. Müller, W. Greiner, “The Casimir effect”, Phys. Rept., 134:1–2 (1986), 87–193 | DOI | MR

[4] K. A. Milton, “Casimir energies and pressures for $\delta$-function potentials”, J. Phys. A: Math. Gen., 37:24 (2004), 6391–6406 | DOI | MR

[5] R. L. Jaffe, “Casimir effect and the quantum vacuum”, Phys. Rev. D, 72:2 (2005), 021301, 5 pp. | DOI

[6] V. N. Marachevsky, “The Casimir effect: medium and geometry”, J. Phys. A: Math. Theor., 45:37 (2012), 374021, 17 pp. | DOI | MR | Zbl

[7] S. Scheel, S. Y. Buhmann, “Macroscopic quantum electrodynamics – concepts and applications”, Acta Phys. Slovaca, 58:5 (2008), 675–809 | DOI

[8] S. Y. Buhmann, Dispersion Forces I: Macroscopic Quantum Electrodynamics and Ground-State Casimir, Casimir–Polder and van der Waals Forces, Springer Tracts in Modern Physics, 247, Springer, Berlin–Heidelberg, 2012 | DOI

[9] D. Fursaev, D. Vassilevich, Operators, Geometry and Quanta: Methods of Spectral Geometry in Quantum Field Theory, Springer, Dordrecht, 2011 | DOI | MR | Zbl

[10] E. M. Santanzhelo, “Vychislenie energii Kazimira s pomoschyu spektralnykh funktsii”, TMF, 131:1 (2002), 98–117 | DOI | DOI | MR | Zbl

[11] M. Bordag, I. Pirozhenko, “Vacuum energy between a sphere and a plane at finite temperature”, Phys. Rev. D, 81:8 (2010), 085023, 12 pp. | DOI

[12] E. M. Lifshits, “Teoriya molekulyarnykh sil prityazheniya mezhdu tverdymi telami”, ZhETF, 29:7 (1955), 94–112

[13] A. Lambrecht, V. N. Marachevsky, “Casimir interaction of dielectric gratings”, Phys. Rev. Lett., 101:16 (2008), 160403, 4 pp. | DOI | MR

[14] A. Lambrecht, V. N. Marachevsky, Internat. J. Modern Phys. A, 24:8–9 (2009), 1789–1795 | DOI | Zbl

[15] V. N. Marachevskii, “Fluktuatsionnyi potentsial vzaimodeistviya neitralnogo atoma s difraktsionnoi reshetkoi”, TMF, 185:1 (2015), 151–161 | DOI | DOI | MR

[16] H. B. G. Casimir, D. Polder, “The influence of retardation on the London–van der Waals forces”, Phys. Rev., 73:4 (1948), 360–372 | DOI | Zbl

[17] S. J. Rahi, T. Emig, N. Graham, R. L. Jaffe, M. Kardar, “Scattering theory approach to electrodynamic Casimir forces”, Phys. Rev. D, 80:8 (2009), 085021, 27 pp. | DOI

[18] H. Bender, C. Stehle, C. Zimmermann, S. Slama, J. Fiedler, S. Scheel, S. Y. Buhmann, V. N. Marachevsky, “Probing atom-surface interactions by diffraction of Bose–Einstein condensates”, Phys. Rev. X, 4:1 (2014), 011029, 10 pp. | DOI

[19] I. V. Fialkovsky, V. N. Marachevsky, D. V. Vassilevich, “Finite-temperature Casimir effect for graphene”, Phys. Rev. B, 84:3 (2011), 035446, 10 pp. | DOI

[20] G. L. Klimchitskaya, U. Mohideen, V. M. Mostepanenko, “Theory of the Casimir interaction from graphene-coated substrates using the polarization tensor and comparison with experiment”, Phys. Rev. B, 89:11 (2014), 115419, 8 pp. | DOI

[21] E. Elizalde, D. V. Vassilevich, “Heat kernel coefficients for Chern–Simons boundary conditions in QED”, Class. Quantum Grav., 16:3 (1999), 813–822 | DOI | MR | Zbl

[22] M. Bordag, D. V. Vassilevich, “Casimir force between Chern–Simons surfaces”, Phys. Lett. A, 268:1–2 (2000), 75–80 | DOI | MR | Zbl

[23] V. N. Markov, Yu. M. Pis'mak, “Casimir effect for thin films in QED”, J. Phys. A: Math. Gen., 39:21 (2006), 6525–6532 | DOI | MR | Zbl

[24] V. N. Marachevsky, Yu. M. Pis'mak, “Casimir–Polder effect for a plane with Chern–Simons interaction”, Phys. Rev. D, 81:6 (2010), 065005, 6 pp. | DOI | MR

[25] D. Yu. Pis'mak, Yu. M. Pis'mak, F. J. Wegner, “Electromagnetic waves in a model with Chern–Simons potential”, Phys. Rev. E, 92:1 (2015), 013204, 7 pp. | DOI | MR

[26] O. Kenneth, I. Klich, “Opposites attract: a theorem about the Casimir force”, Phys. Rev. Lett., 97:16 (2001), 160401, 4 pp. | DOI