Casimir Force Induced on a Plane by an Impenetrable Flux Tube of Finite Radius
DOI:
https://doi.org/10.15407/ujpe58.05.0424Keywords:
vacuum polarization, Casimir effect, magnetic vortexAbstract
A perfectly reflecting (Dirichlet) boundary condition at the edge of an impenetrable magnetic-flux-carrying tube of nonzero transverse size is imposed on the charged massive scalar matter field which is quantized outside the tube on a plane, which is transverse to the tube. We show that the vacuum polarization effects outside the tube give rise to a macroscopic force acting at the increase of the tube radius (if the magnetic flux is held steady).
References
<li> H.B.G. Casimir, Proc. Kon. Ned. Akad. Wetenschap. B 51, 793 (1948);</li>
<li> Physica 19, 846 (1953). <a href="https://doi.org/10.1016/S0031-8914(53)80095-9">https://doi.org/10.1016/S0031-8914(53)80095-9</a></li>
<li> K.A. Milton, The Casimir Effect: Physical Manifestations of Zero-Point Energy (World Scientific, River Edge, 2001).<a href="https://doi.org/10.1142/4505">https://doi.org/10.1142/4505</a></li>
<li> M. Bordag, G.L. Klimchitskaya, U. Mohideen, and V.M. Mostepanenko, Advances in the Casimir Effect (Oxford Univ. Press, Oxford, 2009).<a href="https://doi.org/10.1093/acprof:oso/9780199238743.001.0001">https://doi.org/10.1093/acprof:oso/9780199238743.001.0001</a></li>
<li> S.K. Lamoreax, Phys. Rev. Lett. 78, 5 (1997).<a href="https://doi.org/10.1103/PhysRevLett.78.5">https://doi.org/10.1103/PhysRevLett.78.5</a></li>
<li> G. Bressi, G. Carugno, R. Onofrio, and G. Ruoso, Phys. Rev. Lett. 88, 041804 (2002).<a href="https://doi.org/10.1103/PhysRevLett.88.041804">https://doi.org/10.1103/PhysRevLett.88.041804</a></li>
<li> Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).<a href="https://doi.org/10.1103/PhysRev.115.485">https://doi.org/10.1103/PhysRev.115.485</a></li>
<li> Yu. A. Sitenko and A.Yu. Babansky, Mod. Phys. Lett. A 13, 379 (1998).<a href="https://doi.org/10.1142/S0217732398000437">https://doi.org/10.1142/S0217732398000437</a></li>
<li> L.L. DeRaad, Jr. and K.A. Milton, Ann. Phys. (N.Y.) 136, 229 (1981).<a href="https://doi.org/10.1016/0003-4916(81)90097-X">https://doi.org/10.1016/0003-4916(81)90097-X</a></li>
<li> <li> P. Gosdzinsky and A. Romeo, Phys. Lett. B 441, 265 (1998).<a href="https://doi.org/10.1016/S0370-2693(98)01164-2">https://doi.org/10.1016/S0370-2693(98)01164-2</a></li>
<li> <li> N. Graham, R.L. Jaffe, V. Khemani, M. Quandt, M. Scandurra, and H. Weigel, Phys. Lett. B 572, 196 (2003).<a href="https://doi.org/10.1016/j.physletb.2003.03.003">https://doi.org/10.1016/j.physletb.2003.03.003</a></li>
<li> G. Barton, Phys. Rev. D 73, 065018 (2006).<a href="https://doi.org/10.1103/PhysRevD.73.065018">https://doi.org/10.1103/PhysRevD.73.065018</a></li>
<li> I. Cavero-Pelaez, K.A. Milton, and K. Kirsten, J. Phys. A: Math. Theor. 40, 3607 (2007).<a href="https://doi.org/10.1088/1751-8113/40/13/019">https://doi.org/10.1088/1751-8113/40/13/019</a></li>
<li> M. Schaden, Phys. Rev. A 73, 042102 (2006).<a href="https://doi.org/10.1103/PhysRevA.73.042102">https://doi.org/10.1103/PhysRevA.73.042102</a></li>
<li> R. Penrose, in: Relativity, Groups and Topology, edited by B.S. DeWitt, C. DeWitt (Gordon and Breach, New York, 1964).</li>
<li> N.A. Chernikov and E.A. Tagirov, Ann. Inst. Henri Poincar’e A 9, 109 (1968).</li>
<li> C.G. Callan, S. Coleman, and R. Jackiw, Ann. Phys. (N.Y.) 59, 42 (1970).<a href="https://doi.org/10.1016/0003-4916(70)90394-5">https://doi.org/10.1016/0003-4916(70)90394-5</a></li>
<li> V.M. Gorkavenko, Yu.A. Sitenko, and O.B. Stepanov, Int. J. Mod. Phys. A: 26, 3889 (2011).<a href="https://doi.org/10.1142/S0217751X11054346">https://doi.org/10.1142/S0217751X11054346</a></li>
<li> V.M. Gorkavenko, Yu.A. Sitenko, and O.B. Stepanov, J. Phys. A: Math. Theor. 43, 175401 (2010).<a href="https://doi.org/10.1088/1751-8113/43/17/175401">https://doi.org/10.1088/1751-8113/43/17/175401</a></li>
<li> E.T. Whittaker and G.N. Watson, The Euler-Maclaurin Expansion (Cambridge Univ. Press, Cambridge, 1990).</li>
<li> Yu.A. Sitenko and V.M. Gorkavenko, Phys. Rev. D 67, 085015 (2003).<a href="https://doi.org/10.1103/PhysRevD.67.085015">https://doi.org/10.1103/PhysRevD.67.085015</a></li>
<li> V.M. Gorkavenko and A.V. Viznyuk, Phys. Lett. B 604, 103 (2004).<a href="https://doi.org/10.1016/j.physletb.2004.10.043">https://doi.org/10.1016/j.physletb.2004.10.043</a></li>
</ol>
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