A comment on the analogous confinement of a neutral particle to a quantum dot via noninertial effects

• Authors: Knut Bakke
• Languages of publication: EN

Abstracts

EN

In this contribution, we discuss the nonrelativistic limit of the Dirac equation for a neutral particle with a permanent electric dipole moment interacting with external fields in a noninertial frame. We show a case where the geometry of the manifold can play the role of a hard-wall confining potential due to noninertial effects, and can yield bound states analogous to a confinement of the spin-half neutral particle interacting with external fields to a quantum dot described by a hard-wall confining potential [33].

Keywords

EN

noninertial effects; permanent electric dipole moment; Fermi-Walker reference frame; quantum dot; bound states

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2012
• Volume: 10
• Issue: 5
• Pages: 1089-1094

Dates

published

1 - 10 - 2012

online

21 - 11 - 2012

Contributors

author

Knut Bakke

• Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970, João Pessoa, PB, Brazil

References

• [1] M.G. Sagnac, C. R. Acad. Sci. (Paris) 157, 708 (1913)
• [2] M.G. Sagnac, C. R. Acad. Sci. (Paris) 157, 1410 (1913)
• [3] B. Mashhoon, Phys. Rev. Lett. 61, 2639 (1988) http://dx.doi.org/10.1103/PhysRevLett.61.2639[Crossref]
• [4] J.J. Sakurai, Phys. Rev. D 21, 2993 (1980) http://dx.doi.org/10.1103/PhysRevD.21.2993[Crossref]
• [5] J. Anandan, Phys. Rev. D 15, 1448 (1977) http://dx.doi.org/10.1103/PhysRevD.15.1448[Crossref]
• [6] J. Anandan, Phys. Rev. D 24, 338 (1981) http://dx.doi.org/10.1103/PhysRevD.24.338[Crossref]
• [7] B.R. Iyer, Phys. Rev. D 26, 1900 (1982) http://dx.doi.org/10.1103/PhysRevD.26.1900[Crossref]
• [8] E.J. Post, Rev. Mod. Phys. 39, 475 (1967) http://dx.doi.org/10.1103/RevModPhys.39.475[Crossref]
• [9] S.-M. Cui, H.-H Xu, Phys. Rev. A 44, 3343 (1991) http://dx.doi.org/10.1103/PhysRevA.44.3343[Crossref]
• [10] S.-M. Cui, Phys. Rev. A 45, 5255 (1992) http://dx.doi.org/10.1103/PhysRevA.45.5255[Crossref]
• [11] L.A. Page, Phys. Rev. Lett. 35, 543 (1975) http://dx.doi.org/10.1103/PhysRevLett.35.543[Crossref]
• [12] S.A. Werner, J.-L. Staudenmann, R. Colella, Phys. Rev. Lett. 42, 1103 (1979) http://dx.doi.org/10.1103/PhysRevLett.42.1103[Crossref]
• [13] F.W. Hehl, W.-T. Ni, Phys. Rev. D 42, 2045 (1990) http://dx.doi.org/10.1103/PhysRevD.42.2045[Crossref]
• [14] I. Damião Soares, J. Tiomno, Phys. Rev. D 54, 2808 (1996) http://dx.doi.org/10.1103/PhysRevD.54.2808[Crossref]
• [15] J. Anandan, J. Suzuki, In: Relativity in Rotating Frames, Relativistic Physics in Rotating Reference Frame, Edited by G. Rizzi, M. L. Ruggiero (Kluwer Academic Publishers, Dordrecht, 2004), 361 (Preprint arXiv:quant-ph/0305081)
• [16] K. Bakke, C. Furtado, Phys. Rev. D 80, 024033 (2009) http://dx.doi.org/10.1103/PhysRevD.80.024033[Crossref]
• [17] K. Bakke, C. Furtado, Eur. Phys. J. C 69, 531 (2010) http://dx.doi.org/10.1140/epjc/s10052-010-1431-2[Crossref]
• [18] K. Bakke, A.M. de M. Carvalho, C. Furtado, Eur. Phys. J. C 63, 149 (2009) http://dx.doi.org/10.1140/epjc/s10052-009-1076-1[Crossref]
• [19] K. Bakke, A.M. de M. Carvalho, C. Furtado, Int. J. Quantum Inf. 8, 1277 (2010) http://dx.doi.org/10.1142/S0219749910006952[Crossref]
• [20] L.D. Landau, Z. Phys. 64, 629 (1930) http://dx.doi.org/10.1007/BF01397213[Crossref]
• [21] K. Bakke, C. Furtado, Phys. Rev. D 82, 084025 (2010) http://dx.doi.org/10.1103/PhysRevD.82.084025[Crossref]
• [22] M. Ericsson, E. Sjöqvist, Phys. Rev. A 65, 013607 (2001) http://dx.doi.org/10.1103/PhysRevA.65.013607[Crossref]
• [23] Y. Aharonov, A. Casher, Phys. Rev. Lett. 53, 319 (1984) http://dx.doi.org/10.1103/PhysRevLett.53.319[Crossref]
• [24] K. Bakke, Int. J. Mod. Phys. A 26, 4239 (2011) http://dx.doi.org/10.1142/S0217751X11054437[Crossref]
• [25] K. Bakke, Phys. Rev. A 81, 052117 (2010) http://dx.doi.org/10.1103/PhysRevA.81.052117[Crossref]
• [26] K. Bakke, Ann. Phys. (Berlin) 523, 762 (2011) http://dx.doi.org/10.1002/andp.201100018[Crossref]
• [27] L.R. Ribeiro, C. Furtado, J. R. Nascimento, Phys. Lett. A 348, 135 (2006) http://dx.doi.org/10.1016/j.physleta.2005.08.046[Crossref]
• [28] X.-G. He, B.H.J. McKellar, Phys. Rev. A 47, 3424 (1983) http://dx.doi.org/10.1103/PhysRevA.47.3424[Crossref]
• [29] M. Wilkens, Phys. Rev. Lett. 72, 5 (1994) http://dx.doi.org/10.1103/PhysRevLett.72.5[Crossref]
• [30] K. Bakke, Int. J. Theor. Phys. 51, 759 (2011) http://dx.doi.org/10.1007/s10773-011-0955-z[Crossref]
• [31] K. Bakke, Phys. Lett. A 374, 3143 (2010) http://dx.doi.org/10.1016/j.physleta.2010.05.049[Crossref]
• [32] K. Bakke, Phys. Lett. A 374, 4642 (2010) http://dx.doi.org/10.1016/j.physleta.2010.09.046[Crossref]
• [33] E. Tsitsishvili, G.S. Lozano, A.O. Gogolin, Phys. Rev. B 70, 115316 (2004) http://dx.doi.org/10.1103/PhysRevB.70.115316[Crossref]
• [34] N. Aquino, E. Castaño, E. Ley-Koo, Chinese J. Phys. 41, 276 (2003)
• [35] L. Solimany, B. Kramer, Solid State Commun. 96, 471 (1995) http://dx.doi.org/10.1016/0038-1098(95)00439-4[Crossref]
• [36] R. Rosas, R. Riera, J.L. Marín, J. Phys.: Condens. Matter 12, 6851 (2000) http://dx.doi.org/10.1088/0953-8984/12/30/314[Crossref]
• [37] K. Bakke, C. Furtado, Mod. Phys. Lett. A 26, 1331 (2011) http://dx.doi.org/10.1142/S0217732311035766[Crossref]
• [38] S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (IE-Wiley, New York, 1972)
• [39] C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (W. H. Freeman, San Francisco, 1973)
• [40] L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields, Course of Theoretical Physics, Vol. 2, 4th ed. (Elsevier, Oxford, 1980)
• [41] N.D. Birrell, P.C.W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, UK, 1982) http://dx.doi.org/10.1017/CBO9780511622632[Crossref]
• [42] M. Nakahara, Geometry, Topology and Physics (Institute of Physics Publishing, Bristol, 1998)
• [43] T.C. Mo, J. Math. Phys. 11, 2589 (1969) http://dx.doi.org/10.1063/1.1665428[Crossref]
• [44] J.L. Anderson, J.W. Ryon, Phys, Rev. 181, 1765 (1969) http://dx.doi.org/10.1103/PhysRev.181.1765[Crossref]
• [45] J. van Bladel, Proceedings of the IEEE 64, 301 (1976) http://dx.doi.org/10.1109/PROC.1976.10111[Crossref]
• [46] J. Anandan, Phys. Lett. A 138, 347 (1989) http://dx.doi.org/10.1016/0375-9601(89)90828-1[Crossref]
• [47] J. Anandan, Phys. Rev. Lett. 85, 1354 (2000) http://dx.doi.org/10.1103/PhysRevLett.85.1354[Crossref]
• [48] A. Ya. Silenko, Russian Phys. J. 48, 788 (2005) http://dx.doi.org/10.1007/s11182-005-0203-1[Crossref]
• [49] J.M. Bjorken, S.D. Drell, Relativistic Quantum Mechanics (McGraw-Hill Book Company, New York, 1964)
• [50] P. Schlüter, K.-H. Wietschorke, W. Greiner, J. Phys. A 16, 1999 (1983) http://dx.doi.org/10.1088/0305-4470/16/9/024[Crossref]
• [51] M. Abramowitz, I.A. Stegum, Handbook of mathematical functions (Dover Publications Inc., New York, 1965)
• [52] L.D. Landau, E.M. Lifshitz, Quantum Mechanics, the nonrelativistic theory, 3rd Ed. (Pergamon, Oxford, 1977)
• [53] W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11, 1635 (1996) http://dx.doi.org/10.1088/0268-1242/11/11/001[Crossref]
• [54] W.-C. Tan, J.C. Inkson, Phys. Rev. B 53, 6947 (1996) http://dx.doi.org/10.1103/PhysRevB.53.6947[Crossref]
• [55] W.-C. Tan, J.C. Inkson, Phys. Rev. B 60, 5626 (1999) http://dx.doi.org/10.1103/PhysRevB.60.5626[Crossref]
• [56] M.O. Katanaev, I.V. Volovich, Ann. Phys. (NY) 216, 1 (1992) http://dx.doi.org/10.1016/0003-4916(52)90040-7[Crossref]
• [57] F. Moraes, Braz. J. Phys 30, 304 (2000) http://dx.doi.org/10.1590/S0103-97332000000200011[Crossref]
• [58] L. Dias, F. Moraes, Braz. J. Phys. 35, 636 (2005) http://dx.doi.org/10.1590/S0103-97332005000400009[Crossref]
• [59] N. Byers, N.C. Yang, Phys. Rev. Lett. 7, 46 (1961) http://dx.doi.org/10.1103/PhysRevLett.7.46[Crossref]
• [60] W.-C. Tan, J.C. Inkson, Phys. Rev. B 60, 5626 (1999) http://dx.doi.org/10.1103/PhysRevB.60.5626[Crossref]
• [61] D. Loss, P. Goldbart, A.V. Balatsky, Phys. Rev. Lett. 65, 1655 (1990) http://dx.doi.org/10.1103/PhysRevLett.65.1655[Crossref]
• [62] D. Loss, P. M. Goldbart, Phys. Rev. B 45, 13544 (1992) http://dx.doi.org/10.1103/PhysRevB.45.13544[Crossref]
• [63] X.-C. Gao, T.-Z. Qian, Phys. Rev. B 47, 7128 (1993) http://dx.doi.org/10.1103/PhysRevB.47.7128[Crossref]
• [64] T.-Z. Qian, Z.-B. Su, Phys. Rev. Lett. 72, 2311 (1994) http://dx.doi.org/10.1103/PhysRevLett.72.2311[Crossref]
• [65] A.V. Balatsky, B.L. Altshuler, Phys. Rev. Lett. 70, 1678 (1993) http://dx.doi.org/10.1103/PhysRevLett.70.1678[Crossref]
• [66] S. Oh, C.-M. Ryu, Phys. Rev. B 51, 13441 (1995) http://dx.doi.org/10.1103/PhysRevB.51.13441[Crossref]
• [67] H. Mathur, A.D. Stone, Phys. Rev. B 44, 10957 (1991) http://dx.doi.org/10.1103/PhysRevB.44.10957[Crossref]
• [68] H. Mathur, A.D. Stone, Phys. Rev. Lett. 68, 2964 (1992) http://dx.doi.org/10.1103/PhysRevLett.68.2964[Crossref]

Identifiers

DOI

10.2478/s11534-012-0091-2