Abstract
We study the effects of the spiral dislocation topology on the confinement of a point charge (electron or hole) to a cylindrical wire in a rotating reference frame. In addition, we consider the presence of a magnetic flux in the center of the cylindrical wire. We thus search for bound state solutions to the Schrödinger equation. We go further by discussing the influence of the spiral dislocation topology, magnetic flux and rotation on the persistent currents and the quantum revivals.
Similar content being viewed by others
References
Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959)
U.F. Keyser, S. Borck, R.J. Haug, M. Bichler, G. Abstreiter, W. Wegscheider, Semicond. Sci. Technol. 17, L22 (2002)
Y. Avishai, Y. Hatsugai, M. Kohmoto, Phys. Rev. B 47, 9501 (1993)
W.-C. Tan, J.C. Inkson, Phys. Rev. B 60, 5626 (1999)
B.I. Halperin, Phys. Rev. B 25, 2185 (1982)
D. Loss, P.M. Goldbart, Phys. Rev. B. 45, 13544 (1992)
D. Loss, P.M. Goldbart, A.V. Balatsky, Phys. Rev. Lett. 65, 1655 (1990)
L.G. Wang, Phys. B Condens. Matter 404, 143 (2009)
N.T. Bagraev et al., Phys. B Condens. Matter 378–380, 894 (2006)
Y.-C. Zhou, Y.-Z. Fang, G.-P. He, Phys. B Condens. Matter 226, 413 (1996)
W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11, 1635 (1996)
W.-C. Tan, J.C. Inkson, Phys. Rev. B 53, 6947 (1996)
S.E. Pourmand, G. Rezaei, Phys. B Condens. Matter 543, 27 (2018)
D. Nasri, Phys. B Condens. Matter 540, 51 (2018)
L.F. García, R. Robayo, I.D. Mikhailov, Phys. B Condens. Matter 390, 340 (2017)
S. Klama, Phys. B Condens. Matter 191, 281 (1993)
S. Klama, Phys. B Condens. Matter 193, 295 (1994)
B.K. Ridley, Hybrid Phonons in Nanostructures (Oxford University Press, Oxford, 2017)
M. Razeghi, Fundamentals of Solid State Engineering (Kluwer Academic Publishers, New York, 2002)
W. Tan, J.C. Inkson, G.P. Srivastava, Semicond. Sci. Technol. 9, 1305 (1994)
C. Filgueiras, E.O. Silva, Phys. Lett. A 379, 2110 (2015)
T. Ando, H. Aoki, Phys. B Condens. Matter 184, 365 (1993)
D.V. Bulaev, V.A. Geyler, V.A. Margulis, Phys. Rev. B 69, 195313 (2004)
E. Tsitsishvili, G.S. Lozano, A.O. Gogolin, Phys. Rev. B 70, 115316 (2004)
H.-S. Sim et al., Phys. Rev. Lett. 80, 1501 (1998)
E.V. Anda, C. Busser, G. Chiappe, M.A. Davidovich, Phys. B Condens. Matter 320, 358 (2002)
S. Oh, C.-M. Ryu, Phys. Rev. B 51, 13441 (1995)
H. Mathur, A.D. Stone, Phys. Rev. B 44, 10957 (1991)
H. Mathur, A.D. Stone, Phys. Rev. Lett. 68, 2964 (1992)
A.V. Balatsky, B.L. Altshuler, Phys. Rev. Lett. 70, 1678 (1993)
A.L. Silva Netto, B. Farias, J. Carvalho, C. Furtado, Int. J. Geom. Methods Mod. Phys. 16, 1950167 (2019)
R. Merlin, Phys. Lett. A 181, 421 (1993)
G. Vignale, B. Mashhoon, Phys. Lett. A 197, 444 (1995)
L. Dantas, C. Furtado, Phys. Lett. A 377, 2926 (2013)
M. Peshkin, A. Tonomura, The Aharonov–Bohm Effect, Lecture Notes in Physics, vol. 340. (Springer, Berlin, 1989)
D.J. Griffiths, Introduction to Quantum Mechanics, 2nd edn. (Prentice Hall, 2004)
C. Furtado, V.B. Bezerra, F. Moraes, Phys. Lett. A 289, 160 (2001)
C. Furtado, C.A. de Lima Ribeiro, S. Azevedo, Phys. Lett. A 296, 171 (2002)
V.B. Bezerra, I.B. dos Santos, Eur. J. Phys. 13, 122 (1992)
A.L. Silva Netto, C. Chesman, C. Furtado, Phys. Lett. A 372, 3894 (2008)
L. Dantas, C. Furtado, A.L. Silva Netto, Phys. Lett. A 379, 11 (2015)
W.C.F. da Silva, K. Bakke, Ann. Phys. 421, 168277 (2020)
W.C.F. da Silva, K. Bakke, Eur. Phys. J. Plus 134, 131 (2019)
C. Furtado et al., EPL 79, 57001 (2007)
J. Amaro Neto et al., Eur. Phys. J. Plus 133, 185 (2018)
M.J. Bueno et al., Eur. Phys. J. Plus 129, 201 (2014)
R.R.S. Oliveira, Gen. Relat. Grav. 51, 120 (2019)
R.R.S. Oliveira et al., Eur. Phys. J. Plus 134, 495 (2019)
M.O. Katanaev, I.V. Volovich, Ann. Phys. 216, 1 (1992)
N. Byers, C.N. Yang, Phys. Rev. Lett. 7, 46 (1961)
R. Bluhm et al., Phys. Lett. A 222, 220 (1996)
R.W. Robinett, Phys. Rept. 392, 1 (2004)
R. Bluhm et al., Am. J. Phys. 64, 944 (1996)
R.W. Robinett, Am. J. Phys. 68, 410 (2000)
K.C. Valanis, V.P. Panoskaltsis, Acta Mech. 175, 77 (2005). https://doi.org/10.1007/s00707-004-0196-9
K. Bakke, C. Furtado, Phys. Rev. A 87, 012130 (2013). https://doi.org/10.1103/PhysRevA.87.012130
A.V.D.M. Maia, K. Bakke, Int. J. Mod. Phys. A 34, 1950153 (2019)
A.V.D.M. Maia, K. Bakke, Ann. Phys. 419, 168229 (2020)
A.V.D.M. Maia, K. Bakke, Commun. Theor. Phys. 73, 025103 (2021)
G.A. de Marques et al., J. Phys. A Math. Gen. 34, 5945 (2001)
W.C.F. da Silva, K. Bakke, Class. Quantum Grav. 36, 235002 (2019)
L.D. Landau, E.M. Lifshitz, Mechanics, 3rd edn. (Pergamon Press, Oxford, 1980)
L.D. Landau, E.M. Lifshitz, Statistical Physics—Part 1, 3rd edn. (Pergamon Press, New York, 1980)
J. Anandan, J. Suzuki, in Relativity in Rotating Frames, Relativistic Physics in Rotating Reference Frame, Edited by G. Rizzi and M. L. Ruggiero (Kluwer Academic Publishers, Dordrecht, 2004) pp. 361–369. arXiv:quant-ph/0305081
C.-H. Tsai, D. Neilson, Phys. Rev. A 37, 619 (1988)
V.B. Bezerra, J. Math. Phys. 38, 2553 (1997)
L.A. Page, Phys. Rev. Lett. 35, 543 (1975)
S.A. Werner, J.-L. Staudenmann, R. Colella, Phys. Rev. Lett. 42, 1103 (1979)
F.W. Hehl, W.-T. Ni, Phys. Rev. D 42, 2045 (1990)
D.F. Styer, Am. J. Phys. 69, 56 (2001)
R.W. Robinett, J. Math. Phys. 41, 1801 (2001)
D.L. Aronstein, C.R. Stroud Jr., Phys. Rev. A 55, 4526 (1997)
M.A. Doncheskia, R.W. Robinett, Ann. Phys. 308, 578 (2003)
A.G.M. Schmidt et al., Phys. Lett. A 372, 2774 (2008)
R. Bluhm, V.A. Kostelecký, Phys. Rev. A 50, R4445 (1994)
R. Bluhm, V.A. Kostelecký, Phys. Rev. A 51, 4767 (1995)
R. Bluhm, V.A. Kostelecký, Phys. Lett. A 200, 308 (1995)
D. Sinha, B. Berche, Eur. Phys. J. B 89, 57 (2016)
T. García et al., J. Phys. Condens. Matter 25, 235301 (2013)
M.A. Doncheski et al., Am. J. Phys. 71, 541 (2003)
R. Bluhm et al., Phys. Rev. A 55, 819 (1997)
R.W. Robinett, S. Heppelmann, Phys. Rev. A 65, 062103 (2002)
Acknowledgements
The authors would like to thank the Brazilian agencies CNPq and CAPES for financial support.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
da Silva, W.C.F., Bakke, K. On the effects of rotation and spiral dislocation topology on the persistent currents and quantum revivals in a cylindrical wire. Eur. Phys. J. Plus 136, 920 (2021). https://doi.org/10.1140/epjp/s13360-021-01922-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/s13360-021-01922-x