Skip to main content
SpringerLink
Log in

1D Quantum ring: A Toy Model Describing Noninertial Effects on Electronic States, Persistent Current and Magnetization

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

Inertial effects can affect several properties of physical systems. In particular, in the context of quantum mechanics, such effects has been studied in diverse contexts. In this paper, starting from the Schrödinger equation for a rotating frame, we propose a toy model to describe the influence of noninertial effects on physical properties of a one-dimensional ring in the presence of a uniform magnetic field. We first study how the electronic states are affected by rotation. Then, we investigate how the persistent current and the magnetization in the ring are influenced by temperature and rotating effects.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. See, for example, Eq. (16) of Ref. [30]

References

  1. M.J. Allen, V.C. Tung, R.B. Kaner, Chem. Rev. 110(1), 132 (2009). https://doi.org/10.1021/cr900070d

    Article  Google Scholar 

  2. Q. Tang, Z. Zhou, Prog. Mater Sci. 58(8), 1244 (2013). https://doi.org/10.1016/j.pmatsci.2013.04.003

    Article  Google Scholar 

  3. S. Viefers, P. Koskinen, P.S. Deo, M. Manninen, Physica E 21(1), 1 (2004). https://doi.org/10.1016/j.physe.2003.08.076

    Article  ADS  Google Scholar 

  4. A. Fuhrer, S. Lüscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, M. Bichler, Nature 413(6858), 822 (2001). https://doi.org/10.1038/35101552

    Article  ADS  Google Scholar 

  5. J.I. Climente, J. Planelles, J.L. Movilla, Phys. Rev. B 70, 081301 (2004). https://doi.org/10.1103/PhysRevB.70.081301

    Article  ADS  Google Scholar 

  6. H.F. Cheung, Y. Gefen, E.K. Riedel, W.H. Shih, Phys. Rev. B 37, 6050 (1988). https://doi.org/10.1103/PhysRevB.37.6050

    Article  ADS  Google Scholar 

  7. W.C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11(11), 1635 (1996). https://doi.org/10.1088/0268-1242/11/11/001

    Article  ADS  Google Scholar 

  8. W.C. Tan, J.C. Inkson, Phys. Rev. B 60, 5626 (1999). https://doi.org/10.1103/PhysRevB.60.5626

    Article  ADS  Google Scholar 

  9. D.V. Bulaev, V.A. Geyler, V.A. Margulis, Phys. Rev. B 69, 195313 (2004). https://doi.org/10.1103/PhysRevB.69.195313

    Article  ADS  Google Scholar 

  10. Y.V. Pershin, C. Piermarocchi, Phys. Rev. B 72, 125348 (2005). https://doi.org/10.1103/PhysRevB.72.125348

    Article  ADS  Google Scholar 

  11. R.C.T. da Costa, Phys. Rev. A 23, 1982 (1981). https://doi.org/10.1103/PhysRevA.23.1982

    Article  ADS  MathSciNet  Google Scholar 

  12. A. Bruno-Alfonso, A. Latgé, Phys. Rev. B 77, 205303 (2008). https://doi.org/10.1103/PhysRevB.77.205303

    Article  ADS  Google Scholar 

  13. S. Zhang, H. Chen, E. Zhang, D. Liu, EPL (Europhysics Letters) 103(5), 58005 (2013). https://doi.org/10.1209/0295-5075/103/58005

    Article  ADS  Google Scholar 

  14. M. Omidi, E. Faizabadi, EPL (Europhysics Letters) 110(1), 17005 (2015). https://doi.org/10.1209/0295-5075/110/17005

    Article  ADS  Google Scholar 

  15. N. Xu, H.Y. Zhang, M. Qiu, J.W. Ding, European Phys. J. B 90(8), 159 (2017). https://doi.org/10.1140/epjb/e2017-80226-1

    Article  ADS  Google Scholar 

  16. O. Olendski, T. Barakat, J. Appl. Phys. 115(8), 083710 (2014). https://doi.org/10.1063/1.4866873

    Article  ADS  Google Scholar 

  17. S. Gumber, M. Gambhir, P.K. Jha, M. Mohan, J. Appl. Phys. 119(7), 073101 (2016). https://doi.org/10.1063/1.4942015

    Article  ADS  Google Scholar 

  18. O. Olendski, Phys. Lett. A 383(11), 1110 (2019). https://doi.org/10.1016/j.physleta.2018.12.040

    Article  ADS  MathSciNet  Google Scholar 

  19. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). https://doi.org/10.1103/PhysRev.115.485

    Article  ADS  MathSciNet  Google Scholar 

  20. S. Olariu, I.I. Popescu, Rev. Mod. Phys. 57, 339 (1985). https://doi.org/10.1103/RevModPhys.57.339

    Article  ADS  Google Scholar 

  21. M. Peshkin, Phys. Rev. A 23, 360 (1981). https://doi.org/10.1103/PhysRevA.23.360

    Article  ADS  Google Scholar 

  22. D.J. Griffiths, Introduction to Quantum Mechanics, 2nd edn. (Addison-Wesley, 2005)

  23. J.F. Weisz, R. Kishore, F.V. Kusmartsev, Phys. Rev. B 49, 8126 (1994). https://doi.org/10.1103/PhysRevB.49.8126

    Article  ADS  Google Scholar 

  24. M. Moskalets, Phys. B 291(3–4), 350 (2000). https://doi.org/10.1016/S0921-4526(99)02288-7

    Article  ADS  Google Scholar 

  25. R. Casana, M. Ferreira, V. Mouchrek-Santos, E.O. Silva, Phys. Lett. B 746, 171 (2015). https://doi.org/10.1016/j.physletb.2015.04.053

    Article  ADS  Google Scholar 

  26. M. Szopa, E. Zipper, In: Journal of Physics: Conference Series, vol. 213 (IOP Publishing), 213, 012006 (2010)

  27. L. Wang, Phys. B 404(1), 143 (2009). https://doi.org/10.1016/j.physb.2008.10.040

    Article  ADS  Google Scholar 

  28. S. Ghosh, A. Saha, European Phys. J. B 87(8), 167 (2014). https://doi.org/10.1140/epjb/e2014-50223-1

    Article  ADS  Google Scholar 

  29. I.I. Cotăescu, D.M. Băltăţeanu, I. Cotăescu Jr., Int. J. Mod. Phys. B 30(1), 1550245 (2016). https://doi.org/10.1142/S0217979215502458

    Article  ADS  Google Scholar 

  30. D. Sticlet, B. Dóra, J. Cayssol, Phys. Rev. B 88, 205401 (2013). https://doi.org/10.1103/PhysRevB.88.205401

    Article  ADS  Google Scholar 

  31. G. De Rosi, G.E. Astrakharchik, S. Stringari, Phys. Rev. A 96, 013613 (2017). https://doi.org/10.1103/PhysRevA.96.013613

    Article  ADS  Google Scholar 

  32. R.R. Oliveira, A.A. Araújo Filho, F.C. Lima, R.V. Maluf, C.A. Almeida, European Phys. J. Plus 134(10), 495 (2019). https://doi.org/10.1140/epjp/i2019-12880-x

    Article  ADS  Google Scholar 

  33. Y. Aharonov, T. Kaufherr, Phys. Rev. D 30, 368 (1984). https://doi.org/10.1103/PhysRevD.30.368

    Article  ADS  MathSciNet  Google Scholar 

  34. J. Anandan, Phys. Rev. D 15, 1448 (1977). https://doi.org/10.1103/PhysRevD.15.1448

    Article  ADS  Google Scholar 

  35. B.R. Holstein, Am. J. Phys. 59(12), 1080 (1991)

    Article  ADS  Google Scholar 

  36. V. Bezerra, J. Math. Phys. 30(12), 2895 (1989). https://doi.org/10.1063/1.528472

    Article  ADS  MathSciNet  Google Scholar 

  37. Y. Aharonov, G. Carmi, Found. Phys. 3(4), 493 (1973). https://doi.org/10.1007/BF00709117

    Article  ADS  Google Scholar 

  38. Y. Aharonov, G. Carmi, Found. Phys. 4(1), 75 (1974). https://doi.org/10.1007/BF00708556

    Article  ADS  Google Scholar 

  39. J.H. Harris, M.D. Semon, Found. Phys. 10(1–2), 151 (1980). https://doi.org/10.1007/BF00709020

    Article  ADS  MathSciNet  Google Scholar 

  40. J.Q. Shen, S. He, F. Zhuang, The European Physical Journal D-Atomic. Mol. Opt. Plasma Phys. 33(1), 35 (2005). https://doi.org/10.1140/epjd/e2005-00027-7

    Article  Google Scholar 

  41. S.J. Barnett, Rev. Mod. Phys. 7, 129 (1935). https://doi.org/10.1103/RevModPhys.7.129

    Article  ADS  Google Scholar 

  42. M. Ono, H. Chudo, K. Harii, S. Okayasu, M. Matsuo, J. Ieda, R. Takahashi, S. Maekawa, E. Saitoh, Phys. Rev. B 92, 174424 (2015). https://doi.org/10.1103/PhysRevB.92.174424

    Article  ADS  Google Scholar 

  43. M. Arabgol, T. Sleator, Phys. Rev. Lett. 122, 177202 (2019). https://doi.org/10.1103/PhysRevLett.122.177202

    Article  ADS  Google Scholar 

  44. U.R. Fischer, N. Schopohl, Europhysics Letters (EPL) 54(4), 502 (2001). https://doi.org/10.1209/epl/i2001-00273-1

    Article  ADS  Google Scholar 

  45. B. Johnson, Am. J. Phys. 68(7), 649 (2000). https://doi.org/10.1119/1.19503

    Article  ADS  Google Scholar 

  46. C. Filgueiras, J. Brandão, F. Moraes, EPL (Europhysics Letters) 110(2), 27003 (2015). https://doi.org/10.1209/0295-5075/110/27003

    Article  ADS  Google Scholar 

  47. P. Král, H.R. Sadeghpour, Phys. Rev. B 65, 161401 (2002). https://doi.org/10.1103/PhysRevB.65.161401

    Article  ADS  Google Scholar 

  48. S. Narendar, S. Gopalakrishnan, Results. Phys. 1(1), 17 (2011). https://doi.org/10.1016/j.rinp.2011.06.002

    Article  ADS  Google Scholar 

  49. J.R. Lima, F. Moraes, European. Phys. J. B 88(3), 63 (2015). https://doi.org/10.1140/epjb/e2015-60022-9

    Article  ADS  Google Scholar 

  50. G.Q. Garcia, E. Cavalcante, AMd.M. Carvalho, C. Furtado, European. Phys. J. Plus 132(4), 183 (2017). https://doi.org/10.1140/epjp/i2017-11457-1

    Article  ADS  Google Scholar 

  51. G. Rizzi, M.L. Ruggiero (eds.), Relativistic Physics in Rotating Reference Frames (Springer, Netherlands, 2004)

    MATH  Google Scholar 

  52. T. Chakraborty, Nanoscopic Quantum Rings: A New Perspective (Springer Berlin Heidelberg, Berlin, Heidelberg, 2003), pp. 79–94. https://doi.org/10.1007/978-3-540-44838-9_6

  53. N. Byers, C.N. Yang, Phys. Rev. Lett. 7, 46 (1961). https://doi.org/10.1103/PhysRevLett.7.46

    Article  ADS  Google Scholar 

  54. L. Landau, E. Lifshitz, Statistical Physics. v. 5 (Elsevier Science, 2013)

Download references

Author information

Authors and Affiliations

  1. Departamento de Física, Universidade Federal do Maranhão, 65085-580, São Luís, Maranhão, Brazil

    Luís Fernando C. Pereira, Márcio M. Cunha & Edilberto O. Silva

Authors
  1. Luís Fernando C. Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Márcio M. Cunha
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Edilberto O. Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Márcio M. Cunha.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pereira, L.F.C., Cunha, M.M. & Silva, E.O. 1D Quantum ring: A Toy Model Describing Noninertial Effects on Electronic States, Persistent Current and Magnetization. Few-Body Syst 63, 58 (2022). https://doi.org/10.1007/s00601-022-01761-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00601-022-01761-1

Search

Navigation