Skip to main content
SpringerLink
Log in

Thermodynamic properties of a charged particle in non-uniform magnetic field

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

We solve the Schrödinger equation for a charged particle in the non-uniform magnetic field by using the Nikiforov–Uvarov method. We find the energy spectrum and the wave function, and present an explicit relation for the partition function. We give analytical expressions for the thermodynamic properties such as mean energy and magnetic susceptibility, and analyze the entropy, free energy and specific heat of this system numerically. It is concluded that the specific heat and magnetic susceptibility increase with external magnetic field strength and different values of the non-uniformity parameter, in the low temperature region, while the mentioned quantities are decreased in high temperature regions due to increasing the occupied levels at these regions. The non-uniformity parameter has the same effect with a constant value of the magnetic field on the behavior of thermodynamic properties. On the other hand, the results show that transition from positive to negative magnetic susceptibility depends on the values of non-uniformity parameter in the constant external magnetic field.

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
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications, New York (1965)

    MATH  Google Scholar 

  • Al-Furjan, M.S.H., Habibi, M., Rahimi, A., Chen, G., Safarpour, H., Safarpour, M., Tounsi, A.: Chaotic simulation of the multi-phase reinforced thermo-elastic disk using GDQM. to be published in Eng. Comput. (2020) https://doi.org/10.1007/s00366-020-01144-2

  • Al-Furjan, M.S.H., Safarpour, H., Habibi, M., Safarpour, M., Tounsi, A.: A comprehensive computational approach for nonlinear thermal instability of the electrically FG-GPLRC disk based on GDQ method. to be published in Eng. Comput. (2020). https://doi.org/10.1007/s00366-020-01088-7

  • Ali, M.M., Huang, W.M., Zhang, W.M.: Quantum thermodynamics of single particle systems. Sci. Rep. 10, 13500 (2020)

    Article  ADS  Google Scholar 

  • Alimirzaei, S., Mohammadimehr, M., Tounsi, A.: Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions. Struct. Eng. Mech. 71, 485–502 (2019)

    Google Scholar 

  • Aminfar, H., Mohammadpourfard, M., Kahnamouei, Y.N.: A 3D numerical simulation of mixed convection of a magnetic nanofluid in the presence of non-uniform magnetic field in a vertical tube using two phase mixture model. J. Magn. Mater. 323, 1963–1972 (2011)

    Article  ADS  Google Scholar 

  • Bagchi, B., Quesne, C.: NonHermitian Hamiltonians with real and complex eigenvalues: An sl(2, C) approach. Phys. Lett. A 300, 18–23 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Benedetto, J.J., Zimmermann, G.: Sampling multipliers and the Poisson summation formula. J. Fourier Anal. Appl. 3, 505–523 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • Bliokh, Y.P., Freilikher, V., Nori, F.: Tunable electronic transport and unidirectional quantum wires in graphene subjected to electric and magnetic fields. Phys. Rev. B 81, 075410 (2010)

    Article  ADS  Google Scholar 

  • Bogachek, E.N., Landman, U.: Edge states, Aharonov-Bohm oscillations, and thermodynamic and spectral properties in a two-dimensional electron gas with an antidot. Phys. Rev. B 52(19), 14067 (1995)

    Article  ADS  Google Scholar 

  • Boyacioglu, B., Chatterjee, A.: Heat capacity and entropy of a GaAs quantum dot with Gaussian confinement. J. Appl. Phys. 112, 083514 (2012)

    Article  ADS  Google Scholar 

  • Contreras-Astorga, A., Negro, J., Tristao, S.: Confinement of an electron in a non-homogeneous magnetic field: integrable vs superintegrable quantum systems. Phys. Lett. A 380, 48–55 (2016)

    Article  ADS  MATH  Google Scholar 

  • Dubrovskii, V.G., Sibirev, N.V.: Growth thermodynamics of nanowires and its application to polytypism of zinc blende III-V nanowires. Phy. Rev. B 77, 035414 (2008)

    Article  ADS  Google Scholar 

  • Eshghi, M., Mehraban, H.: Study of a 2D charged particle confined by a magnetic and AB flux fields under the radial scalar power potential. Eur. Phys. J. Plus 132, 121–133 (2017)

    Article  Google Scholar 

  • Faridfathi, G., Sever, R., Aktas, M.: Supersymmetric Solutions of PT-/non-PT-symmetric and Non-Hermitian Central Potentials via Hamiltonian Hierarchy Method. J. Math. Chem. 38, 533–540 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Ghosh, T.K.: Exact solutions for a Dirac electron in an exponentially decaying magnetic field. J. Phys. Condens. Matter 21, 045505 (2009)

    Article  ADS  Google Scholar 

  • Goharkhah, M., Ashjaee, M.: Effect of an alternating nonuniform magnetic field on ferrofluid flow and heat transfer in a channel. J. Magn. Mater 362, 80–89 (2014)

    Article  ADS  Google Scholar 

  • Hassanabadi, H., Zarrinkamar, S., Rajabi, A.A.: Exact solutions of D-dimensional Schrdinger equation for an energy-dependent potential by NU method. Commun. Theor. Phys. 55, 541–544 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Hosseini, M., Hassanabadi, H., Hassanabadi, S.: Solutions of the Dirac-Weyl equation in graphene under magnetic fields in the Cartesian coordinate system. Eur. Phys. J. Plus 134, 6–11 (2019)

    Article  Google Scholar 

  • Jia, C.S., Zhang, L.H., Wang, C.W.: Thermodynamic properties for the lithium dimer. Chem. Phys. Lett. 667, 211–215 (2017)

    Article  ADS  Google Scholar 

  • Jia, C.S., Wang, C.W., Zhang, L.H., Peng, X.L., Zeng, R., You, X.T.: Partition function of improved Tietz oscillators. Chem. Phys. Lett. 676, 150–153 (2017)

    Article  ADS  Google Scholar 

  • Jia, C.S., Wang, C.W., Zhang, L.H., Peng, X.L., Tang, H.M., Liu, J.Y., Xiong, Y., Zeng, R.: Predictions of entropy for diatomic molecules and gaseous substances. Chem. Phys. Lett. 692, 57–60 (2018)

    Article  ADS  Google Scholar 

  • Jia, C.S., Zhang, L.H., Peng, X.L., Luo, J.X., Zhao, Y.L., Liu, J.Y., Guo, J.J., Tang, L.D.: Prediction of entropy and Gibbs free energy for nitrogen. Chem. Eng. Sci. 202, 70–74 (2019)

    Article  Google Scholar 

  • Jia, C.S., Li, J., Liu, Y.S., Peng, X.L., Jia, X., Zhang, L.H., Jiang, R., Li, X.P., Liu, J.Y., Zhao, Y.L.: Predictions of thermodynamic properties for hydrogen sulfide. J. Mol. Liq. 315, 113751 (2020)

    Article  Google Scholar 

  • Karami, B., Janghorban, M., Tounsi, A.: On pre-stressed functionally graded anisotropic nanoshell in magnetic field. J. Braz. Soc. Mech. Sci. Eng 41, 495–511 (2019)

    Article  Google Scholar 

  • Khorasani, M., Eyvazian, A., Karbon, M., Tounsi, A., Lampani, L., Sebaey, T.A.: Smart. Struct. Syst. 26, 331–343 (2020)

    Google Scholar 

  • Khordad, R.: Effect of temperature on magnetic susceptibility and thermodynamic properties of an asymmetric quantum dot in tilted magnetic field. Mod. Phys. Lett. B 29, 1550127 (2015)

    Article  ADS  Google Scholar 

  • Khordad, R., Ghanbari, A.: Theoretical prediction of thermodynamic functions of TiC: morse ring-shaped potential. J. Low Temp. Phys. 199, 1198–1210 (2020)

    Article  ADS  Google Scholar 

  • Khordad, R., Rastegar Sedehi, H.R.: Thermodynamic properties of a double ring-shaped quantum dot at low and high temperatures. J. Low Temp. Phys. 190, 200–212 (2018)

    Article  ADS  Google Scholar 

  • Khordad, R., Rastegar Sedehi, H.R.: Low temperature behavior of thermodynamic properties of 1D quantum wire under the Rashba spin-orbit interaction and magnetic field. Solid State Commun. 269, 118–124 (2018)

    Article  ADS  Google Scholar 

  • Lee, S.J., Jeon, H.C., Kang, T.W., Souma, S.: Transitions of density of states and heat capacity in spherical quantum structure formed by a thin barrier. Physica E 40, 2198–2200 (2008)

    Article  ADS  Google Scholar 

  • Loukopoulos, V.C., Tzirtzilakis, E.E.: Biomagnetic channel flow in spatially varying magnetic field. Int. J. Eng. Sci. 42, 571–590 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Marikhin, V.G.: Two new integrable cases of two-dimensional quantum mechanics with a magnetic field. JETP Lett. 103, 489–493 (2016)

    Article  ADS  Google Scholar 

  • Marikhina, A.V., Marikhin, V.G.: Calculation of the discrete spectrum of some two-dimensional Schrdinger equations with a magnetic field. Theor. Math. Phys. 197(3), 1797–1805 (2018)

    Article  MATH  Google Scholar 

  • Matouk, H., Bousahla, A.A., Heireche, H., Bourada, F., Bedia, F.A., Tounsi, Mahmoud, S.R., A., Tounsi, A., Benrahou, K.H.: Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory. Advances in Nano Research, 8, 293–305 (2020)

  • Midya, B., Fernandez, D.J.: Dirac electron in graphene under supersymmetry generated magnetic fields. J. Phys. A 47, 28–38 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Myoung, N., Ihm, G.: Tunneling of Dirac fermions through magnetic barriers in graphene. Physica E 42, 70–72 (2009)

    Article  ADS  Google Scholar 

  • Negrete, O.A., Pena, F.J., Vargas, P.: Magnetocaloric effect in an antidot: the effect of the Aharonov-Bohm flux and antidot radius. Entropy 20, 888–902 (2018)

    Article  ADS  Google Scholar 

  • Nguyen, N.T.T., Peeters, F.M.: Magnetic field dependence of the many-electron states in a magnetic quantum dot: the ferromagnetic-antiferromagnetic transition. Phys. Rev. B 78, 045321 (2008)

    Article  ADS  Google Scholar 

  • Nikiforov, A.F., Uvarov, V.B.: Special Functions of Mathematical Physics. Birkhauser, Basel (1988)

    Book  MATH  Google Scholar 

  • Olendski, O.: Renyi and Tsallis entropies of the aharonovbohm ring in uniform magnetic fields. Entropy 21(11), 1060–1082 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  • Peng, X.L., Jiang, R., Jia, C.S., Zhang, L.H., Zhao, Y.L.: Gibbs free energy of gaseous phosphorus dimer. Chem. Eng. Sci. 190, 122–125 (2018)

    Article  Google Scholar 

  • Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., Benrahou, K.M., Tounsi, A.: Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations. Comput. Concrete 25, 311–325 (2020)

    Google Scholar 

  • Sargolzaeipor, S., Hassanabadi, H., Chung, W.S.: q-deformed superstatistics of the Schrdinger equation in commutative and noncommutative spaces with magnetic field. Eur. Phys. J. Plus 133, 5–11 (2018)

    Article  Google Scholar 

  • Schmidt, V., Wittemann, J.V., Gsele, U.: Growth, thermodynamics, and electrical properties of silicon nanowires. Chem. Rev. 110, 361–388 (2010)

    Article  Google Scholar 

  • Setare, M.R., Karimi, E.: An algebraic approach for a charged particle in a certain magnetic field. Phys. Scr. 75, 250–253 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Sever, R., Tezcan, C.: 1/N expansion for the exponential-cosine-screened Coulomb potential. Phy. Rev. A 35, 2725–2728 (1987)

    Article  ADS  Google Scholar 

  • She, D., Feng, S.Q., Zhong, Y., Yin, Z.B.: Chiral magnetic currents with QGP medium response in heavy-ion collisions at RHIC and LHC energies. Eur. Phys. J. A 54, 48–57 (2018)

    Article  ADS  Google Scholar 

  • Singh, R.K.: On the classical dynamics of charged particle in special class of spatially non-uniform magnetic field. Indian J. Phys. 93, 503–509 (2019)

    Article  ADS  Google Scholar 

  • Song, X.Q., Wang, C.W., Jia, C.S.: Thermodynamic properties for the sodium dimer. Chem. Phys. Lett. 673, 50–55 (2017)

    Article  ADS  Google Scholar 

  • Strekalov, M.L.: An accurate closed-form expression for the partition function of Morse oscillators. Chem. Phys. Lett. 439, 209–212 (2007)

    Article  ADS  Google Scholar 

  • Tan, W.C., Inkson, J.C.: Magnetization, persistent currents, and their relation in quantum rings and dots. Phys. Rev. B 60, 5626 (1999)

    Article  ADS  Google Scholar 

  • Tezcan, C., Sever, R.: A General Approach for the Exact Solution of the Schrodinger Equation. Int. J. Theor. Phys. 48, 337–350 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Tzirtzilakis, E.E., Loukopoulos, V.C.: Biofluid flow in a channel under the action of a uniform localized magnetic field. Comput. Mech. 36(5), 360–374 (2005)

    Article  MATH  Google Scholar 

  • Wang, J., Jia, C.S., Li, C.J., Peng, X.L., Zhang, L.H., Liu, J.Y.: Thermodynamic properties for carbon dioxide. ACS Omega 4, 19193–19198 (2019)

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank the kind referee for positive suggestions which have improved deeply the present paper.

Author information

Authors and Affiliations

  1. Department of Physics, Jahrom University, 74137-66171, Jahrom, Iran

    H. R. Rastegar Sedehi

  2. Division of Physics Education, Hacettepe University, 06800, Ankara, Turkey

    Altuğ Arda

  3. Department of Physics, Middle East Technical University, 06800, Ankara, Turkey

    Ramazan Sever

Authors
  1. H. R. Rastegar Sedehi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Altuğ Arda
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ramazan Sever
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. R. Rastegar Sedehi.

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

Rastegar Sedehi, H.R., Arda, A. & Sever, R. Thermodynamic properties of a charged particle in non-uniform magnetic field. Opt Quant Electron 53, 142 (2021). https://doi.org/10.1007/s11082-021-02783-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-021-02783-5

Keywords

Search

Navigation