Generalised two-dimensional nonlinear oscillator with a position-dependent effective mass and the thermodynamic properties

Authors

  • S. E. Bokpe Institut de Mathématiques et de Sciences Physiques (IMSP), Université d’Abomey-Calavi (UAC), 01 BP 613 Porto-Novo, République du Bénin https://orcid.org/0009-0006-4939-6941
  • F. A. Dossa Laboratory of Physics and Applications (LPA), Université Nationale des Sciences, Technologies, Ingénierie et Mathématiques (UNSTIM) Abomey, BP: 2282 Goho Abomey, République du Bénin https://orcid.org/0000-0002-2694-4144
  • G. Y. H. Avossevou Institut de Mathématiques et de Sciences Physiques (IMSP), Université d’Abomey-Calavi (UAC), 01 BP 613 Porto-Novo, République du Bénin https://orcid.org/0000-0002-9609-0340

DOI:

https://doi.org/10.5488/cmp.28.33701

Keywords:

nonlinear oscillator, Nikiforov-Uvarov, thermodynamic properties

Abstract

We investigate a two-dimensional nonlinear oscillator with a position-dependent effective mass in the framework of nonrelativistic quantum mechanics. Using the Nikiforov-Uvarov method, we obtain exact analytical expressions for the energy spectrum and wave functions. Based on the canonical partition function, we derive key thermodynamic quantities, including internal energy, specific heat, free energy, and entropy. Our results show that, unlike the one-dimensional case, where the specific heat is unaffected by the nonlinearity parameter k, the two-dimensional system exhibits a strong k−dependence. At high temperatures, the specific heat becomes temperature-independent for fixed values of k, in line with the Dulong–Petit law. However, these behaviors occur only for negative values of k. These findings highlight the impact of effective mass nonlinearity on macroscopic thermodynamic quantities and suggest that tuning the parameter k could serve as an effective strategy for enhancing the performance of quantum devices, including thermal machines and optoelectronic components.

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Published

2025-09-23

How to Cite

[1]
S. E. Bokpe, F. A. Dossa, and G. Y. H. Avossevou, “Generalised two-dimensional nonlinear oscillator with a position-dependent effective mass and the thermodynamic properties”, Condens. Matter Phys., vol. 28, no. 3, p. 33701, Sep. 2025, doi: 10.5488/cmp.28.33701.

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