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