Position-dependent mass from noncommutativity and its statistical descriptions

Abstract

A set of position-dependent noncommutative algebra in two dimension (2D) that describes the space near the Planck scale had been introduced [J. Phys. A: Math. Theor. 53 (2020) 115303]. This algebra predicted the existence of maximal length of graviton measurable at low energy. From this algebra, we deduce in the present paper, a new noncommutative algebra that is compatible with the deformed algebra proposed by Costa Filho et al. [Phys. Rev. A 84 (2011) 050102] to describe the Position-Dependent Mass (PDM) system in 1D. To this aim, we derive from the momentum operators, the Schrödinger-like equation which describes PDM system in null quantum well potential. The spectrum of this system is asymetrically deformed and exhibits different behaviours from the one obtained by Costa Filho et al. Thus, we observe that by increasing the PDM, the energy decreases and this decrease is more pronounced as the quantum number increases. Finally, we evaluate the thermodynamic quantities within the canonical ensemble and we show that these results are consistent with the ones recently obtained by Bensalem and Bouaziz [Phys. A Stat. Mech. Appl. 523 (2019) 583–592].