Thermodynamic properties and algebraic solution of the N-dimensional harmonic oscillator with minimal length uncertainty relations

Abstract

The algebraic solution of the deformed N-dimensional harmonic oscillator in the presence of a minimal length is determined. To reach this goal, we identify a hidden symmetry for the N free deformed harmonic oscillators. This allows us to algebraically determine the spectrum of the system. After determining the deformed partition function, we give some thermodynamics properties such as the mean energy, the mean free energy, the entropy, and the specific heat. The effect of the minimal length on all thermodynamic properties is very clear and considerable. In particular, from the curve of the entropy function no abrupt change has been identified for different values of the deformation parameter β. This means that the curvature observed in the specific heat curve does not present or indicate the existence of a phase transition. In the limit β = 0, the specific heat of a crystalline body is independent of the temperature and of the body considered for large values of the temperature.