Thermodynamic properties of ideal Bose gas trapped in different external power-law potentials under generalized uncertainty principle*

Significant evidence is available to support the quantum effects of gravity that leads to the generalized uncertainty principle (GUP) and the minimum observable length. Usually quantum mechanics, statistical physics doesn't take gravity into account. Thermodynamic properties of ideal Bose gases in different external power-law potentials are studied under GUP with statistical physical method. Critical temperature, internal energy, heat capacity, entropy, particles number of ground state and excited state are calculated analytically to ideal Bose gases in the external potentials under GUP. Below the critical temperature, taking rubidium and sodium atoms ideal Bose gases whose particle densities are under standard and experimental conditions, respectively, as examples, the relations of internal energy, heat capacity and entropy with temperature are analyzed numerically. Theoretical and numerical calculations show that: GUP leads to an increase in the critical temperature. When the temperature is lower than the critical temperature and slightly higher than zero Kelvin, GUP's amendments to internal energy, heat capacity and entropy are positive; As the temperature increases to a certain value, these amendments become negative. The external potentials can increase or decrease the influence of GUP on thermodynamic properties. Under the initial experimental conditions when Bose-Einstein condensation was first verified by sodium atomic gas, the influence of GUP can be completely ignored. Under certain conditions, GUP may become the dominant factor governing the thermodynamic properties of the system.