Programme

P.8 -- Poster, VCTP-44

Date: Tuesday, 30 July 2019

Time: 08:30 - 10:00

On the derivation of the entropy of ideal quantum gases condined in a three-dimensional harmonic potential

A. T. Nguyen (1,2), Tran Duong Anh-Tai (3), Uyen T. Nguyen (3), Duc Anh Dinh (4), T. V. N. Hao (5), Vinh N. T. Pham (3)

(1) Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam (2) Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Viet Nam (3) Ho Chi Minh City University of Education, Ho Chi Minh City 748342, Vietnam (4) NTT Hi-Tech Institute, Nguyen Tat Thanh University, Ho Chi Minh City 700000, Vietnam (5) Faculty of Physics, University of Education, Hue University, 34 Le Loi Street, Hue City, Vietnam

This study provides a rigorously analytical derivation of the entropy of ideal quantum gases confined in a three-dimensional harmonic trap as functions of the temperature. The numerical calculation is also taken into account for evaluating the applicability of the derived formulas. The results indicate that the entropy of the ideal Bose gas exhibits high consistence between analytical and numerical approaches, the maximum deviation is $7.5%$ around the vicinity of the critical temperature $T_c$ which is the lowest temperature at which all particles are in the excited state with maximum chemical potential. Nevertheless, in case of Fermi gas, the analytical result fairly departs from numerical one in the interval of $0.3T_F - 0.5T_F$ where $T_F$ is the Fermi temperature associating with Fermi energy level. Besides, the differences between ideal quantum and classical gases in three-dimensional harmonic trap are also presented.

Presenter: Pham Nguyen Thanh Vinh