Quantum thermodynamics of a strongly interacting bose-fermi mixture in a three-dimensional anharmonic potential

Abstract

Thermodynamic properties of Bose-Fermi mixture at ultra-low temperatures were studied using perturbation theory in three Cartesian coordinates. The Hamiltonian for the mixture was developed in terms of boson-boson, boson-fermion and fermion-fermion interactions. In both first and second excited states the mixture had about 150 joules of energy at about 40 kelvins. In both first and third excited states, the mixture had energy value of about 200 joules at a temperature of about 48 kelvins. The mixture had energy value of about 240 joules at about 58 kelvins in both the second and the third excited states. The specific heat capacity versus temperature curves showed sharp turning points with peak values of specific heat capacity being 11.58J/mol/ at about 6.9 kelvins for first excited state, 7.88J/mol/ at about 13.7 kelvins for second excited state and 6.758J/mol/ at about 20.9 kelvins for third excited state. Entropy of the BF mixture in an excited state was found to increase with temperature and became constant at higher temperatures.