The Ground States of Noninteracting Fermi- and Bose-Many Particle Systems

Xian Zhi Wang

A much simpler method is proposed for the evaluation of the exact finite-temperature particle and energy densities for noninteracting Bose and Fermi gases in d-dimensional anisotropic harmonic traps. For the Bose gas in the whole range of temperature, the exact results are obtained. For the Fermi gas with chemical potential less than the single-particle ground-state energy, the exact results are obtained.

Léon Van Hove

Lev Deych

Xiaoming Cai, Liming Guan, Shu Chen +2 more

We study a mixture of $N_{b}$ bosons with point hard-core boson-boson interactions and $N_{f}$ noninteracting spinless fermions with point hard-core boson-fermion interactions in 1D optical lattice with external harmonic confine potential. Using an extended Jordan-Winger transformation (JWT) which maps the hard-core Bose-Fermi mixture into two component noninteracting spinless fermions with hard-core interactions between them, we get the ground states of the system. Then we determine in details the one particle density matrix, density profile, momentum distribution, the natural orbitals and their occupations based on the constructed ground state wavefunctions. We also discuss the ground state properties of the system with large but finite interactions which lead to the lift of ground degeneracy. Our results show that, although the total density profile is almost not affected, the distributions for bosons and fermions strongly depend on the relative strengthes of boson-boson interactions and boson-fermion interactions.

William R. Minor

A calculation of the ground-state energy per particle of two-dimensional (2D) dilute quantum gases is given. The method of calculation is based on the free t-matrix approach and the phase shifts associated with 2D scattering. The continuous interpolation of energy from a Fermi to a Bose gas via the anyon gas is demonstrated both for particles undergoing hard-disk repulsions and for noninteracting gases subject to the statistical interaction alone.

Theoretical Physics