Theoretical study of excitations in interacting Bose and Fermi systems

Zhou Li, Hang Dong, Yong-li Ma

We present a quasi-one-dimensional (Q1D) Bose–Fermi mixture model of strongly interacting Fermi gases through the confinement-induced resonance (CIR) to describe 3D fermions trapped in a Q1D geometry along the z axis. Based on the 1D Bethe ansatz method, we analyse the ground and excited states of the Q1D system and derive their integral equations in terms of the momentum distributions in the thermodynamic limit. By applying a Legendre expansion method, the crossover from the BCS superfluid of singlet pairs to the BEC of molecules is calculated in the ground and excited states. We then obtain the dependence of several physical quantities on the inverse of a dimensionless coupling parameter a ⊥ / a with a dimensionless density parameter na ⊥ of Q1D where is the transverse size and ω ⊥ is the 2D harmonic trap frequency in the xy plane. Our results can go back to the smooth 1D crossover when na ⊥ → 0. The theoretical results quantitatively show that the strongly coupling Fermi gas in the Q1D behaves as a Bose–Fermi mixture near the crossover.

C. A. Bertulani, L. Felipe Canto, Mahir Saleh Hussein

Xiangguo Yin, Shu Chen, Yunbo Zhang

We investigate theoretically the behavior of a one-dimensional interacting Bose-Fermi mixture with equal masses and equal repulsive interactions between atoms at finite temperature in the scheme of thermodynamic Bethe ansatz. Combining the Yang-Yang thermodynamic formalism with local-density approximation in a harmonic trap, we calculate the density distribution of bosons and fermions numerically by treating the radially and axially excited states as discrete and continuous ones, respectively. Our result from exactly solvable solutions may be used as a touchstone for one-dimensional interacting Bose-Fermi mixture for experimental data fitting where mean-field theoretical approaches fail.

Carsten Robens, Yiqi Ni, Zoe Z. Yan +2 more

Ernst A. Pashitskii

The spectrum of elementary excitations in the system of interacting Bose- and Fermi-particles was obtained at a temperature of absolute zero (Dose- condensation being taken into account by means of the Bogolyabov canonic transformations. In terms of a model of permeable spheres'' with finite repulsion it(is shown that the boson spectrum omega (p) in a definite region of parameter has the minimum at p = 0. By selecting parameters one succeeds in obtaining a quite satisfactory quantitative agreement of the theoretical and experimental spectra for superfluid helium. In the case when the Fermi energy is considerably higher than the bosorins maximum energy, a gap characterizing bond energy of the copper pairs can appear in the fermion speetrum due to exchange of virtual supercondensate'' bosons. If in this case the interaction between fermions at infinity is of attraction character, then under certain conditions sustained longitudinal collective excitations of Pose-type with a finite gap'' in the energy spectrum may exist in the superfluid fermion subsystem. Possibility of appearance of similar excitations in superfluid nuclear matter of neutron stars (pulsars) due to gravitational interaction between nucleons is discussed. (auth)

Thaddeus V. Samulski