The TCLE method (a method in which the admittance of a system is directly calculated from time-convolutionless equations with external driving terms) formulated in terms of thermo-field dynamics, is applied to a boson system interacting with its surroundings, referred to as the “heat reservoir”, and with an external driving field. For a boson system interacting with its heat reservoir, the fluctuation-dissipation theorem, a dispersion relation, and sum rules are studied through application of the TCLE method. The effects of the interference between the external driving field and the heat reservoir, which give the effects of the initial correlation and memory, as well as the effects of the boson-boson interaction, are numerically investigated for a non-degenerate boson system interacting with its heat reservoir, up to first order in powers of the boson-boson interaction.
We consider a dilute homogeneous mixture of bosons and spin-polarized fermions at zero temperature. We first construct the formal scheme for carrying out systematic perturbation theory in terms of single particle Green's functions. We especially focus on the description of the boson-fermion interaction. To do so we need to introduce the renormalized boson-fermion
T matrix, which we determine to second order in the boson-fermion
s-wave scattering length. We also discuss how to incorporate the usual boson-boson
T matrix in mean field approximation to obtain the total ground-state properties of the system. The next-order term beyond mean field stems from the boson-fermion interaction and is proportional to
aBFkF. The total ground-state energy density to this order is the sum of the kinetic energy of the free fermions, the boson-boson mean-field interaction, the usual mean-field contribution to the boson-fermion interaction energy, and the first boson-fermion correction beyond mean field. We also compute the bosonic and the fermionic chemical potentials, the compressibilities, and the modification to the induced fermion-fermion interaction. We discuss the behavior of the total ground-state energy and the importance of the correction beyond mean field for various parameter regimes, in particular considering mixtures of
6Li and
7Li and of
3He and
4He. Moreover, we determine the modification of the induced fermion-fermion interaction due to the effects beyond mean field. We show that there is no effect on the depletion of the Bose condensate to first order in the boson-fermion scattering length
aBF.Abstract We demonstrate the possibility of creating a self-bound stable three-dimensional matter-wave spherical boson–fermion quantum ball in the presence of an attractive boson–fermion interaction and a small repulsive three-boson interaction. The two-boson interaction could be attractive or repulsive whereas the fermions are taken to be in a fully-paired super-fluid state in the Bardeen–Cooper–Schreifer (quasi-noninteracting weak-coupling) limit. We also include the Lee–Huang–Yang (LHY) correction to a repulsive bosonic interaction term. The repulsive three-boson interaction and the LHY correction can stop a global collapse while acting jointly or separately. The present study is based on a mean-field model, where the bosons are subject to a Gross–Pitaevskii (GP) Lagrangian functional and the fully-paired fermions are described by a Galilean-invariant density functional Lagrangian. The boson–fermion interaction is taken to be the mean-field Hartree interaction, quite similar to the interaction term in the GP equation. The study is illustrated by a variational and a numerical solution of the mean-field model for the boson–fermion 7 Li– 6 Li system.