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)
We study the process of absorption or emission of a bosonic collective excitation by a fermionic quasiparticle in a superfluid of paired fermions. From the random phase approximation equation of motion of the bosonic excitation annihilation operator, we obtain an expression of the coupling amplitude of this process, which is limited neither to resonant processes nor to the long wavelength limit. We confirm our result by independently deriving it in the functional integral approach using the gaussian fluctuation approximation, and by comparing it in the long wavelength limit to the quantum hydrodynamic result. Lastly, we give a straightforward application of the coupling amplitude we obtain by calculating the lifetime of the bosonic excitations of an arbitrary wave number. We find a mode quality factor that decreases from its maximum at low wave numbers and vanishes when the bosonic branch hits the continuum of fermionic biexcitations.
We investigate the fermion spectrum within the Bose–Fermi–Hubbard model used for the description of boson-fermion mixtures of ultra-cold atoms in optical lattices. We used the method based on the Hubbard operator approach for an on-site basis. The equation for fermion Green’s function in the Bose–Fermi–Hubbard model is built; Green’s functions of higher orders are decoupled in the Hubbard-I approximation (the case of the strong on-site interaction). The corresponding spectral densities are calculated. In the case of hard-core bosons, the condition of appearance of additional bands in the fermion spectrum is investigated. It is shown that these bands exist only in the state with a Bose–Einstein condensate and appear because of the mixing of states with different numbers of bosons. These additional bands can be interpreted as a manifestation of composite excitations (when the appearance of a fermion on the site is accompanied by the simultaneous creation (or annihilation) of a boson).
The spectral properties of a mixture of bosons hybridized with fermion pairs are studied in the superconducting state. Such a model exhibits two limiting behaviors. One is reminiscent of a BCS system, provided that the total concentration n of particles is below a certain critical concentration
nc, in which case bosons exist only in thermally excited states. The other limit for n\ensuremath{\geqslant}
nc describes a situation largely controlled by the condensation of the bosons. The variation of the single-boson as well as collective excitations as a function of n and for the entire temperature regime from T=0 K to
Tc will be discussed, both with and without long-range Coulomb interaction between the charge carriers. The method for calculation applied here is based on the dielectric formalism and the use of Ward identities, currently used in the theory of the interacting Bose gas, which allows us to derive the density and current correlation functions consistent with local charge-current conservation laws. In the absence of a Coulomb interaction the behavior of the system is characterized by the existence of a sound-wave-like branch in the Bose single-particle and collective excitation spectrum. In the BCS regime the sound velocity is proportional to the Fermi velocity while in the Bose regime it is proportional to the strength of the boson-fermion hybridization and decreases with the superfluid density as we approach
Tc. In the presence of a long-range Coulomb interaction and in the Bose regime one observes, besides the usual optical plasmon mode at high frequency and corresponding to in-phase density oscillation of the two subsytems, an out-of-phase collective mode in the two particle continuum just above the gap. Moreover, upon approaching
Tc a relatively well-defined quasiparticle feature starts to emerge within the gap and is seen in both the Bose single-particle excitation and the density oscillation spectrum. In the BCS regime, due to the very small number of occupied bosonic states, the low-energy quasiparticle features are absent. \textcopyright{} 1996 The American Physical Society.
A method is developed to calculate all excitations of trapped gases using hydrodynamics at zero temperature for any equation of state $\ensuremath{\mu}=\ensuremath{\mu}(n)$ and for any trapping potential. It is shown that a natural scalar product can be defined for the mode functions, by which the wave operator is Hermitian and the mode functions are orthogonal. It is also shown that the Kohn modes are exact for harmonic trapping in the hydrodynamic theory. Excitations for fermions are calculated in the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation transition region using the equation of state of the mean-field Leggett model for isotropic harmonic trap potential.
An effective Hamiltonian for the Bose subsystem in the mixture of ultracold atomic clouds of bosons and fermions with mutual attractive interaction is used for investigating the collective excitation spectrum. The ground state and mode frequencies of the 87 Rb and 40 K mixture are analysed quantitatively at zero temperature. We find analytically solutions of the hydrodynamics equations in the Thomas–Fermi approximation. We discuss the relation between the onset of collapse and collective modes softening and the dependence of collective oscillations on scattering length and number of boson atoms.