We show that in dilute boson-fermion mixtures with fermions in two internal states, even when the bare fermion-fermion interaction is repulsive, the exchange of density fluctuations of the Bose condensate may lead to an effective fermion-fermion attraction, and thus to a Cooper instability in the s-wave channel. We give a simple condition to know when this is going to happen, and an analytic expression for the associated ${T}_{c}$ in the most important limit where the phonon branch of the Bogoliubov excitation spectrum of the bosons is important. We find a ${T}_{c}$ of the same order as for a pure Fermi gas with bare attraction.We show that in dilute boson-fermion mixtures with fermions in two internal states, even when the bare fermion-fermion interaction is repulsive, the exchange of density fluctuations of the Bose condensate may lead to an effective fermion-fermion attraction, and thus to a Cooper instability in the s-wave channel. We give a simple condition to know when this is going to happen, and an analytic expression for the associated ${T}_{c}$ in the most important limit where the phonon branch of the Bogoliubov excitation spectrum of the bosons is important. We find a ${T}_{c}$ of the same order as for a pure Fermi gas with bare attraction.

arXiv:cond-mat/0112354Physical Review AAug 15, 200264 citations

Bosonization of coupled electron-phonon systems

Peter Kopietz

arXiv:cond-mat/9508021Zeitschrift für Physik B Condensed MatterDec 1, 19969 citations

Interaction of an Individual Particle with Phonons in an Interacting Many-Boson System

T. Nishiyama

Progress of Theoretical PhysicsJul 1, 19690 citations

Ground-state properties of a dilute Bose-Fermi mixture

Luciano Viverit, S. Giorgini

We investigate the properties of a dilute boson-fermion mixture at zero temperature. The ground-state energy of the system is calculated to second order in the Bose-Fermi coupling constant. The Green's function formalism is applied to obtain results for the effect of Bose-Fermi interactions on the spectrum of phonon excitations, the momentum distribution, the condensate fraction, and the superfluid density of the bosonic component. A quantitative discussion of these effects is presented in the case of mixtures with attractive interspecies interaction.We investigate the properties of a dilute boson-fermion mixture at zero temperature. The ground-state energy of the system is calculated to second order in the Bose-Fermi coupling constant. The Green's function formalism is applied to obtain results for the effect of Bose-Fermi interactions on the spectrum of phonon excitations, the momentum distribution, the condensate fraction, and the superfluid density of the bosonic component. A quantitative discussion of these effects is presented in the case of mixtures with attractive interspecies interaction.

arXiv:cond-mat/0207260Physical Review ADec 19, 200292 citations

Low energy physics of interacting bosons with a moat spectrum, and the implications for condensed matter and cold nuclear matter

Robert D. Pisarski, Alexei M. Tsvelik

We discuss bosonic models with a moat spectrum, where in momentum space the minimum of the dispersion relation is on a sphere of nonzero radius. For spinless bosons with $O(N)$ symmetry, we emphasize the essential difference between $N=2$ and $N > 2$ . When $N=2$ , there are two phase transitions: at zero temperature, a transition to a state with Bose condensation, and at nonzero temperature, a transition to a spatially inhomogeneous state. When $N > 2$ , previous analysis suggests that a mass gap is generated dynamically at any temperature. In condensed matter, a moat spectrum is important for spin-orbit-coupled bosons. For cold nuclear or quarkyonic matter, we suggest that the transport properties, such as neutrino emission, are dominated by the phonons related to a moat spectrum; also, that at least in the quarkyonic phase the nucleons may be a non-Fermi liquid.We discuss bosonic models with a moat spectrum, where in momentum space the minimum of the dispersion relation is on a sphere of nonzero radius. For spinless bosons with $O(N)$ symmetry, we emphasize the essential difference between $N=2$ and $N > 2$. When $N=2$, there are two phase transitions: at zero temperature, a transition to a state with Bose condensation, and at nonzero temperature, a transition to a spatially inhomogeneous state. When $N > 2$, previous analysis suggests that a mass gap is generated dynamically at any temperature. In condensed matter, a moat spectrum is important for spin-orbit-coupled bosons. For cold nuclear or quarkyonic matter, we suggest that the transport properties, such as neutrino emission, are dominated by the phonons related to a moat spectrum; also, that at least in the quarkyonic phase the nucleons may be a non-Fermi liquid.

arXiv:2103.15835Mar 29, 20218 citations

{T}_{c}

in the most important limit where the phonon branch of the Bogoliubov excitation spectrum of the bosons is important. We find a

{T}_{c}

of the same order as for a pure Fermi gas with bare attraction.

We discuss bosonic models with a moat spectrum, where in momentum space the minimum of the dispersion relation is on a sphere of nonzero radius. For spinless bosons with

O(N)

symmetry, we emphasize the essential difference between

N=2

and

N > 2

. When

N=2

, there are two phase transitions: at zero temperature, a transition to a state with Bose condensation, and at nonzero temperature, a transition to a spatially inhomogeneous state. When

N > 2

, previous analysis suggests that a mass gap is generated dynamically at any temperature. In condensed matter, a moat spectrum is important for spin-orbit-coupled bosons. For cold nuclear or quarkyonic matter, we suggest that the transport properties, such as neutrino emission, are dominated by the phonons related to a moat spectrum; also, that at least in the quarkyonic phase the nucleons may be a non-Fermi liquid.