Pairing between two fermionic excitations in a non-Fermi liquid is considered in terms of the Bethe-Salpeter equation. We consider the pairing in a Fermi system with vanishing spectral weight. It is well known that the quasiparticle pole in the single-particle Green's function in a Non-Fermi liquid is absent or weak. The examples of such systems can be viewed as the "Marginal" Fermi liquid and Luttinger liquid. Another example that has also been considered is the Fermi system with pseudogap behavior in the spectral weight. Although the pairing between two excitations in a non-Fermi liquid is, in general, absent, nevertheless we show that the Cooper's type of pairing can occur and the conditions for such a kind of pairing are discussed. The results have also been applied to the systems with smeared or non-monotonic Fermi distribution. A system that transits from Fermi-type to Bose-type behavior can serve as an example of such systems as discussed.Pairing between two fermionic excitations in a non-Fermi liquid is considered in terms of the Bethe-Salpeter equation. We consider the pairing in a Fermi system with vanishing spectral weight. It is well known that the quasiparticle pole in the single-particle Green's function in a Non-Fermi liquid is absent or weak. The examples of such systems can be viewed as the "Marginal" Fermi liquid and Luttinger liquid. Another example that has also been considered is the Fermi system with pseudogap behavior in the spectral weight. Although the pairing between two excitations in a non-Fermi liquid is, in general, absent, nevertheless we show that the Cooper's type of pairing can occur and the conditions for such a kind of pairing are discussed. The results have also been applied to the systems with smeared or non-monotonic Fermi distribution. A system that transits from Fermi-type to Bose-type behavior can serve as an example of such systems as discussed.

International Journal of Modern Physics BJul 30, 200710 citations

Pairing in Marignal Fremi Liquid and Luttinger Liquid in Terms of the Bethe-Salpeter Equation

YURIY M. MALOZOVSKY

Bulletin of the American Physical SocietyMar 14, 20060 citations

A low-energy effective Hamiltonian for Landau quasiparticles: I. A unified theory of transport and superfluidity in Fermi liquids

Pierre-Louis Taillat, Hadrien Kurkjian

We introduce a new renormalisation scheme to construct the Landau quasiparticles of Fermi fluids. The scheme introduces an energy cutoff $Λ$ to remove the resonant couplings, enabling the dressing of the particles into quasiparticles via a unitary transformation. The dynamics of the quasiparticles is then restricted to low-energy transitions and is fully determined by an effective Hamiltonian which unifies the Landau function $f$ , the pair interaction $g$ responsible for superfluidity, and the collision amplitude $\mathcal{A}$ responsible for transport and equilibration. Studying the flow equation that results from infinitesimal variations of the cutoff, we recover the Bethe-Salpeter relation between $f$ and the forward limit of $\mathcal{A}$ , and we demonstrate an analogue relation between $g$ and the frontal limit of $\mathcal{A}$ . We show that our effective theory captures all the low-energy phenomena of Fermi liquids, from the equation of state to the transport properties, both in the normal and in the superfluid phase. We apply it to the calculation of non-Fermi liquid corrections to the quasiparticle lifetime. This publication is continued by arXiv:2607.07041 where we apply the effective theory to a Fermi fluid of ultracold atoms.We introduce a new renormalisation scheme to construct the Landau quasiparticles of Fermi fluids. The scheme introduces an energy cutoff $Λ$ to remove the resonant couplings, enabling the dressing of the particles into quasiparticles via a unitary transformation. The dynamics of the quasiparticles is then restricted to low-energy transitions and is fully determined by an effective Hamiltonian which unifies the Landau function $f$, the pair interaction $g$ responsible for superfluidity, and the collision amplitude $\mathcal{A}$ responsible for transport and equilibration. Studying the flow equation that results from infinitesimal variations of the cutoff, we recover the Bethe-Salpeter relation between $f$ and the forward limit of $\mathcal{A}$, and we demonstrate an analogue relation between $g$ and the frontal limit of $\mathcal{A}$. We show that our effective theory captures all the low-energy phenomena of Fermi liquids, from the equation of state to the transport properties, both in the normal and in the superfluid phase. We apply it to the calculation of non-Fermi liquid corrections to the quasiparticle lifetime. This publication is continued by arXiv:2607.07041 where we apply the effective theory to a Fermi fluid of ultracold atoms.

cond-mat.quant-gasCross-listedarXiv:2511.15938Nov 21, 20250 citations

Pairing in Fermion Systems

S. Mazumdar

Physical Review LettersNov 30, 19872 citations

Pairing in Small, 2D Fermi Systems

J. R. Armstrong, Massimo Rontani, Sven Åberg +2 more

Bulletin of the American Physical SocietyOct 25, 20080 citations

We introduce a new renormalisation scheme to construct the Landau quasiparticles of Fermi fluids. The scheme introduces an energy cutoff

Λ

to remove the resonant couplings, enabling the dressing of the particles into quasiparticles via a unitary transformation. The dynamics of the quasiparticles is then restricted to low-energy transitions and is fully determined by an effective Hamiltonian which unifies the Landau function

f

, the pair interaction

g

responsible for superfluidity, and the collision amplitude

\mathcal{A}

responsible for transport and equilibration. Studying the flow equation that results from infinitesimal variations of the cutoff, we recover the Bethe-Salpeter relation between

f

and the forward limit of

\mathcal{A}

, and we demonstrate an analogue relation between

g

and the frontal limit of

\mathcal{A}

. We show that our effective theory captures all the low-energy phenomena of Fermi liquids, from the equation of state to the transport properties, both in the normal and in the superfluid phase. We apply it to the calculation of non-Fermi liquid corrections to the quasiparticle lifetime. This publication is continued by arXiv:2607.07041 where we apply the effective theory to a Fermi fluid of ultracold atoms.