The moderately dense quantum Boltzmann gas at equilibrium is shown to be equivalent to a gas of "dressed particles," or "quasiparticles," like those of Landau's theory of a Fermi liquid. The Landau quasiparticle interaction energy $F(p)$ is related to the second virial coefficient by means of an inverse Laplace transform. Expressions are obtained for $F(p)$ , and consequently the "renormalized" single-quasiparticle energy ${\ensuremath{\epsilon}}_{p}$, in terms of both scattering phase shifts and the M\o{}ller operator. The theory is compared with the Hartree approximation, the results of Allen, Nicolis et al., the work of Baerwinkel and Grossmann, and with expressions from Fermi-fluid theory.The moderately dense quantum Boltzmann gas at equilibrium is shown to be equivalent to a gas of "dressed particles," or "quasiparticles," like those of Landau's theory of a Fermi liquid. The Landau quasiparticle interaction energy $F(p)$ is related to the second virial coefficient by means of an inverse Laplace transform. Expressions are obtained for $F(p)$, and consequently the "renormalized" single-quasiparticle energy ${\ensuremath{\epsilon}}_{p}$, in terms of both scattering phase shifts and the M\o{}ller operator. The theory is compared with the Hartree approximation, the results of Allen, Nicolis et al., the work of Baerwinkel and Grossmann, and with expressions from Fermi-fluid theory.

Physical Review AMar 1, 19765 citations

Quasiclassical motion of quasiparticles in Fermi superfluids

Richard J. Watts-Tobin

Czechoslovak Journal of PhysicsJan 1, 19960 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

Collinear scattering and long-lived excitations in two-dimensional electron fluids

Serhii Kryhin, Leonid S Levitov

For a long time, it has been thought that two-dimensional (2D) Fermi gases could support long-lived excitations, owing to the collinear quasiparticle scattering controlled by phase-space constraints at a 2D Fermi surface. We present a direct calculation that reveals such excitations. The excitation lifetimes are found to exceed the fundamental bound set by the Landau Fermi-liquid theory by a factor as large as ${({T}_{F}/T)}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\approx}2$. These excitations represent Fermi-surface modulations of an odd parity, one per each odd angular momentum. To explain this surprising behavior, we employ a connection between the linearized quantum kinetic equation and the dynamics of a fictitious quantum particle moving in a 1D reflectionless ${\mathrm{sech}}^{2}$ potential. In this framework, we identify the long-lived excitations in Fermi gases as zero modes that arise from supersymmetry.For a long time, it has been thought that two-dimensional (2D) Fermi gases could support long-lived excitations, owing to the collinear quasiparticle scattering controlled by phase-space constraints at a 2D Fermi surface. We present a direct calculation that reveals such excitations. The excitation lifetimes are found to exceed the fundamental bound set by the Landau Fermi-liquid theory by a factor as large as ${({T}_{F}/T)}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\approx}2$. These excitations represent Fermi-surface modulations of an odd parity, one per each odd angular momentum. To explain this surprising behavior, we employ a connection between the linearized quantum kinetic equation and the dynamics of a fictitious quantum particle moving in a 1D reflectionless ${\mathrm{sech}}^{2}$ potential. In this framework, we identify the long-lived excitations in Fermi gases as zero modes that arise from supersymmetry.

arXiv:2112.05076Physical review. B./Physical review. BMay 16, 202316 citations

F(p)

is related to the second virial coefficient by means of an inverse Laplace transform. Expressions are obtained for

F(p)

, and consequently the "renormalized" single-quasiparticle energy ${\ensuremath{\epsilon}}_{p}$, in terms of both scattering phase shifts and the M\o{}ller operator. The theory is compared with the Hartree approximation, the results of Allen, Nicolis et al., the work of Baerwinkel and Grossmann, and with expressions from Fermi-fluid theory.

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.

{\mathrm{sech}}^{2}

potential. In this framework, we identify the long-lived excitations in Fermi gases as zero modes that arise from supersymmetry.