Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Журнал Экспериментальной и Теоретической Физики

FERMI-LIQUID THEORY AND POMERANCHUK INSTABILITIES: FUNDAMENTALS AND NEW DEVELOPMENTS

V. CHUBUKOV, Avraham Klein, Dmitrii L. Maslov

Published Jan 1, 2018• 1 citation
Publisher

Abstract

This paper is a short review on the foundations and recent advances in the microscopic Fermiliquid (FL) theory.We demonstrate that this theory is built on five identities, which follow from conservation of total charge (particle number), spin, and momentum in a translationally and SU (2)invariant FL.These identities allows one to express the effective mass and quasiparticle residue in terms of an exact vertex function and also impose constraints on the "quasiparticle" and "incoherent" (or "low-energy" and "high-energy") contributions to the observable quantities.Such constraints forbid certain Pomeranchuk instabilities of a FL, e.g., towards phases with order parameters that coincide with charge and spin currents.We provide diagrammatic derivations of these constraints and of the general (Leggett) formula for the susceptibility in arbitrary angular momentum channel, and illustrate the general relations through simple examples treated in the perturbation theory.It is our great pleasure to write this article for the special volume in celebration of the 85th birthday of Lev Petrovich Pitaevskii, who, in our view, is one the greatest physicist of his generation and the model of a scientist and citizen.His seminal volumes on Statistical Physics (with E. M. Lifshitz), 1 Physical Kinetics 2 (also with E. M. Lifshitz), and Quantum Electrodynamics 3 (with V. B. Berestetskii and E. M. Lifshitz), all parts of the Landau and Lifshitz Course on Theoretical Physics, as well as on Bose-Einstein condensation and superfluidity 4 (with S. Stringari) are not only used by every contemporary physicist but also, as we are positive, will serve the future generations of scientists from around the world.The paper we present for this volume is devoted to the microscopic theory of a Fermi liquid, which was pioneered by Lev Petrovich in the early 1960s.The general relations he obtained with Landau, which express the effective mass m * /m and the quasiparticle residue Z in terms of the vertex function (the Pitaevskii-Landau relations), set the gold standard for many-body theory.We hope that Lev Petrovich and other readers of this volume will find our summary of recent developments in this field interesting.

DOI
10.1134/s0044451018110032

Related papers

Fermi-Liquid Theory and Pomeranchuk Instabilities: Fundamentals and New Developments

A. V. Chubukov, A. Klein, D. L. Maslov

Abstract This paper is a short review on the foundations and recent advances in the microscopic Fermi-liquid (FL) theory. We demonstrate that this theory is built on five identities, which follow from conservation of the total charge (particle number), spin, and momentum in a translationally and SU(2)-invariant FL. These identities allow one to express the effective mass and quasiparticle residue in terms of an exact vertex function and also impose constraints on the “quasiparticle” and “incoherent” (or “low-energy” and “high-energy”) contributions to the observable quantities. Such constraints forbid certain Pomeranchuk instabilities of a FL, e.g., towards phases with order parameters that coincide with charge and spin currents. We provide diagrammatic derivations of these constraints and of the general (Leggett) formula for the susceptibility in arbitrary angular momentum channel, and illustrate the general relations through simple examples treated in perturbation theory.

arXiv:1805.05562•Journal of Experimental and Theoretical Physics•Nov 1, 2018•21 citations

Fermi liquid near Pomeranchuk quantum criticality

Dmitrii L. Maslov, Andrey V. Chubukov

We analyze the behavior of an itinerant two-dimensional Fermi system near a charge nematic $(n=2)$ Pomeranchuk instability in terms of the Landau Fermi-liquid (FL) theory. A key object of our study is the fully renormalized vertex function ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$, related to the Landau interaction function. We derive ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$ for a model case of the long-range interaction in the nematic channel. Already within the random-phase approximation (RPA), the vertex is singular near the instability. The full vertex, obtained by resumming the ladder series composed of the RPA vertices, differs from the RPA result by a multiplicative renormalization factor ${Z}_{\ensuremath{\Gamma}}$, related to the single-particle residue $Z$ and effective-mass renormalization ${m}^{\ensuremath{\ast}}/m$. We employ the Pitaevski-Landau identities, which express the derivatives of the self-energy in terms of ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$, to obtain and solve a set of coupled nonlinear equations for ${Z}_{\ensuremath{\Gamma}}$, $Z$, and ${m}^{\ensuremath{\ast}}/m$. We show that near the transition the system enters a critical FL regime, where ${Z}_{\ensuremath{\Gamma}}\ensuremath{\sim}Z\ensuremath{\propto}{(1+{g}_{c,2})}^{1/2}$ and ${m}^{\ensuremath{\ast}}/m\ensuremath{\approx}1/Z$, where ${g}_{c,2}$ is the $n=2$ charge Landau component which approaches $\ensuremath{-}1$ at the instability. We construct the Landau function of the critical FL and show that all but ${g}_{c,2}$ Landau components diverge at the critical point. We also show that in the critical regime the one-loop result for the self-energy $\ensuremath{\Sigma}(K)\ensuremath{\propto}\ensuremath{\int}dPG(P)D(K\ensuremath{-}P)$ is asymptotically exact if one identifies the effective interaction $D$ with the RPA form of ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$.

arXiv:0911.1251•Physical Review B•Jan 11, 2010•75 citations

MANY-BODY ASPECTS OF THE THEORY OF FERMI LIQUIDS NEAR BOUNDARIES Dierk

Rainer Physikalisches

Landau (1958) gave a rigorous microscopic derivation of his phenomenological Fermi -liquid theory starting from the first principles Hamiltonian of strongly interacting Fermions. The derivation is based on an asymptotic expansion in small parameters such as q/kF, bc.>/EF, kT/EF, where q and c.> represent the wave numbers and frequencies of real excitations of the system. Landau showed that the dynamics of these low-lying excitations (quasiparticles and collective modes) is governed by classical transport equations with all quantum many-body effects absorbed into effective interaction parameters. Landau's approach has been generalized to superfluid Fermi liquids and superconductors by Leggett (1965) and, going beyond linear response, by Eliashberg (1971). Their ideas merged into a recent review on the quasiclassical approach to superfluid 3 He by Serene and Rainer (1983). I will use the notation of this review throughout this paper. Landau's transport theory together with its offsprings will be called 'quasiclassical theory in the following. In this context it is important to mention that Eilenberger (1968) and Larkin and Ovchinnikov (1968) have shown that the complete theory of superconductors can be formulated as a quasiclassical transport theory. Surprisingly, this theory permits calculating microscopic properties, e.g. the quasiparticle excitation spectrum, which are predominantly governed by quantum effects.

•Jan 1, 2011•0 citations

Marginal Fermi Liquids

Vikram Tripathi

The Landau Fermi liquid theory of metals has been so successful that exceptions to it draw a fair amount of attention. The theory rests on the assumption that the low‐energy properties of interacting electrons in a metal in three dimensions may be described in terms of weakly repulsive charged spin 1 2 $ \frac{1}{2} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351121996/259a876e-1ad1-4598-839f-e9587e88d783/content/inline-math13_1.tif"/> fermionic excitations— the quasiparticles. This is of course not generally expected to hold following a phase transition, for example, in the form of a Pomeranchuk instability or a superconducting transition. In Chapter 2 we showed that Pomeranchuk instabilities occur whenever some Landau F function satisfies the condition F l s ( a ) / ( 2 l + 1 ) = - 1 $ F_{l}^{s(a)} /(2l + 1) = - 1 $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351121996/259a876e-1ad1-4598-839f-e9587e88d783/content/inline-math13_2.tif"/> , where l = 0, 1, 2, . . . denotes the relevant angular momentum channel where the instability occurs. The l = 0 instability in the spin‐symmetric channel is associated with a divergence of compressibility that leads to phase separation and consequent breakdown of the Fermi liquid. In the spin‐antisymmetric channel, the l = 0 instability corresponds to ferromagnetism. In the ferromagnetic quantum critical region (“classical” Gaussian regime in Hertz theory), we found in Sec. 9.6.2.3 that spin fluctuations lead to the destruction of the Landau Fermi liquid and this is evident, for example, in the ln ( 1 / T ) $ {\text{ln }}(1/T) $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351121996/259a876e-1ad1-4598-839f-e9587e88d783/content/inline-math13_3.tif"/> divergence of the specific heat coefficient γ ( T ) . Proximity to an electronic instability is however not a necessary condition for the breakdown of the Fermi liquid. In Sec. 10.2 we found that transverse electromagnetic fluctuations are only weakly screened by conduction electrons and that results in a γ ( T ) ∼ ln ( 1 / T ) $ \gamma (T) \sim {\text{ln }}(1/T) $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351121996/259a876e-1ad1-4598-839f-e9587e88d783/content/inline-math13_4.tif"/> divergence for the specific heat coefficient without needing to be in the vicinity of a ferromagnetic quantum critical point 1 . The lack of screening of such electromagnetic fluctuations is a feature shared with low energy spin fluctuations in the Hertz theory of quantum critical ferromagnets. Another route to non Fermi‐liquid behavior, not reliant on the existence of long‐range interactions, appeared in Sec. 11.4 where we analyzed non‐optimally screened Kondo models. It was found that singularities in properties such as the susceptibility and specific heat coefficient may be expected in the event that residual low‐energy degeneracies associated with spin‐flip scattering with conduction electrons persist down to the lowest temperatures. Finally, weak potential disorder was found to preserve the Fermi liquid (in three dimensions) down to the lowest temperatures (see Chapter 8 ).

CRC Press eBooks•Feb 2, 2018•0 citations

Theory of a Superfluid Fermi Liquid. I. General Formalism and Static Properties

A. J. Leggett

The microscopic theory of a superfluid Fermi liquid at finite temperature is developed for the case of a pure system with $S$-wave pairing, and applied to the calculation of the static properties. As a function of $\ensuremath{\theta}\ensuremath{\equiv}\frac{T}{{T}_{c}}$ these properties are determined entirely by the Landau parameters ${F}_{0}$, ${F}_{1}$, ${Z}_{0}$, etc., characterizing quasiparticle interactions in the normal phase. In particular the spin susceptibility $\ensuremath{\chi}$ and the density of the normal component ${\ensuremath{\rho}}_{n}$ are given by $\frac{\ensuremath{\chi}(\ensuremath{\theta})}{\ensuremath{\chi}(1)}=(1+\frac{1}{4}{Z}_{0})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{4}{Z}_{0}f(\ensuremath{\theta})]},$ $\frac{{\ensuremath{\rho}}_{n}}{\ensuremath{\rho}}=(1+\frac{1}{3}{F}_{1})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{3}{F}_{1}f(\ensuremath{\theta})]},$ where the universal function $f(\ensuremath{\theta})\ensuremath{\equiv}\ensuremath{-}{[\ensuremath{\nu}(0)]}^{\ensuremath{-}1}{\ensuremath{\Sigma}}_{\mathrm{p}}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is the "effective density of states near the Fermi surface" relative to its value $\ensuremath{\nu}(0)$ in the normal phase. Thus the often-quoted expression ${\ensuremath{\rho}}_{n}=\frac{1}{3}{\ensuremath{\Sigma}}_{\mathrm{p}}{\mathrm{p}}^{2}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is valid for an interacting system only in the limit $T\ensuremath{\rightarrow}0$. In the latter part of the paper a simple phenomenological theory of "Fermi-liquid" effects on $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ is developed for arbitrary conditions (including the presence of impurities and pairing with $l\ensuremath{\ne}0$); it is found that under most circumstances explicit expressions for $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ may be obtained which involve only the Landau parameters and a suitably generalized effective density of states. The theory should apply to the possible superfluid phase of ${\mathrm{He}}^{3}$ and to most superconductors. It is suggested that the Knight shift in nontransition-metal superconductors should display some "Fermi-liquid" effects. The weak-field dc penetration depth $\ensuremath{\lambda}(T)$ is shown to be insensitive to such effects both in the Pippard limit and near ${T}_{c}$; however, in a London superconductor at lower temperatures the correction to $\ensuremath{\lambda}(T)$ should be observable and yield a direct estimate of ${F}_{1}$.

Physical Review•Dec 13, 1965•284 citations

Conditions for l=1 Pomeranchuk instability in a Fermi liquid

Yiming Wu, Avraham Klein, Andrey V. Chubukov

In a Fermi liquid, the stability of the Fermi surface to deformation is encoded in the angular moments of the interaction between quasiparticles via the Pomeranchuk criterion ${F}_{l}$ $\ensuremath{\ge}$ $-1$. Interestingly, charge and spin conservation prevent interactions from destabilizing the $l$=1 channel even when ${F}_{l}$ = -1, indicating that high-energy processes play a nontrivial role in the low-energy Fermi liquid dynamics. The authors identify, analytically and numerically, that conservation laws imply an equivalence between processes near and away from the Fermi surface, preventing $l$=1 instabilities. Then, they construct $l$=1 order parameters without this equivalence, identifying possible novel instabilities in strongly correlated electron systems.

arXiv:1801.06571•Physical review. B./Physical review. B•Apr 2, 2018•21 citations
This paper is a short review on the foundations and recent advances in the microscopic Fermiliquid (FL) theory.We demonstrate that this theory is built on five identities, which follow from conservation of total charge (particle number), spin, and momentum in a translationally and SU (2)invariant FL.These identities allows one to express the effective mass and quasiparticle residue in terms of an exact vertex function and also impose constraints on the "quasiparticle" and "incoherent" (or "low-energy" and "high-energy") contributions to the observable quantities.Such constraints forbid certain Pomeranchuk instabilities of a FL, e.g., towards phases with order parameters that coincide with charge and spin currents.We provide diagrammatic derivations of these constraints and of the general (Leggett) formula for the susceptibility in arbitrary angular momentum channel, and illustrate the general relations through simple examples treated in the perturbation theory.It is our great pleasure to write this article for the special volume in celebration of the 85th birthday of Lev Petrovich Pitaevskii, who, in our view, is one the greatest physicist of his generation and the model of a scientist and citizen.His seminal volumes on Statistical Physics (with E. M. Lifshitz), 1 Physical Kinetics 2 (also with E. M. Lifshitz), and Quantum Electrodynamics 3 (with V. B. Berestetskii and E. M. Lifshitz), all parts of the Landau and Lifshitz Course on Theoretical Physics, as well as on Bose-Einstein condensation and superfluidity 4 (with S. Stringari) are not only used by every contemporary physicist but also, as we are positive, will serve the future generations of scientists from around the world.The paper we present for this volume is devoted to the microscopic theory of a Fermi liquid, which was pioneered by Lev Petrovich in the early 1960s.The general relations he obtained with Landau, which express the effective mass m * /m and the quasiparticle residue Z in terms of the vertex function (the Pitaevskii-Landau relations), set the gold standard for many-body theory.We hope that Lev Petrovich and other readers of this volume will find our summary of recent developments in this field interesting.
Abstract This paper is a short review on the foundations and recent advances in the microscopic Fermi-liquid (FL) theory. We demonstrate that this theory is built on five identities, which follow from conservation of the total charge (particle number), spin, and momentum in a translationally and SU(2)-invariant FL. These identities allow one to express the effective mass and quasiparticle residue in terms of an exact vertex function and also impose constraints on the “quasiparticle” and “incoherent” (or “low-energy” and “high-energy”) contributions to the observable quantities. Such constraints forbid certain Pomeranchuk instabilities of a FL, e.g., towards phases with order parameters that coincide with charge and spin currents. We provide diagrammatic derivations of these constraints and of the general (Leggett) formula for the susceptibility in arbitrary angular momentum channel, and illustrate the general relations through simple examples treated in perturbation theory.
We analyze the behavior of an itinerant two-dimensional Fermi system near a charge nematic (n=2)(n=2)(n=2) Pomeranchuk instability in terms of the Landau Fermi-liquid (FL) theory. A key object of our study is the fully renormalized vertex function ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$, related to the Landau interaction function. We derive ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$ for a model case of the long-range interaction in the nematic channel. Already within the random-phase approximation (RPA), the vertex is singular near the instability. The full vertex, obtained by resumming the ladder series composed of the RPA vertices, differs from the RPA result by a multiplicative renormalization factor ${Z}_{\ensuremath{\Gamma}}$, related to the single-particle residue ZZZ and effective-mass renormalization ${m}^{\ensuremath{\ast}}/m$. We employ the Pitaevski-Landau identities, which express the derivatives of the self-energy in terms of ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$, to obtain and solve a set of coupled nonlinear equations for ${Z}_{\ensuremath{\Gamma}}$, ZZZ, and ${m}^{\ensuremath{\ast}}/m$. We show that near the transition the system enters a critical FL regime, where ${Z}_{\ensuremath{\Gamma}}\ensuremath{\sim}Z\ensuremath{\propto}{(1+{g}_{c,2})}^{1/2}$ and ${m}^{\ensuremath{\ast}}/m\ensuremath{\approx}1/Z$, where gc,2{g}_{c,2}gc,2​ is the n=2n=2n=2 charge Landau component which approaches $\ensuremath{-}1$ at the instability. We construct the Landau function of the critical FL and show that all but gc,2{g}_{c,2}gc,2​ Landau components diverge at the critical point. We also show that in the critical regime the one-loop result for the self-energy $\ensuremath{\Sigma}(K)\ensuremath{\propto}\ensuremath{\int}dPG(P)D(K\ensuremath{-}P)$ is asymptotically exact if one identifies the effective interaction DDD with the RPA form of ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$.
Landau (1958) gave a rigorous microscopic derivation of his phenomenological Fermi -liquid theory starting from the first principles Hamiltonian of strongly interacting Fermions. The derivation is based on an asymptotic expansion in small parameters such as q/kF, bc.>/EF, kT/EF, where q and c.> represent the wave numbers and frequencies of real excitations of the system. Landau showed that the dynamics of these low-lying excitations (quasiparticles and collective modes) is governed by classical transport equations with all quantum many-body effects absorbed into effective interaction parameters. Landau's approach has been generalized to superfluid Fermi liquids and superconductors by Leggett (1965) and, going beyond linear response, by Eliashberg (1971). Their ideas merged into a recent review on the quasiclassical approach to superfluid 3 He by Serene and Rainer (1983). I will use the notation of this review throughout this paper. Landau's transport theory together with its offsprings will be called 'quasiclassical theory in the following. In this context it is important to mention that Eilenberger (1968) and Larkin and Ovchinnikov (1968) have shown that the complete theory of superconductors can be formulated as a quasiclassical transport theory. Surprisingly, this theory permits calculating microscopic properties, e.g. the quasiparticle excitation spectrum, which are predominantly governed by quantum effects.
The Landau Fermi liquid theory of metals has been so successful that exceptions to it draw a fair amount of attention. The theory rests on the assumption that the low‐energy properties of interacting electrons in a metal in three dimensions may be described in terms of weakly repulsive charged spin 1 2 $ \frac{1}{2} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351121996/259a876e-1ad1-4598-839f-e9587e88d783/content/inline-math13_1.tif"/> fermionic excitations— the quasiparticles. This is of course not generally expected to hold following a phase transition, for example, in the form of a Pomeranchuk instability or a superconducting transition. In Chapter 2 we showed that Pomeranchuk instabilities occur whenever some Landau F function satisfies the condition F l s ( a ) / ( 2 l + 1 ) = - 1 $ F_{l}^{s(a)} /(2l + 1) = - 1 $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351121996/259a876e-1ad1-4598-839f-e9587e88d783/content/inline-math13_2.tif"/> , where l = 0, 1, 2, . . . denotes the relevant angular momentum channel where the instability occurs. The l = 0 instability in the spin‐symmetric channel is associated with a divergence of compressibility that leads to phase separation and consequent breakdown of the Fermi liquid. In the spin‐antisymmetric channel, the l = 0 instability corresponds to ferromagnetism. In the ferromagnetic quantum critical region (“classical” Gaussian regime in Hertz theory), we found in Sec. 9.6.2.3 that spin fluctuations lead to the destruction of the Landau Fermi liquid and this is evident, for example, in the ln ( 1 / T ) $ {\text{ln }}(1/T) $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351121996/259a876e-1ad1-4598-839f-e9587e88d783/content/inline-math13_3.tif"/> divergence of the specific heat coefficient γ ( T ) . Proximity to an electronic instability is however not a necessary condition for the breakdown of the Fermi liquid. In Sec. 10.2 we found that transverse electromagnetic fluctuations are only weakly screened by conduction electrons and that results in a γ ( T ) ∼ ln ( 1 / T ) $ \gamma (T) \sim {\text{ln }}(1/T) $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351121996/259a876e-1ad1-4598-839f-e9587e88d783/content/inline-math13_4.tif"/> divergence for the specific heat coefficient without needing to be in the vicinity of a ferromagnetic quantum critical point 1 . The lack of screening of such electromagnetic fluctuations is a feature shared with low energy spin fluctuations in the Hertz theory of quantum critical ferromagnets. Another route to non Fermi‐liquid behavior, not reliant on the existence of long‐range interactions, appeared in Sec. 11.4 where we analyzed non‐optimally screened Kondo models. It was found that singularities in properties such as the susceptibility and specific heat coefficient may be expected in the event that residual low‐energy degeneracies associated with spin‐flip scattering with conduction electrons persist down to the lowest temperatures. Finally, weak potential disorder was found to preserve the Fermi liquid (in three dimensions) down to the lowest temperatures (see Chapter 8 ).
The microscopic theory of a superfluid Fermi liquid at finite temperature is developed for the case of a pure system with SSS-wave pairing, and applied to the calculation of the static properties. As a function of $\ensuremath{\theta}\ensuremath{\equiv}\frac{T}{{T}_{c}}$ these properties are determined entirely by the Landau parameters F0{F}_{0}F0​, F1{F}_{1}F1​, Z0{Z}_{0}Z0​, etc., characterizing quasiparticle interactions in the normal phase. In particular the spin susceptibility $\ensuremath{\chi}$ and the density of the normal component ${\ensuremath{\rho}}_{n}$ are given by $\frac{\ensuremath{\chi}(\ensuremath{\theta})}{\ensuremath{\chi}(1)}=(1+\frac{1}{4}{Z}_{0})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{4}{Z}_{0}f(\ensuremath{\theta})]},$ $\frac{{\ensuremath{\rho}}_{n}}{\ensuremath{\rho}}=(1+\frac{1}{3}{F}_{1})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{3}{F}_{1}f(\ensuremath{\theta})]},$ where the universal function $f(\ensuremath{\theta})\ensuremath{\equiv}\ensuremath{-}{[\ensuremath{\nu}(0)]}^{\ensuremath{-}1}{\ensuremath{\Sigma}}_{\mathrm{p}}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is the "effective density of states near the Fermi surface" relative to its value $\ensuremath{\nu}(0)$ in the normal phase. Thus the often-quoted expression ${\ensuremath{\rho}}_{n}=\frac{1}{3}{\ensuremath{\Sigma}}_{\mathrm{p}}{\mathrm{p}}^{2}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is valid for an interacting system only in the limit $T\ensuremath{\rightarrow}0$. In the latter part of the paper a simple phenomenological theory of "Fermi-liquid" effects on $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ is developed for arbitrary conditions (including the presence of impurities and pairing with $l\ensuremath{\ne}0$); it is found that under most circumstances explicit expressions for $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ may be obtained which involve only the Landau parameters and a suitably generalized effective density of states. The theory should apply to the possible superfluid phase of He3{\mathrm{He}}^{3}He3 and to most superconductors. It is suggested that the Knight shift in nontransition-metal superconductors should display some "Fermi-liquid" effects. The weak-field dc penetration depth $\ensuremath{\lambda}(T)$ is shown to be insensitive to such effects both in the Pippard limit and near Tc{T}_{c}Tc​; however, in a London superconductor at lower temperatures the correction to $\ensuremath{\lambda}(T)$ should be observable and yield a direct estimate of F1{F}_{1}F1​.
In a Fermi liquid, the stability of the Fermi surface to deformation is encoded in the angular moments of the interaction between quasiparticles via the Pomeranchuk criterion Fl{F}_{l}Fl​ $\ensuremath{\ge}$ −1-1−1. Interestingly, charge and spin conservation prevent interactions from destabilizing the lll=1 channel even when Fl{F}_{l}Fl​ = -1, indicating that high-energy processes play a nontrivial role in the low-energy Fermi liquid dynamics. The authors identify, analytically and numerically, that conservation laws imply an equivalence between processes near and away from the Fermi surface, preventing lll=1 instabilities. Then, they construct lll=1 order parameters without this equivalence, identifying possible novel instabilities in strongly correlated electron systems.