Abstract
A generalization of the random-phase approximation of the theory of Coulomb correlation energy is applied to the theory of superconductivity. With no further approximations it is shown that most of the elementary excitations have the Bardeen-Cooper-Schrieffer energy gap spectrum, but that there are collective excitations also. The most important of these are the longitudinal waves which have a velocity ${v}_{F}{{\frac{1}{3}[1\ensuremath{-}4N(0)|V|]}}^{\frac{1}{2}}$ in the neutral Fermi gas, and are essentially unperturbed plasma oscillations in the charged case. Other collective excitations resembling higher bound pair states may or may not exist but do not seriously affect the energy gap. The theory obeys the sum rules and is gauge invariant to an adequate degree throughout.
Keywords
PhysicsRandom phase approximationSuperconductivityCoulombQuasiparticleQuantum mechanicsBCS theoryGauge theoryCondensed matter physicsCooper pairQuantum electrodynamicsPairingElectron
Related Publications
Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
The aim of this paper is to advocate the usefulness of the spin-density-functional (SDF) formalism. The generalization of the Hohenberg-Kohn-Sham scheme to and SDF formalism is ...
Weak interactions at very high energies: The role of the Higgs-boson mass
We give an $S$-matrix-theoretic demonstration that if the Higgs-boson mass exceeds ${M}_{c}={(8\ensuremath{\pi}\frac{\sqrt{2}}{3}{G}_{F})}^{\frac{1}{2}}$, parital-wave unitarity...
Exchange and correlation energy in density functional theory: Comparison of accurate density functional theory quantities with traditional Hartree–Fock based ones and generalized gradient approximations for the molecules Li2, N2, F2
The density functional definition of exchange and correlation differs from the traditional one. In order to calculate the density functional theory (DFT), quantities accurately,...
Theory of Boundary Effects of Superconductors
An extension of the phenomenological London equations to take into account a space variation of the concentration of superconducting electrons is presented. The theory differs f...
Ensemble Dependence of Fluctuations with Application to Machine Computations
The standard theory of fluctuations in thermodynamic variables in various ensembles is generalized to nonthermodynamic variables: e.g., the mean-square fluctuations of the kinet...
Publication Info
- Year
- 1958
- Type
- article
- Volume
- 112
- Issue
- 6
- Pages
- 1900-1916
- Citations
- 1356
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
1356
OpenAlex
Cite This
Philip W. Anderson
(1958).
Random-Phase Approximation in the Theory of Superconductivity.
Physical Review
, 112
(6)
, 1900-1916.
https://doi.org/10.1103/physrev.112.1900
Identifiers
- DOI
- 10.1103/physrev.112.1900