Short-distance properties of Coulomb systems

Abstract

We use the operator product expansion to derive exact results for the momentum distribution and the static structure factor at high momentum for a jellium model of electrons in both two and three dimensions. It is shown that independent of the precise state of the Coulomb system and for arbitrary temperatures, the asymptotic behavior is a power law in the momentum, whose strength is determined by the contact value of the pair distribution function $g(0)$. The power-law tails are quantum effects which vanish in the classical limit $\hslash \to 0$. A leading order virial expansion shows that the classical and the high-temperature limit do not agree.

13 pages, 4 figures, updated to status of published version

References in corpus (10)

• Bose-Einstein condensation of chromium
• Bose-Einstein Condensation of Erbium
• Quantum degenerate dipolar Fermi gas
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• OPE Convergence in Conformal Field Theory
• Universal Properties of the Ultra-Cold Fermi Gas
• High-momentum tails from low-momentum effective theories
• Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid
• Universality in a 2-component Fermi System at Finite Temperature

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• Pairing effects in the non-degenerate limit of the two-dimensional Fermi gas
• Momentum distribution function and short-range correlations of the warm dense electron gas -- ab initio quantum Monte Carlo results
• Scale dependence of deuteron electrodisintegration
• OPE convergence in non-relativistic conformal field theories
• Universal relations for dipolar quantum gases
• Universal Short Range Correlations in Bosonic Helium Clusters
• Exact Quantum Virial Expansion for the Optical Response of Doped Two-Dimensional Semiconductors
• Scaling behavior of the Compton profile of alkali metals
• Large-momentun tail of one-dimensional Fermi gases with spin-orbit coupling
• Dynamic properties of the warm dense uniform electron gas with the qSTLS dielectric scheme
• Momentum distribution of the Uniform Electron Gas at finite temperature: Effects of spin-polarization
• Deciphering the coalescence behavior of Coulomb-Schrödinger atomic wave functions from an operator product expansion
• Kinetic contribution to the arbitrary order odd frequency moments of the dynamic structure factor
• Scaling behavior of the momentum distribution of a quantum Coulomb system in a confining potential