General Properties of the Electron

A. Holas

The calculational scheme for an approximate ground-state energy of a many-electron system, recently proposed by Goedecker and Umrigar (GU) [Phys. Rev. Lett. 81, 866 (1998)], is analyzed in terms of the reduced-density-matrix approach. Its underlying object, the GU density-matrix functional, is generalized, possibly leading to improved energies. Properties of the solutions of the ground-state problem obtained from the original and the generalized GU functionals are established.

Heling Li, Jinxiu Ren, Wenwei Wang +2 more

Abstract Using the semi-classical (Thomas–Fermi) approximation, the thermodynamic properties of ideal Fermi gases in a harmonic potential in an n -dimensional space are studied under the generalized uncertainty principle (GUP). The mean particle number, internal energy, heat capacity and other thermodynamic variables of the Fermi system are calculated analytically. Then, analytical expressions of the mean particle number, internal energy, heat capacity, chemical potential, Fermi energy, ground state energy and amendments of the GUP are obtained at low temperatures. The influence of both the GUP and the harmonic potential on the thermodynamic properties of a copper-electron gas and other systems with higher electron densities are studied numerically at low temperatures. We find: (1) When the GUP is considered, the influence of the harmonic potential is very much larger, and the amendments produced by the GUP increase by eight to nine orders of magnitude compared to when no external potential is applied to the electron gas. (2) The larger the particle density, or the smaller the particle masses, the bigger the influence of the GUP. (3) The effect of the GUP increases with the increase in the spatial dimensions. (4) The amendments of the chemical potential, Fermi energy and ground state energy increase with an increase in temperature, while the heat capacity decreases. T F0 is the Fermi temperature of the ideal Fermi system in a harmonic potential. When the temperature is lower than a certain value (0.22 times T F0 for the copper-electron gas, and this value decreases with increasing electron density), the amendment to the internal energy is positive, however, the amendment decreases with increasing temperature. When the temperature increases to the value, the amendment is zero, and when the temperature is higher than the value, the amendment to the internal energy is negative and the absolute value of the amendment increases with increasing temperature. (5) When electron density is greater than or equal to 10 37 m −3 , the influence of the GUP becomes the dominant factor affecting the thermodynamic properties of the system.

Clinton J. Davisson

A. I. Panin

General properties of new models of the electronic Fock spaces based on the notion of (p,q)-sheaves are studied. Interrelation between simple sheaves and density operators is established. Explicit expressions for the transformed reduced Hamiltonians in terms of the standard creation-annihilation operators are presented. General scheme of parametrization of p-electron states by k-electron means (k=2,3,...) is described and studied in detail for the case of sheaves induced by k-electron wavefunctions. It is demonstrated that under certain conditions p-electron problem may be reformulated as the eigenvalue problem in k-electron space equipped with certain p-electron metric. Simple numerical examples are given to illustrate our approach.