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Correlation effects of an electron gas in an external potential are derived using an Effective Action functional method. Corrections beyond the random phase approximation (RPA) are naturally incorporated by this method. The Effective Action functional is made to depend explicitly on two-point correlation functions. The calculation is carried out at imaginary time. For a homogeneous electron gas, we calculate the effect of exchange on the ring diagrams at zero temperature and show how to include some of the ladder diagrams. Our results agree well with known numerical calculations. We conclude by showing that this method is in fact a variant of the time dependent density functional method and suggest that it is suitable to be applied to the study of correlation effects in the non-homogeneous case.

The conserving sum rules for the electron gas form a set of fundamental and powerful constraints on the description of electronic transport, at any length scale. We examine the particular role of the compressibility sum rule for open mesoscopic conductors, and show that the compressibility in such systems is absolutely invariant under nonequilibrium transport. The compressibility sum rule provides a stringent consistency check on models of mesoscopic conduction.

Standard results for the fluctuations of thermodynamic quantities are derived under the assumption of sampling identical systems that are in different, not fully equilibrated states. These results apply to fluctuations with time in a particular macroscopic body and can be traced to the fluctuations of thermal occupancy. When many identically prepared — but not identical — systems are studied, mesoscopic fluctuations due to variations from sample-to-sample contribute to the fluctuations of thermodynamic quantities. We study the combined effect of mesoscopic fluctuations and fluctuations of thermal occupancy. In particular, we evaluate the total particle number and specific heat fluctuations in a two-dimensional, noninteracting electron gas in classically integrable and chaotic circumstances.

We calculate the inelastic scattering lifetime of an excited quasiparticle at low (or zero) temperature, due to electron-electron interaction for a clean two-dimensional (2D) electron gas within the random-phase approximation (RPA) and compare it with the lifetime measured from the tunnelling experiment. Our result obtained by direct numerical calculation increases the electron relaxation rate considerably, hence decreases the size of discrepancy (roughly by a factor of 4) between theory and experiment which exists in the literature. We also show that including local-field factors in the effective electron interaction yields small correction to the result calculated within the RPA for r_s ~ 1, corresponding to electron density of the sample in the tunnelling experiment. This result suggests that the RPA is reasonably accurate for a 2D electron gas in weak coupling limit.

In this paper, due to the effect of positively-charged screening holes, Coulomb potential energy 1/r is modified to be 1/r^p, which is assumed to deviate slightly from the former. Using many-body perturbation theory, we obtain a simple analytic representation of the ground-state energy and correlation energy for a uniform electron gas. Our results agree with those obtained by the numerical and semi-analytic methods at low-density limit. Higher ground-state energies at high-density limit are calculated from our model. High order r expansion terms are found at high-density region. A curve of transition density versus p is drawn via the Misawa spin-scaling relation, which is in consistent with Perdew's study at low-density limit.

The relaxation of hot electrons is considered in a metal nanoparticle. When the particle size is of the order of electron mean free path, the main channel of hot electron energy loss is through surface-phonon generation, rather than bulk phonon generation. A calculation for the hot electron relaxation by the generation of surface-phonons is given, assuming that electrons and surface-phonons are described by their equilibrium Fermi and Bose distribution functions. The assumption is valid because the time required to establish equilibrium in the electron gas is much less than the time for achieving equilibrium between the electrons and the surface-phonons. The expressions obtained for low-temperature and high-temperature regimes are inversely proportional to the radius of the particle. This shows that size dependency of electron surface-phonon energy exchange arises from the geometric effect.

For a two-dimensional electron gas with equal Rashba and Dresselhaus spin-orbit coupling strength (ReD model), and the Dresselhaus [110] model, the influence of an external magnetic field on the lifetime of the Spin Helix (SH) has been considered. A perpendicular magnetic field has no influence on the lifetime of the SH for the Dresselhaus [110] model, independent of the strength of the magnetic field. But for the ReD model, when the magnetic field is weak, and we only take the linear term of the magnetic field B into account, the conclusion is still so. In addition, if the external magnetic field is in-plane with a suitable angle between the x and y component, the lifetime of the SH will also be infinite.

In this paper, the anisotropic magnetoresistance (AMR) and electron conductivity of electron gas in presence of the Rashba and Dresselhaus spin-orbit coupling are investigated. Boltzmann equation is solved exactly for low temperature, including electron scattering. Calculations have been performed within the coherent potential approximation. Results of the transport study demonstrate that the AMR enhances as the Rashba strength increases. It is also observed that the AMR depends critically on spin-orbit coupling strength, wave vector and Dresselhaus strength.

The properties of nuclei embedded in an electron gas are studied within the relativistic mean-field approach. These studies are relevant for nuclear properties in astrophysical environments such as neutron-star crusts and supernova explosions. The electron gas is treated as a constant background in the Wigner–Seitz cell approximation. We investigate the stability of nuclei with respect to α and β decay. We find that the presence of the electrons leads to stabilizing effects for α decay at high electron densities. Furthermore, the screening effect shifts the proton drip-line to more proton-rich nuclei, and the stability line with respect to β decay is shifted to more neutron-rich nuclei. Implications for the creation and survival of very heavy nuclear systems are discussed.