Many-body effective mass enhancement in a two-dimensional electron liquid

Motivated by a large number of recent magnetotransport studies we have revisited the problem of the microscopic calculation of the quasiparticle effective mass in a paramagnetic two-dimensional (2D) electron liquid (EL). Our systematic study is based on a generalized $GW$ approximation which makes use of the many-body local fields and takes advantage of the results of the most recent QMC calculations of the static charge- and spin-response of the 2D EL. We report extensive calculations for the many-body effective mass enhancement over a broad range of electron densities. In this respect we critically examine the relative merits of the on-shell approximation, commonly used in weak-coupling situations, {\it versus} the actual self-consistent solution of the Dyson equation. We show that already for $r_s \simeq 3$ and higher, a solution of the Dyson equation proves here necessary in order to obtain a well behaved effective mass. Finally we also show that our theoretical results for a quasi-2D EL, free of any adjustable fitting parameters, are in good qualitative agreement with some recent measurements in a GaAs/AlGaAs heterostructure.Comment: 12 pages, 3 figures, CMT28 Conference Proceedings, work related to cond-mat/041226

Single-particle and collective excitations in a charged Bose gas at finite temperature

The main focus of this work is on the predictions made by the dielectric formalism in regard to the relationship between single-particle and collective excitation spectra in a gas of point-like charged bosons at finite temperature $T$ below the critical region of Bose-Einstein condensation. Illustrative numerical results at weak coupling ($r_s = 1$) are presented within the Random Phase Approximation. We show that within this approach the single-particle spectrum forms a continuum extending from the transverse to the longitudinal plasma mode frequency and leading to a double-peak structure as $T$ increases, whereas the density fluctuation spectrum consists of a single broadening peak. We also discuss the momentum distribution and the superfluidity of the gas.Comment: 15 pages, 5 figure

Analytic theory of ground-state properties of a three-dimensional electron gas at varying spin polarization

We present an analytic theory of the spin-resolved pair distribution functions $g_{\sigma\sigma'}(r)$ and the ground-state energy of an electron gas with an arbitrary degree of spin polarization. We first use the Hohenberg-Kohn variational principle and the von Weizs\"{a}cker-Herring ideal kinetic energy functional to derive a zero-energy scattering Schr\"{o}dinger equation for $\sqrt{g_{\sigma\sigma'}(r)}$. The solution of this equation is implemented within a Fermi-hypernetted-chain approximation which embodies the Hartree-Fock limit and is shown to satisfy an important set of sum rules. We present numerical results for the ground-state energy at selected values of the spin polarization and for $g_{\sigma\sigma'}(r)$ in both a paramagnetic and a fully spin-polarized electron gas, in comparison with the available data from Quantum Monte Carlo studies over a wide range of electron density.Comment: 13 pages, 8 figures, submitted to Phys. Rev.

Pair Densities in a Two-dimensional Electron Gas (Jellium) at Strong Coupling from Scattering Theory with Kukkonen-Overhauser Effective Interactions

We present a calculation of the spin-averaged and spin-resolved pair distribution functions for a homogeneous gas of electrons moving in a plane with e2/r interactions at coupling strength rs = 10. The calculation is based on the solution of a two-electron scattering problem for both parallelspin- and antiparallel-spin-pairs interacting via effective spin-dependent many-body potentials. The scattering potentials are modeled within the approach proposed by Kukkonen and Overhauser to treat exchange and correlations under close constraints imposed by sum rules. We find very good agreement with quantum MonteCarlo data for the spin-averaged pair density. We also find that short-range pairing between parallel-spin electrons is beginning to emerge in the paramagnetic fluid at this coupling strength, as a precursor of a transition to a fully spin-polarized fluid state occurring at stronger coupling

Hard-core Yukawa model for two-dimensional charge stabilized colloids

The hyper-netted chain (HNC) and Percus-Yevick (PY) approximations are used to study the phase diagram of a simple hard-core Yukawa model of charge-stabilized colloidal particles in a two-dimensional system. We calculate the static structure factor and the pair distribution function over a wide range of parameters. Using the statics correlation functions we present an estimate for the liquid-solid phase diagram for the wide range of the parameters.Comment: 7 pages, 9figure

Comparing the Regression Analysis and Artificial Neural Network in Modeling the Submerged Arc Welding (SAW) Process

Abstract: 6 T Complexities of6 T 6 T submerged arc6 T 6 T welding6 T 6 T variables6 T on the one hand and its widespread use in producing the sensitive and expensive parts on the other hand have doubled the importance of precise control of its adjusting parameters. In general, in order to create high-quality joints in welding processes it is necessary to control three parameters of welding 6 T current6 T , voltage and speed precisely from various variables. On this basis, the mentioned variables have been considered as the criteria for quality of the weld joints in this study as the adjusting parameters and weld bead geometry, which include the bead height, width and penetration. Thus, the accurate equations have been proposed for estimating the weld bead height, width and penetration based on the input parameters by the regression analysis and neural network. Based on the results, the designed neural network is markedly more accurate than the regression equations, but both models have high capabilities for optimizing the parameters of submerged arc welding and also predicting the weld bead geometry for a set of input values

Correlation effects and the high-frequency spin susceptibility of an electron liquid: Exact limits

Spin correlations in an interacting electron liquid are studied in the high-frequency limit and in both two and three dimensions. The third-moment sum rule is evaluated and used to derive exact limiting forms (at both long- and short-wavelengths) for the spin-antisymmetric local-field factor, $\lim_{\omega \to \infty}G_-({\bf q, \omega})$. In two dimensions $\lim_{\omega \to \infty}G_-({\bf q, \omega})$ is found to diverge as $1/q$ at long wavelengths, and the spin-antisymmetric exchange-correlation kernel of time-dependent spin density functional theory diverges as $1/q^2$ in both two and three dimensions. These signal a failure of the local-density approximation, one that can be redressed by alternative approaches.Comment: 5 page