Collisionless hydrodynamics for 1D motion of inhomogeneous degenerate electron gases: equivalence of two recent descriptions

Recently I. Tokatly and O. Pankratov (''TP'', Phys. Rev. B 60, 15550 (1999)) used velocity moments of a semiclassical kinetic equation to derive a hydrodynamic description of electron motion in a degenerate electron gas. Independently, the present authors (Theochem 501-502, 327 (2000)) used considerations arising from the Harmonic Potential Theorem (Phys. Rev. Lett. 73, 2244 (1994)) to generate a new form of high-frequency hydrodynamics for inhomogeneous degenerate electron gases (HPT-N3 hydrodynamics). We show here that TP hydrodynamics yields HPT-N3 hydrodynamics when linearized about a Thomas-Fermi groundstate with one-dimensional spatial inhomnogeneity.Comment: 17p

Asymptotically exact dispersion relations for collective modes in a confined charged Fermi liquid

Using general local conservations laws we derive dispersion relations for edge modes in a slab of electron liquid confined by a symmetric potential. The dispersion relations are exact up to $\lambda^{2} q^{2}$, where $q$ is a wave vector and $\lambda$ is an effective screening length. For a harmonic external potential the dispersion relations are expressed in terms of the {\em exact} static pressure and dynamic shear modulus of a homogeneous liquid with the density taken at the slab core. We also derive a simple expression for the frequency shift of the dipole (Kohn) modes in nearly parabolic quantum dots in a magnetic field.Comment: RevTeX4, 4 pages. Revised version with new results on quantum qots and wires. Published in Phys.Rev.

Correlation energies of inhomogeneous many-electron systems

We generalize the uniform-gas correlation energy formalism of Singwi, Tosi, Land and Sjolander to the case of an arbitrary inhomogeneous many-particle system. For jellium slabs of finite thickness with a self-consistent LDA groundstate Kohn-Sham potential as input, our numerical results for the correlation energy agree well with diffusion Monte Carlo results. For a helium atom we also obtain a good correlation energy.Comment: 4 pages,1 figur

Local exchange-correlation vector potential with memory in Time-Dependent Density Functional Theory: the generalized hydrodynamics approach

Using Landau Fermi liquid theory we derive a nonlinear non-adiabatic approximation for the exchange-correlation (xc) vector potential defined by the xc stress tensor. The stress tensor is a local nonlinear functional of two basic variables - the displacement vector and the second-rank tensor which describes the evolution of momentum in a local frame moving with Eulerian velocity. For irrotational motion and equilibrium initial state the dependence on the tensor variable reduces to that on a metrics generated by a dynamical deformation of the system.Comment: RevTex, 5 pages, no figures. Final version published in PR

A Closed Class of Hydrodynamical Solutions for the Collective Excitations of a Bose-Einstein Condensate

A trajectory approach is taken to the hydrodynamical treatment of collective excitations of a Bose-Einstein condensate in a harmonic trap. The excitations induced by linear deformations of the trap are shown to constitute a broad class of solutions that can be fully described by a simple nonlinear matrix equation. An exact closed-form expression is obtained for the solution describing the mode {n=0, m=2} in a cylindrically symmetric trap, and the calculated amplitude-dependent frequency shift shows good agreement with the experimental results of the JILA group.Comment: RevTex, 4 pages, 1 eps figure, identical to the published versio

Excitations of a Bose-condensed gas in anisotropic traps

We investigate the zero-temperature collective excitations of a Bose-condensed atomic gas in anisotropic parabolic traps. The condensate density is determined by solving the Gross-Pitaevskii (GP) equation using a spherical harmonic expansion. The GP eigenfunctions are then used to solve the Bogoliubov equations to obtain the collective excitation frequencies and mode densities. The frequencies of the various modes, classified by their parity and the axial angular momentum quantum number, m, are mapped out as a function of the axial anisotropy. Specific emphasis is placed upon the evolution of these modes from the modes in the limit of an isotropic trap.Comment: 7 pages Revtex, 9 Postscript figure

Tractable non-local correlation density functionals for flat surfaces and slabs

A systematic approach for the construction of a density functional for van der Waals interactions that also accounts for saturation effects is described, i.e. one that is applicable at short distances. A very efficient method to calculate the resulting expressions in the case of flat surfaces, a method leading to an order reduction in computational complexity, is presented. Results for the interaction of two parallel jellium slabs are shown to agree with those of a recent RPA calculation (J.F. Dobson and J. Wang, Phys. Rev. Lett. 82, 2123 1999). The method is easy to use; its input consists of the electron density of the system, and we show that it can be successfully approximated by the electron densities of the interacting fragments. Results for the surface correlation energy of jellium compare very well with those of other studies. The correlation-interaction energy between two parallel jellia is calculated for all separations d, and substantial saturation effects are predicted.Comment: 10 pages, 6 figure

Magnetoplasmon excitations in an array of periodically modulated quantum wires

Motivated by the recent experiment of Hochgraefe et al., we have investigated the magnetoplasmon excitations in a periodic array of quantum wires with a periodic modulation along the wire direction. The equilibrium and dynamic properties of the system are treated self-consistently within the Thomas-Fermi-Dirac-von Weizsaecker approximation. A calculation of the dynamical response of the system to a far-infrared radiation field reveals a resonant anticrossing between the Kohn mode and a finite-wavevector longitudinal excitation which is induced by the density modulation along the wires. Our theoretical calculations are found to be in excellent agreement with experiment.Comment: 9 pages, 8 figure

Correlation energy of a two-dimensional electron gas from static and dynamic exchange-correlation kernels

We calculate the correlation energy of a two-dimensional homogeneous electron gas using several available approximations for the exchange-correlation kernel $f_{\rm xc}(q,\omega)$ entering the linear dielectric response of the system. As in the previous work of Lein {\it et al.} [Phys. Rev. B {\bf 67}, 13431 (2000)] on the three-dimensional electron gas, we give attention to the relative roles of the wave number and frequency dependence of the kernel and analyze the correlation energy in terms of contributions from the $(q, i\omega)$ plane. We find that consistency of the kernel with the electron-pair distribution function is important and in this case the nonlocality of the kernel in time is of minor importance, as far as the correlation energy is concerned. We also show that, and explain why, the popular Adiabatic Local Density Approximation performs much better in the two-dimensional case than in the three-dimensional one.Comment: 9 Pages, 4 Figure

A real-space, rela-time method for the dielectric function

We present an algorithm to calculate the linear response of periodic systems in the time-dependent density functional thoery, using a real-space representation of the electron wave functions and calculating the dynamics in real time. The real-space formulation increases the efficiency for calculating the interaction, and the real-time treatment decreases storage requirements and the allows the entire frequency-dependent response to be calculated at once. We give as examples the dielectric functions of a simple metal, lithium, and an elemental insulator, diamond.Comment: 17 pages, Latex, 5 figure