High-density Limit Research Articles

Harmonic properties of hard-sphere crystals: a one-dimensional study

We show that the hard rod fluid in one dimension behaves like a harmonic crystal when the high density limit is suitably defined. We highlight analogies and differences with analogous results for hard-sphere solids in higher dimensions.

Correlation-energy functional and its high-density limit obtained from a coupling-constant perturbation expansion.

A perturbation theory is developed for the correlation energy ${\mathit{E}}_{\mathit{c}}$[n], of a finite-density system, with respect to the coupling constant \ensuremath{\alpha} which multiplies the electron-electron repulsion operator in ${\mathit{H}}^{\mathrm{\ensuremath{\alpha}}}$=T^+\ensuremath{\alpha}V${\mathrm{^}}_{\mathit{e}\mathit{e}}$+${\mathit{tsum}}_{\mathit{i}}$${\mathit{v}}_{\mathrm{\ensuremath{\alpha}}}$(${\mathbf{r}}_{\mathit{i}}$). The external potential ${\mathit{v}}_{\mathrm{\ensuremath{\alpha}}}$ is constrained to keep the gound-state density n fixed for all \ensuremath{\alpha}\ensuremath{\ge}0. ${\mathit{v}}_{\mathrm{\ensuremath{\alpha}}}$ is given completely in terms of functional derivatives at full charge (\ensuremath{\alpha}=1), from which ${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\ensuremath{\lambda}}$]=${\mathit{e}}_{\mathit{c},2}$[n]+ ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$${\mathit{e}}_{\mathit{c},3}$[n]+${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}2}$${\mathit{e}}_{\mathit{c},4}$[n]+..., where each ${\mathit{e}}_{\mathit{c},}$j[n] is expressed in terms of integrals involving Kohn-Sham determinants. Here, ${\mathit{n}}_{\ensuremath{\lambda}}$(x,y,x)=${\ensuremath{\lambda}}^{3}$n(\ensuremath{\lambda}x,\ensuremath{\lambda}y,\ensuremath{\lambda}z) and \ensuremath{\lambda}=${\mathrm{\ensuremath{\alpha}}}^{\mathrm{\ensuremath{-}}1}$. The identification of ${\mathrm{lim}}_{\ensuremath{\lambda}\ensuremath{\rightarrow}\mathrm{\ensuremath{\infty}}}$${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\ensuremath{\lambda}}$], which is a high-density limit, as the second-order energy ${\mathit{e}}_{\mathit{c},2}$[n] allows one to compute bounds upon ${\mathrm{lim}}_{\ensuremath{\lambda}\ensuremath{\rightarrow}\mathrm{\ensuremath{\infty}}}$${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\ensuremath{\lambda}}$]; the bounds imply that ${\mathrm{lim}}_{\ensuremath{\lambda}\ensuremath{\rightarrow}\mathrm{\ensuremath{\infty}}}$${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\ensuremath{\lambda}}$]\ensuremath{\simeq}${\mathit{E}}_{\mathit{c}}$[n] for a large class of small atoms and molecules, and suggest that ${\mathrm{lim}}_{\ensuremath{\lambda}\ensuremath{\rightarrow}\mathrm{\ensuremath{\infty}}}$${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\ensuremath{\lambda}}$] should be of the same order of magnitude as ${\mathit{E}}_{\mathit{c}}$[n] in finite insulators and semiconductors.Approximations to ${\mathit{E}}_{\mathit{c}}$[n] should reflect all this. In contrast, perhaps the well-known overbinding of the local-density approximation (LDA) in molecules and solids is due, in part, to the fact that the LDA correlation energy is too sensitive to a coordinate scaling of n. Indeed, the LDA for ${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\ensuremath{\lambda}}$] diverges when \ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty} because of the presence of the -ln(\ensuremath{\lambda}) term in the Gell-Mann and Brueckner high-density expression for the correlation energy, per particle, of a homogeneous density, which is infinite. In a sense, the derived perturbation expansion transforms the Gell-Mann and Brueckner expression into one that applies specifically to an inhomogeneous density which integrates to a finite number of electrons.

Supersymmetric long-range t- J model as a new canonical model for strongly correlated fermions

The origin of the characteristic spectrum in the t- J model is ascribed to a hidden continuous symmetry. The Lie group theory gives the exact eigenstates as generalized plane waves in a fictitious Riemannian space. In the high-density limit, the model is exactly mapped to the nonlinear σ model.

A description of the high-density electron system in terms of bosons

Tomonaga's idea of describing the one-dimensional jellium model in terms of bosons is adopted for the three-dimensional case, but worked out in a completely different way. An algorithm is given for the construction of a boson Hamiltonian that takes into account the full dynamics of the jellium model at all densities. The algorithm is applied to a reduced form of the jellium model, which has the same ground state energy as the jellium model in the high-density limit. The resulting boson Hamiltonian is compared with Sawada's Hamiltonian, which also has this ground state energy in the limit of high density. Finally, the present boson formulation is discussed briefly.

Pair-distribution function and its coupling-constant average for the spin-polarized electron gas.

The pair-distribution function g describes physical correlations between electrons, while its average g\ifmmode\bar\else\textasciimacron\fi{} over coupling constant generates the exchange-correlation energy. The former is found from the latter by g=(1-${\mathit{a}}_{0}$\ensuremath{\partial}/\ensuremath{\partial}${\mathit{a}}_{0}$)g\ifmmode\bar\else\textasciimacron\fi{}, where ${\mathit{a}}_{0}$ is the Bohr radius. We present an analytic representation of g\ifmmode\bar\else\textasciimacron\fi{} (and hence g) in real space for a uniform electron gas with density parameter ${\mathit{r}}_{\mathit{s}}$ and spin polarization \ensuremath{\zeta}. This expression has the following attractive features: (1) The exchange-only contribution is treated exactly, apart from oscillations we prefer to ignore. (2) The correlation contribution is correct in the high-density (${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0) and nonoscillatory long-range (R\ensuremath{\rightarrow}\ensuremath{\infty}) limits. (3) The value and cusp are properly described in the short-range (R\ensuremath{\rightarrow}0) limit. (4) The normalization and energy integrals are respected. The result is found to agree with the pair-distribution function g from Ceperley's quantum Monte Carlo calculation. Estimates are also given for the separate contributions from parallel and antiparallel spin correlations, and for the long-range oscillations at a high finite density.

Persistence of critical multitype particle and measure branching processes

We consider a class of systems of particles ofk types inR d undergoing spatial diffusion and critical multitype branching, where the diffusions, the particle lifetimes and the branching laws depend on the types. We prove persistence criteria for such systems and for their corresponding high density limits known as multitype Dawson-Watanabe processes. The main tool is a representation of the Palm distributions for a general class of inhomogeneous critical branching particle systems, constructed by means of a “backward tree”.

Raman scattering by plasmon-phonon modes in highly doped n-InAs grown by molecular beam epitaxy

Raman scattering by coupled plasmon-phonon modes is studied with Si-doped InAs epilayers grown by MBE with carrier concentrations from 7.5*1017 cm-3 to 4*1019 cm-3. Unexpectedly, an unscreened LO line is observed throughout the whole carrier concentration range together with a low frequency (L-) line arising from wavevector dependent LO phonon-plasmon coupling. The frequency of the L- branch lies between the LO and TO phonon frequencies and approaches the TO frequency asymptotically from the high-frequency side as the carrier concentration increases. This behaviour is attributed to competition between screening (dominant in the high-density limit) and large-wavevector induced decoupling. The L+ branch of the plasmon-phonon system is observed for the first time in Raman experiments with InAs.

Theory of insulator charging

Data are presented which suggest that the contact electrostatic charging of insulators occurs to neutralize an electric field created in the interface during the contact event, sometimes called the high density limit of the surface state theory. Such a theory accounts for almost all available metal-insulator and insulator-insulator electrostatic contact charging experiments.

Atomic versus ionized states in many-particle systems and the spectra of reduced density matrices: A model study

We study the spectrum of appropriate reduced density matrices for a model consisting of one quantum particle (“electron”) in a classical fluid (of “protons”) at thermal equilibrium. The quantum and classical particles interact by a shortrange, attractive potential such that the quantum particle can form “atomic” bound states with a single classical particle. We consider two models for the classical component: an ideal gas and the “cell model of a fluid.” We find that when the system is at low density the spectrum of the “electron-proton” pair density matrix has, in addition to a continuous part, a discrete part that is associated with “atomic” bound states. In the high-density limit the discrete eigenvalues disappear in the case of the cell model, indicating the existence of pressure ionization or a Mott effect according to a general criterion for characterizing bound and ionized electron-proton pairs in a plasma proposed recently by M. Girardeau. For the ideal gas model, on the other hand, eigenvalues remain even at high density.

Correlation energy of a spin-polarized electron gas at high density.

This paper extends the result of Gell-Mann and Brueckner to include spin polarization. The contributions to the correlation energy of a spin-polarized electron gas that do not vanish in the high-density limit are evaluated exactly. In the process a closed-form expression is given for the generalization of an integral that has previously been evaluated numerically.

Contact-Complex Formation Reaction between Solvent Molecules in Square-Well Fluids 1. One-Dimensional Fluid

Contact-complex formation reaction between solvent molecules in square-well fluids has been studied for the one-dimensional system. The packing effect due to the hard repulsive interaction stabilizes the contact complex, while the effect of the attractive interaction always restrains the contact-complex formation in one-dimensional fluids. The density dependence of the equilibrium constant shows an interesting behavior due to the trade-off between these two factors. When the attractive interaction is sufficiently large, the equilibrium constant may decrease with increasing density. On the other hand, the equilibrium constant of the contact-complex formation converges to that in the hard rod fluid at the high density limit. The results qualitatively agree with the findings for the solvent effects on the electron-donor-acceptor-complex formation reaction.

Investigation of hot-carrier relaxation in quantum well and bulk GaAs at high carrier densities

An investigation of the hot carrier relaxation in GaAs/(AlGa)As quantum wells and bulk GaAs in the high carrier density limit is presented. Using a time-resolved luminescence up-conversion technique with <or=80 fs temporal resolution, carrier temperatures are measured in the 100 fs to 2 ns range. The results show that hot carrier cooling in quantum wells becomes significantly slower than in the bulk for carrier densities greater than 2*1018 cm-3.

Temperature dependence of short-range correlations in the homogeneous electron gas.

The temperature-dependent behavior of short-range correlations in a homogeneous three-dimensional electron gas at finite temperatures and finite degeneracies is presented. From the physical meaning of the pair distribution function for two electrons at the same location, one would expect a function which increases monotonically with the temperature. Instead, a decrease is found for small temperatures. This effect is investigated extensively within the framework of the random-phase approximation of static-local-field-corrected approaches. Moreover, by applying first-order perturbation theory the nonmonotonic behavior is proven to appear in the high-density limit also. Using a density-functional based model for short-range correlations, a physical interpretation is obtained. Finally, the results are discussed in a comprehensive way.

Mean spherical approximation algorithm for multicomponent multi-Yukawa fluid mixtures: Study of vapor–liquid, liquid–liquid, and fluid–glass transitions

An efficient algorithm is given to find the Blum and Ho/ye mean spherical approximation (MSA) solution for mixtures of hard-core fluids with multi-Yukawa interactions. The initial estimation of the variables is based on the asymptotic high-temperature behavior of the fluid. From this initial estimate only a few Newton–Raphson iterations are required to reach the final solution. The algorithm consistently yields the unique thermodynamically stable solution, whenever it exists, i.e., whenever the fluid appears as a single, homogeneous phase. For conditions in which no single phase can appear, the algorithm will declare the absence of solutions or, less often, produce thermodynamically unstable solutions. A simple criterion reveals the instability of those solutions. Furthermore, this Yukawa-MSA algorithm can be used in a most simple way to estimate the onset of thermodynamic instability and to predict the nature of the resulting phase separation (whether vapor–liquid or liquid–liquid). Specific results are presented for two binary multi-Yukawa mixtures. For both mixtures, the Yukawa interaction parameters were adjusted to fit, beyond the hard-core diameters σ, Lennard-Jones potentials. Therefore the potentials studied, although strictly negative, included a significant repulsion interval. The characteristics of the first mixture were chosen to produce a nearly ideal solution, while those of the second mixture favored strong deviations from ideality. The MSA algorithm was able to reflect correctly their molecular characteristics into the appropriate macroscopic behavior, reproducing not only vapor–liquid equilibrium but also liquid–liquid separations. Finally, the high-density limit of the fluid phase was determined by requiring the radial distribution function to be non-negative. A case is made for interpreting that limit as the fluid–glass transition.

Exactly soluble supersymmetric t-J-type model with long-range exchange and transfer.

The Gutzwiller wave function is shown to be the exact solution of a supersymmetric t-J-type model. The model realizes a Fermi-liquid state in one dimension with a discontinuity in the momentum distribution. Analytic results are obtained for spin and charge susceptibilities, and the specific-heat coefficient with the help of the Luttinger-liquid theory. In the high-density limit the model exhibits a Mott-Hubbard gap and reduces to an antiferromagnetic spin chain with long-range exchange solved by Haldane and Shastry.

Confinement degradation and enhanced microturbulence as long-time precursors to high-density-limit tokamak disruptions.

Long-time precursors of order 5 times the global energy confinement time are observed for disrupting plasmas at the high-density limit on the Texas Experimental Tokamak. These precursors, occurring well in advance of any change in the plasma MHD activity, are reflected in the electron particle and heat transport along with the density fluctuation level. Enhanced microturbulence is proposed as the physical mechanism for the confinement degradation and subsequent disruption.

Collective modes in relativistic nuclear matter: Classical approach.

A classical relativistic approach based in the Vlasov equation is applied to the study of infinite nuclear matter. Hadronic matter couples to massive scalar and vector fields. The small-amplitude oscillations around a stationary state are studied. Orthogonality and completeness relations and the energy-weighted sum rule are obtained for the longitudinal modes. The appearance of the zero-sound mode and the distribution of the strength among the different modes are discussed. It is seen that the scalar field only couples to the low-energy excitations at high densities and for wavelengths not too long. The vector field couples strongly to the low-energy excitations. The long-wavelength limit and high-density limit are studied.

Thermonuclear reactions in dense stellar matter - Electron screening revisited

Relativistic degenerate electrons have a considerable screening effect on Coulomb repulsion between reacting nuclei even in the limit of high densities. The enhancement factor of the thermonuclear reaction rate resulting from such an electron screening is recalculated. It is shown that the enhancement is significant in high-Z materials such as carbon and oxygen at the densities near ignition. 13 refs.

Subband dependent mobilities and carrier saturation mechanisms in thin Si doping layers in GaAs in the high density limit

Shubnikov-de Haas and persistent photoconductivity measurements have been performed as a function of hydrostatic pressure to study the saturation of the free electron concentration and the mobilities of the individual subbands at high doping densities in very thin sheets (2, 5, 10 nm) of silicon donors in MBE GaAs. The samples were grown at very low temperature (400 degrees C) in order to limit dopant diffusion, and silicon concentrations were close to the solubility limit at this temperature. As has been shown previously with spike-doped GaAs(Si), the relative occupancies and the mobilities of the lower subbands are very sensitive to the spreading of the dopant distribution. A routine was developed for the analysis of the Fourier transforms of the complex pattern of Shubnikov-de Haas peaks in order to provide quantitative values for the mobilities of the individual subbands. The results of this analysis are compared with values deduced from the magnetic field dependence of the resistivity and Hall effect. On applying hydrostatic pressures of the order of 15 kbar in the dark, a decrease of the free electron concentration of a factor of two was observed. This was accompanied by an increase in the mobility of all the subbands due to the change in the charge state of the silicon donors in the doping slab. With the two thinnest slabs the mobility at ambient pressure is so low in the i=0 subband that Shubnikov-de Haas peaks from this subband could not be detected at fields up to 15 T, although strong peaks could be observed from the higher order subbands. After illumination of the thinnest sample at high pressure the measured free electron concentration is not restored to the zero pressure value. One possibility is that the missing electrons occupy a localized non-metastable Si state resonant with the conduction band rather than a DX centre. The pressure coefficient of the carrier density yields an extrapolated position for the energy level for the Si localized state of 270+or-10 meV above the Gamma -conduction band edge at ambient pressure.

Spin scaling of the electron-gas correlation energy in the high-density limit.

The ground-state correlation energy per particle in a uniform electron gas with spin densities ${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$ and ${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$ may be expressed as ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(\ensuremath{\zeta},${\mathit{r}}_{\mathit{s}}$)=I(\ensuremath{\zeta},${\mathit{r}}_{\mathit{s}}$)${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(0,${\mathit{r}}_{\mathit{s}}$), where ${\mathit{r}}_{\mathit{s}}$=[3/4\ensuremath{\pi}(${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$+${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$)${]}^{1/3}$ is the density parameter and \ensuremath{\zeta}=(${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$-${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$)/(${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$+${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$) is the relative spin polarization. We find an analytic expression for the spin-scaling factor (SSF) I(\ensuremath{\zeta},${\mathit{r}}_{\mathit{s}}$) in the high-density limit ${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0. It decreases from the value 1 at \ensuremath{\zeta}=0, approaching the value 1/2 with slope -\ensuremath{\infty} as \ensuremath{\zeta} approaches 1. A simple approximation to this SSF which displays the correct qualitative behavior is ${\mathit{g}}^{3}$(\ensuremath{\zeta}), where g(\ensuremath{\zeta})=[(1+\ensuremath{\zeta}${)}^{2/3}$+(1-\ensuremath{\zeta}${)}^{2/3}$]/2. We find that g(\ensuremath{\zeta}) is the SSF for the coefficient of the \ensuremath{\Vert}\ensuremath{\nabla}n${\mathrm{\ensuremath{\Vert}}}^{2}$/${\mathit{n}}^{4/3}$ term of the spin-density gradient expansion of the exchange energy, and a good approximation to the SSF for that of correlation: ${\mathit{scrC}}_{\mathit{x}}$(\ensuremath{\zeta})/${\mathit{scrC}}_{\mathit{x}}$(0)=g(\ensuremath{\zeta}) and ${\mathit{scrC}}_{\mathit{c}}$(\ensuremath{\zeta},${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0)/${\mathit{scrC}}_{\mathit{c}}$(0, ${\mathrm{r}}_{\mathrm{s}}$\ensuremath{\rightarrow}0)\ensuremath{\approxeq}g(\ensuremath{\zeta}). We also find that the \ensuremath{\Vert}\ensuremath{\nabla}\ensuremath{\zeta}${\mathrm{\ensuremath{\Vert}}}^{2}$ contribution to the correlation energy is always negligible.