High-density Limit Research Articles

Bounded soft-sphere fluids by molecular dynamics and integral equation techniques

The structural properties are determined for fluids composed of particles interacting with the Bounded Soft-sphere (BSS) potential, V(r) = εσ 2 n /(a 2 + r 2) n , where a is a variable parameter, r is the separation between the particle centres, n is an integer exponent, and ε and σ, respectively, set the energy and length scales of the potential. The density and temperature dependence of the radial distribution function, g(r), of the BSS fluid have been calculated using Molecular Dynamics (MD) simulation and by numerical solution of the Ornstein–Zernike (OZ), integral equation with various closures. Comparisons with the Gaussian Core Model (GCM) potential fluid are also made. As previously found for the GCM, the Hypernetted Chain (HNC) closure of the OZ equation reproduces the MD g(r) very well over essentially the complete fluid range. Another integral equation approach, which we call the Mean Field Approximation (MFA), is applied and gives comparable accuracy to the HNC OZ closure for not too high values of the potential at the origin. Part of the equation of state of these fluids is computed and the exact low and high density limits determined. It is shown that the BSS and GCM fluids in the high density limit are far less compressible than the ideal gas at the same density and temperature.

Zero energy of plane-waves for ELKOs

We consider the ELKO field in interaction through contorsion with its own spin density, and we investigate the form of the consequent autointeractions; to do so we take into account the high-density limit and find plane wave solutions: such plane waves give rise to contorsional autointeractions for which the Ricci metric curvature vanishes and therefore the energy density is equal to zero identically. Consequences are discussed.

Anomalous reflection properties in high density limit fibril shaped PIC‐J aggregates in microcavity structure

AbstractWe report our recent observations on anomalous reflection properties of organic microcavity containing PIC J‐aggregates in fibril‐shaped structures as one of their highest‐density limiting case. Even in ordinary low density PIC‐Js dispersed in polymer matrices, they easily go into the exciton‐photon strong coupling regime and new quantum states, i.e. exciton‐polaritons, are formed. Vacuum Rabi‐splitting, an indicator of the coupling strength, can be controlled by the density of PIC‐Js in the microcavities in low density regime. Fibril‐shaped PIC‐J aggregates are bundle‐like, self‐assembled higher‐order structure of Js and are considered as a high‐density limiting case. Angular dependence of the local reflection spectra are observed by our improved microscopy. While in the low density cases, clear anti‐crossing behaviours of the two branches appear, which is the evidence of the polariton formations, the highest‐density limiting cases show one or two anomalous reflection dip structures with almost no angular dependence. The result is inconsistent with neither ordinary polariton reflection property nor bare exciton nor cavity photon properties. We tentatively consider that the anomaly is inherent to the fibril formation and is caused by possible breakdown of polariton coherence due to the inter‐fiber energy transfer. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

From exciton to photon condensation via polariton in electron-holephoton systems

We present a unified theoretical description of the quantum condensates in the electron-hole-photon (ehp) systems, which covers all condensates of exciton, polariton, and photon. To build such model, a phenomenological mean-field treatment for the exciton condensation is employed and extended to include the photon degree of freedom. We clarify changes from exciton/polariton condensations in the low-density limit to photon condensation in the high-density limit as a function of the detuning and the density. Clear change in the microscopic quantities are also found; the carrier distribution function shows broadening in the momentum space, and the minimal excitation energy for breaking an electron-hole (eh) pair increases even in the high density limit. Along this change, relative motion of electron and hole is confined within a tiny radius. In other words, the Wannier-type exciton-polariton picture is replaced by the Frenkel-type. This indicates that the smallest length scale of the system (corresponding to some ultraviolet cutoff) plays important roles due to the presence of coupling between carriers and coherent photons. These features show a remarkable contrast from the scenario of BEC-BCS crossover in the eh systems.

Demonstration of Intrinsic Tristability in Double-Barrier Resonant Tunneling Diodes With the Wigner Transport Equation

The operation of double-barrier resonant tunneling diodes (RTDs) is investigated through self-consistent numerical solution of the Wigner transport equation. Prevalent boundary conditions are demonstrated to lead to unphysical boundary layers in electrostatically self-consistent calculations. New boundary conditions based on nonequilibrium statistics are proposed and validated. Unphysical solutions are also associated with the application of the popular Boltzmann collision operator in the limit of high electron density. An original formulation of the collision operator in the relaxation time approximation is proposed leading to proper asymptotic behavior in both limits of the relaxation time. Coupled solutions of the Wigner transport equation and the Poisson equation for an RTD structure reveal current to be a continuous but multivalued function of applied bias and tristability to be an intrinsic property of device operation.

BCS Wave-Function Approach to the BEC-BCS Crossover of Exciton-Polariton Condensates

The crossover between low and high density regimes of exciton-polariton condensates is examined using a BCS wave-function approach. Our approach is an extension of the BEC-BCS crossover theory for excitons, but includes a cavity photon field. The approach can describe both the low density limit, where the system can be described as a Bose-Einstein condensate (BEC) of exciton-polaritons, and the high density limit, where the system enters a photon-dominated regime. In contrast to the exciton BEC-BCS crossover where the system approaches an electron-hole plasma, the polariton high density limit has strongly correlated electron-hole pairs. At intermediate densities, there is a regime with BCS-like properties, with a peak at nonzero momentum of the singlet pair function. We calculate the expected photoluminescence and give several experimental signatures of the crossover.

The high‐density electron gas: How momentum distribution n (k) and static structure factor S(q) are mutually related through the off‐shell self‐energy Σ (k, ω)

AbstractFor the spin‐unpolarized uniform electron gas, rigorous theorems are used (Migdal, Galitskii‐Migdal, Hellmann‐Feynman) which allow the calculation of the pair density, g(r), or equivalently its Fourier transform, the static structure factor, S(q), from the dynamical 1‐body self‐energy Σ (k, ω), supposing the self‐energy is (approximately) known as a functional, depending on the kinetic energy of a single electron, t(k), and on the bare Coulomb repulsion between two electrons, v(q). With the momentum distribution, n(k), and with the kinetic (t) and potential (v) components of the total energy e = t + v, the respective steps are: (i) Σ (k, ω) → n(k) → t, (ii) Σ (k, ω) → v, (iii) t + v = e→ S(q). How this general scheme works in detail is shown explicitly for the high‐density limit (as an illustration). For this case the ring‐diagram partial summation or random‐phase approximation applies. In this way, the results of Macke (1950), Gell‐Mann/Brueckner (1957), Daniel/Vosko (1960), Kulik (1961), and Kimball (1976) are summarized in a coherent manner. Besides, several identities were brought to the light, e.g. the Kimball function for S(q) proves to be identical with Macke's momentum transfer function I(q) for e.

Shock Compression of a Fifth Period Element: Liquid Xenon to 840 GPa

Current equation of state (EOS) models for xenon show substantial differences in the Hugoniot above 100 GPa, prompting the need for an improved understanding of xenon's behavior at extreme conditions. We performed shock compression experiments on liquid xenon to determine the Hugoniot up to 840 GPa, using these results to validate density functional theory (DFT) simulations. Despite the nearly fivefold compression, we find that the limiting Thomas-Fermi theory, exact in the high density limit, does not accurately describe the system. Combining the experimental data and DFT calculations, we developed a free-energy-based, multiphase EOS capable of describing xenon over a wide range of pressures and temperatures.

Wormlike Polymer Brush: A Self-Consistent Field Treatment

We investigate a homopolymer brush system on the basis of the wormlike-chain model, incorporating an Onsager-type interaction between polymer segments in the excluded-volume interaction. The model depends on the ratio between the total polymer length and the persistent length and a reduced grafting density as two basic parameters. Our numerical solutions to the self-consistent field theory are compared with scaling properties that can be deduced in various limits. In the limit of long chain and weak-to-moderate grafting density, our numerical results follow the scaling power law predicted by the classical-trajectory theory of a flexible polymer brush. In the limit of long chain and high grafting density, our numerical results show that the brush properties are comparable to the conformational properties of a nematic wormlike solution. In the limit of rod brush, our numerical results are consistent with the solution of a trial-function treatment from a previous mean-field theory.

Correlation energy of the uniform electron gas from an interpolation between high- and low-density limits

We show that known or knowable information about the high-$({r}_{s}\ensuremath{\rightarrow}0)$ and low-density $({r}_{s}\ensuremath{\rightarrow}\ensuremath{\infty})$ asymptotes can be used to predict the correlation energy per electron, ${e}_{c}({r}_{s},\ensuremath{\zeta})$, of the three-dimensional uniform gas over the whole range of the density parameter $(0\ensuremath{\le}{r}_{s}l\ensuremath{\infty})$ and relative spin polarization $(0\ensuremath{\le}|\ensuremath{\zeta}|\ensuremath{\le}1)$, without quantum Monte Carlo or other input. For $\ensuremath{\zeta}=0$, the high-density limit through order ${r}_{s}$ is known exactly from many-body perturbation theory, and for all $\ensuremath{\zeta}$, the low-density limit through order $1/{r}_{s}^{2}$ is known accurately from a simple, intuitive, and accurate model. We propose a single interpolation formula with the expected analytic structure to all orders in both limits, and use it to predict ${e}_{c}({r}_{s},0)$ in excellent agreement with quantum Monte Carlo data. For $|\ensuremath{\zeta}|g0$, we derive the $\ensuremath{\zeta}$ dependence of the coefficient ${a}_{1}(\ensuremath{\zeta})$ of the ${r}_{s}\text{ }\text{ln}\text{ }{r}_{s}$ term, previously known only for $|\ensuremath{\zeta}|=0$ and 1. For ${b}_{1}(\ensuremath{\zeta})$, the coefficient of the ${r}_{s}$ term (not yet derived for $\ensuremath{\zeta}\ensuremath{\ne}0$), we approximately extend the known ${b}_{1}(0)$ by using a simplification of the available quantum Monte Carlo information that replaces the second-order transition over $50l{r}_{s}l100$ by a sudden transition to full spin polarization at ${r}_{s}=75$.

Bulk viscosities of a cold relativistic superfluid: Color-flavor locked quark matter

We consider the phonon contribution to the bulk viscosities ${\ensuremath{\zeta}}_{1}$, ${\ensuremath{\zeta}}_{2}$ and ${\ensuremath{\zeta}}_{3}$ of a cold relativistic superfluid. We assume the low temperature $T$ regime and that the transport properties of the system are dominated by the phonons. We use kinetic theory in the relaxation time approximation and the low energy effective field theory of the corresponding system. The parametric dependence of the bulk viscosity coefficients is fixed once the equation of state is specified, and the phonon dispersion law to cubic order in momentum is known. We first present a general discussion, valid for any superfluid, then we focus on the color-flavor locked superfluid because all the parameters needed in the analysis can be computed in the high density limit of QCD, and also because of the possible astrophysical applications. For the three independent bulk viscosity coefficients we find that they scale with the temperature as ${\ensuremath{\zeta}}_{i}\ensuremath{\sim}1/T$, and that in the conformal limit only the third coefficient ${\ensuremath{\zeta}}_{3}$ is nonzero.

Searching for partially reactive sites: Analytical results for spherical targets

How do single or multiple (sub)diffusing particles search for a target with a partially reactive boundary? A finite reaction rate which is typical for many chemical or biochemical reactions is introduced as the possibility for a particle to find a target but not to "recognize" it. The search is not finished until the target is found and recognized. For a single searching particle, the short- and long-time regimes are investigated, with a special focus on comparison between perfectly and partially reactive boundaries. For multiple searching particles, explicit formulas for the probability density of the search time are given for subdiffusion in one and three dimensions. The dependence of the mean search time on the density of particles and the reaction rate is analyzed. Unexpectedly, in the high density limit, the particles undergoing slower subdiffusive motion find a target faster.

Experimental Confinement Studies Beyond ITER

The advantages of stellarators are discussed with an emphasis on the high density limit more than 10 times higher than that of tokamaks with the equivalent magnetic field strength. The comparison between stellerators and tokamaks in the light of the new paradigm of plasma turbulence and zonal flows is presented to propose a new optimization principle of magnetic field configuration. The roles of low-temperature devices should be recognized for further understanding of the plasma confinement even in the era of burning state plasmas

Correlation energy of two electrons in the high-density limit

We consider the high-density-limit correlation energy E(c) in D > or = 2 dimensions for the (1)S ground states of three two-electron systems: helium (in which the electrons move in a Coulombic field), spherium (in which they move on the surface of a sphere), and hookium (in which they move in a quadratic potential). We find that the E(c) values are strikingly similar, depending strongly on D but only weakly on the external potential. We conjecture that for large D, the limiting correlation energy E(c) approximately -delta(2)/8 in any confining external potential, where delta = 1/(D-1).

On the lower bound on the exchange-correlation energy in two dimensions

We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature.

When does static correlation scale to the high-density limit as exchange does?

In density functional theory, the exchange–correlation energy is usually decomposed as the sum of exchange and correlation contributions. In the absence of static correlation, this decomposition can be made by uniform coordinate scaling to the high-density limit, because the exchange part dominates in this limit. The estimate of static correlation provided by semilocal, global hybrid, and some more-advanced approximate exchange–correlation functionals scales up as exchange does in this limit. Here we argue that a proper estimate of static correlation should scale up in magnitude less strongly than exchange in the high-density limit, except in special circumstances. Such a special circumstance can occur when there is an exact degeneracy at the non-interacting Fermi level, or when another limit is taken first, in which a degeneracy develops between occupied and unoccupied Kohn–Sham orbital energies. Examples of the latter case are the H 2 molecule as the bond length is stretched to infinity, and the four-electron atomic ion as the nuclear charge tends to infinity.

PRIMORDIAL NON-GAUSSIANITY, SCALE-DEPENDENT BIAS, AND THE BISPECTRUM OF GALAXIES

The three-point correlation function of cosmological fluctuations is a sensitive probe of the physics of inflation. We calculate the bispectrum, Bg(k1, k2, k3), Fourier transform of the three-point function of density peaks (e.g., galaxies), using two different methods: the Matarrese–Lucchin–Bonometto formula and the locality of galaxy bias. The bispectrum of peaks is not only sensitive to that of the underlying matter density fluctuations, but also to the four-point function. For a physically motivated, local form of primordial non-Gaussianity in the curvature perturbation, Φ = ϕ + fNLϕ2 + gNLϕ3, where ϕ is a Gaussian field, we show that the galaxy bispectrum contains five physically distinct pieces: (1) non-linear gravitational evolution, (2) non-linear galaxy bias, (3) fNL, (4) f2NL, and (5) gNL. While (1), (2), and a part of (3) have been derived in the literature, (4) and (5) are derived in this paper for the first time. We also find that, in the high-density peak limit, (3) receives an enhancement of a factor of ∼15 relative to the previous calculation for the squeezed triangles (k1 ≈ k2 ≫ k3). Our finding suggests that the galaxy bispectrum is more sensitive to fNL than previously recognized, and is also sensitive to a new term, gNL. For a more general form of local-type non-Gaussianity, the coefficient f2NL can be interpreted as τNL, which allows us to test multi-field inflation models using the relation between the three- and four-point functions. The usual terms from Gaussian initial conditions, (1) and (2), have the smallest signals in the squeezed configurations, while the others have the largest signals; thus, we can distinguish them easily. We cannot interpret the effects of fNL on Bg(k1, k2, k3) as a scale-dependent bias, and thus replacing the linear bias in the galaxy bispectrum with the scale-dependent bias known for the power spectrum results in an incorrect prediction. As the importance of primordial non-Gaussianity relative to the non-linear gravity evolution and galaxy bias increases toward higher redshifts, galaxy surveys probing a high-redshift universe are particularly useful for probing the primordial non-Gaussianity.

Ground state energy of spin polarized quark matter with correlation

We calculate the ground-state energy of cold and dense spin-polarized quark matter with corrections due to correlation energy $({E}_{\mathrm{corr}})$. Expressions for ${E}_{\mathrm{corr}}$ both in the nonrelativistic and ultrarelativistic regimes have been derived and compared with the exchange and kinetic term present in the perturbation series. It is observed that the inclusion of correlation energy does not rule out the possibility of the ferromagnetic phase transition at low density within the model proposed by Tatsumi [Phys. Lett. B489, 280 (2000)]. We also derive the spin stiffness constant in the high-density limit of such a spin-polarized matter.

Structural, continuity, and asymptotic properties of a branching particle system

We delineate a connection between the stochastic evolution of the cluster structure of a specific branching–diffusing particle system and a certain previously unknown structure-invariance property of a related class of distributions. Thus, we demonstrate that a Polya–Aeppli sum of i.i.d.r.v.’s with a common zero-modified geometric distribution also follows a Polya–Aeppli law. The consideration of these classes is motivated by and applied to studying subtle properties of this branching–diffusing particle system, which belongs to the domain of attraction of a continuous Dawson–Watanabe superprocess. We illustrate this structure-invariance property by considering the Athreya–Ney-type representation of the cluster structure of our particle system. Also, we apply this representation to prove the continuity in mean square of a related real-valued stochastic process. In contrast to other works in this field, we impose the condition that the initial random number of particles follows a Polya–Aeppli law – a condition that is consistent with stochastic models that emerge in such varied fields as population genetics, ecology, insurance risk, and bacteriophage growth. Our results extend some recent work of Vinogradov. Specifically, we resolve the issue of noninvariance of the initial field and manage to avoid related anomalies that arose in earlier studies. Also, we demonstrate that under natural additional assumptions, our particle system must have evolved from a scaled Poisson field starting at a specified time. In some sense, this result provides a partial justification for assuming that the system had originated at a certain time in the past from a Poisson field of particles. We demonstrate that the corresponding high-density limit of our branching–diffusing particle system inherits an analogous backward-evolution property. Several of our results illustrate a general convergence theorem of Jorgensen et al. to members of the power-variance family of distributions. Finally, combining a Poisson mixture representation for the branching particle system considered with certain sharp analytical methods gives us an explicit representation for the leading error term of the high-density approximation as a linear combination of related Bessel functions. This refines a theorem of Vinogradov on the rate of convergence.

Spin resolved energy parametrization of a quasi-one-dimensional electron gas

By carrying out extensive lattice regularized diffusion Monte Carlo calculations, we study the spin and density dependence of the ground-state energy for a quasi-one-dimensional electron gas, with harmonic transverse confinement and long-range 1/r interactions. We present a parametrization of the exchange–correlation energy suitable for spin density functional calculations, which fulfils exact low and high density limits.