Static Structure Function Research Articles

STRONGLY CORRELATED BOSONS AT NONZERO TEMPERATURES

We investigate the structure of strongly correlated normal Bose liquids and fluids by employing correlated density-matrix (CDM) theory, a generalization of correlated basis functions (CBF) theory to nonzero temperatures. The formalism is applied in a study of structural properties of various correlation functions that characterize the one-body and two-body reduced density matrix elements of a boson system and the associated Fourier transforms such as the static structure function, the exchange structure function, the momentum distribution, and related thermodynamic quantities. We perform a numerical analysis for liquid para-hydrogen, close to the triple point, supercritical 4 He gas at temperatures T ≥ 12 K , and fluid and liquid 4 He in the normal phase below T = 12 K . The results reveal that H 2 and 4 He , at T > 12 K , are typical quantum Boltz-mann systems following classical statistics. In contrast, liquid 4 He exhibits non-classical effects of particle exchange correlations, when the temperature is lowered toward the Bose-Einstein transition regime.

1848 臨界点近傍の流体中の揺らぎに関する分子動力学的研究(GO6-6 MD応用・伝熱応用(1),G06 熱工学)

Molecular dynamics computer simulation of pure argon fluid was performed under NTV or NEV ensemble around critical point. Macroscopic fluctuation behavior drastically changed around the critical point. Atom level density of the liquid fluctuates in space and time. Spatial fluctuation is analyzed by time averaged pair correlation function g(r) and static structure function S(q). Temporal fluctuation is done by instantaneous them. Long and medium range spatial density fluctuation shows low q correlation in S(q) profile. The fluctuation size is derived from S(q)q^<-2>.

RADIAL DISTRIBUTION AND LIQUID STRUCTURE FUNCTION FOR LIQUID PARA-HYDROGEN AT LOW TEMPERATURES

We present theoretical results for the radial distribution function g(r) and the static liquid structure function S(k) of liquid para-hydrogen at low temperatures. The results have been obtained via quantum Monte Carlo Path Integral simulations, classical Monte Carlo calculations, and correlated density matrix theory.

Homogeneous Fermi liquid with ‘artificial’ repulsive inverse square law interparticle potential energy

A good deal is known by now on the so-called jellium model of the homogeneous electron liquid. However, much of the quantitative progress at experimentally realizable densities has come from quantal computer simulation. Therefore, we here consider a homogeneous Fermion liquid with ‘artificial’ repulsive interaction λ/(rij )2 between Fermions i and j at separation rij . We discuss first of all the way the static structure function S(q), essentially the Fourier transform of the pair correlation function, is changed because of non-zero λ from the ‘Fermi hole’ form due entirely to Pauli principle effects between parallel spin Fermions. Unlike jellium with e 2/rij repulsive interactions, S(q) is proportional to q at long wavelengths, whereas the plasmon in jellium annulls the q term and S(q) is quadratic in q as q tends to zero. However for λ/(rij )2 interactions, the coefficient of q appearing in the Fermi hole structure factor, is renormalized by particle repulsions. Then some discussion is given of Fermion quasiparticle lifetimes τ as the Fermi surface is approached. Arguments are presented that τ−1 is proportional to |E − E F| as E tends to the Fermi energy. This is already interesting, in fact, in connection with the jellium model and therefore an approximate analytic form of τ is finally derived.

Equilibrium properties and phase diagram of two-dimensional Yukawa systems

Properties of two-dimensional strongly coupled Yukawa systems are explored through molecular dynamics simulations. An effective coupling coefficient gamma* for the liquid phase is introduced on the basis of the constancy of the first peak amplitude of the pair-correlation functions. Thermodynamic quantities are calculated from the pair-correlation function. The solid-liquid transition of the system is investigated through the analysis of the bond-angular order parameter. The static structure function satisfies consistency relation, attesting to the reliability of the computational method. The response is shown to be governed by the correlational part of the inverse compressibility. An analysis of the velocity autocorrelation demonstrates that this latter also exhibits a universal behavior.

Fluctuations for Kawasaki Dynamics

In this paper Kawasaki dynamics are considered. Lower bounds are obtained for the variance of the occupation time of a site in any dimension and for temperature above critical temperature. These lower bounds are expressed in terms of the density correlation function and hence relate the fluctuations to some phase transition quantities. At critical temperature, under a reasonable assumption of the static structure function, lower bounds for the variance of the occupation time are obtained. These lower bounds are consistent with the supposed value of the critical exponent. This paper also examines the same problem for Glauber dynamics and shows that the phase transition may not be of importance for the behavior of fluctuations.

Simulations of strongly coupled charged particle systems: static and dynamical properties of classical bilayers

This paper reviews our recent molecular dynamics simulation studies of the static and dynamical behaviour of classical bilayers in their liquid phase. The pair correlation functions obtained in the static calculations make it possible to trace the structural changes of the system as well as to calculate the energy and static structure functions of the bilayer. The dynamical calculations show the existence of two (in-phase and out-of-phase) longitudinal and two (in-phase and out-of-phase) transverse collective modes. We present the full dispersion relations for these modes at different layer separations. At low layer separations the out-of-phase modes are found to possess a finite frequency at wave numbers k → 0, confirming the existence of the long-wavelength energy gap in the bilayer system predicted by the quasi-localized charge approximation. It is only at higher layer separations that the dominant portion of the longitudinal out-of-phase mode is well approximated by the acoustic behaviour, resulting from the random phase approximation theory.

Multi-particle–hole excitations in many-body Fermi systems

We formulate a microscopic theory for calculating the dynamic structure function of 3 He and other strongly interacting Fermi liquids. The theory is a generalization of the correlated basis function theory for the dynamics of 4 He and includes time-dependent two-particle—two-hole excitations. It may also be interpreted as a systematic extension of the random-phase approximation (RPA). Comparison of numerical results with experiments show a significant improvement of the excitation spectrum over RPA predictions while maintaining the accuracy of prediction of ground-state quantities like the static structure function.

Charged particle layers in the Debye limit.

We develop an equivalent of the Debye-Hückel weakly coupled equilibrium theory for layered classical charged particle systems composed of one single charged species. We consider the two most important configurations, the charged particle bilayer and the infinite superlattice. The approach is based on the link provided by the classical fluctuation-dissipation theorem between the random-phase approximation response functions and the Debye equilibrium pair correlation function. Layer-layer pair correlation functions, screened and polarization potentials, static structure functions, and static response functions are calculated. The importance of the perfect screening and compressibility sum rules in determining the overall behavior of the system, especially in the r--> infinity limit, is emphasized. The similarities and differences between the quasi-two-dimensional bilayer and the quasi-three-dimensional superlattice are highlighted. An unexpected behavior that emerges from the analysis is that the screened potential, the correlations, and the screening charges carried by the individual layers exhibit a marked nonmonotonic dependence on the layer separation.

Submonolayer molecular hydrogen on graphite: A path-integral Monte Carlo study

We have used path-integral Monte Carlo (PIMC) to simulate molecular hydrogen on graphite at submonolayer coverage. First we use a flat substrate and we study the first layer for various values of the coverage up to layer completion. We found that the first layer has a solid-gas coexistence phase at low densities and a triangular solid phase at and above the equilibrium density ${\ensuremath{\rho}}_{0}=0.0705 {\AA{}}^{\ensuremath{-}2}.$ We also determine that the first layer promotion coverage is at $0.094 {\AA{}}^{\ensuremath{-}2}$ in agreement with experiment. Second we introduce the full ${\mathrm{H}}_{2}$-graphite interaction, i.e., we include the effects of substrate corrugations. In this case we carry our PIMC simulations on a variety of systems at and below the 1/3 coverage. We calculate the energy as a function of coverage, contour plots of the molecule probability distribution, the pair distribution function, the static structure function and the specific heat. When the substrate corrugation part of the interaction is included we find that at 1/3 coverage the system is in a $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ commensurate solid phase. At coverages below that and at low enough temperature the system exists in solid clusters surrounded by vapor. At coverages below a critical density, defining a tricrical point, as the system is heated up these clusters melt into a uniform fluid phase. We find that below the commensurate density and above the tricritical point, as the clusters are heated up, first they undergo a transition into a phase where the vapor phase disappears and a commensurate phase with vacancies arises. This commensurate solid melts at higher temperature into a uniform fluid phase.

CORRELATIONS AND REALISTIC INTERACTIONS IN DOUBLY CLOSED SHELL NUCLEI

We review the latest variational calculations of the ground state properties of doubly closed shell nuclei, from 12 C to 208 Pb , with semirealistic and realistic two- and three-nucleon interactions. The studies are carried on within the framework of the correlated basis function theory and integral equations technique, with state dependent correlations having central and tensor components. We report results for the ground-estate energy, one- and two-body densities and static structure functions. For 16 O and 40 Ca we use modern interactions and find that the accuracy of the method is comparable to that attained in nuclear matter with similar hamiltonians, giving nuclei underbound by ~2 MeV/A. The computed Coulomb sums are in complete agreement with the latest analysis of the experimental data.

Clusters and fluctuations at mean-field critical points and spinodals

We show that the structure of the fluctuations close to spinodals and mean-field critical points is qualitatively different from the structure close to non-mean-field critical points. This difference has important implications for many areas including the formation of glasses in supercooled liquids. In particular, the divergence of the measured static structure function in near-mean-field systems close to the glass transition is suppressed relative to the mean-field prediction in systems for which a spatial symmetry is broken.

Scattering of light and atoms in a Fermi-Dirac gas with Bardeen-Cooper-Schrieffer pairing

We theoretically study the optical properties of a Fermi-Dirac gas in the presence of a superfluid state. We calculate the leading quantum-statistical corrections to the standard column density result of the electric susceptibility. We also consider the Bragg diffraction of atoms by means of light-stimulated transitions of photons between two intersecting laser beams. Bardeen-Cooper-Schrieffer pairing between atoms in different internal levels magnifies incoherent scattering processes. The absorption linewidth of a Fermi-Dirac gas is broadened and shifted. Bardeen-Cooper-Schrieffer pairing introduces a collisional local-field shift that may dramatically dominate the Lorentz-Lorenz shift. For the case of the Bragg spectroscopy the static structure function may be significantly increased due to superfluidity in the near-forward scattering.

Diplons in the degenerate regime: exchange and correlation effects

We study the exchange and correlation effects on the ground-state properties of dipolar complexes (diplons) formed by the surface electrons on a liquid helium film and positive ions in the substrate supporting the helium film. We use the self-consistent-field approximation including the short-range correlations. The local-field correction, static structure function, exchange and correlation energies, and collective mode dispersions are calculated for systems with different substrates.

THE TRANSVERSE ISING MODEL BY CBF

The method of correlated basis functions (CBF) is applied at the variational level to the transverse Ising model in two and three spatial dimensions (D=2,3). The model consists of Pauli spins arranged on a simple square or cubic lattice, experiencing nearest-neighbor interactions through their x components and subject to a transverse field in the z direction of strength λ. Working at zero temperature, full optimization of a Hartree-Jastrow trial wave function is performed by solving two Euler-Lagrange equations, namely a renormalized Hartree equation for the order parameter characterizing the ferromagnetic phase and a paired-magnon equation for the optimal two-spin spatial distribution function. The optimized trial wave function yields a second-order transition with a numerically determined critical coupling of λc=3.14(D=2) or λc= 5.10(D=3). Numerical results have been obtained for the magnetization order parameter, the energy per spin and its potential component, the static structure function at zero wave number, and the magnon energy gap corresponding to a Feynman description of the elementary excitations. Correlated density matrix theory provides for a natural extension of this approach to finite temperature.

Fermi-fluid description of the half-filled Landau level

We present a many-body approach to calculate the ground state properties of a system of electrons in a half-filled Landau level. Our starting point is a simplified version of the recently proposed trial wave function where one includes the antisymmetrization operator to the bosonic Laughlin state. Using the classical plasma analogy, we calculate the pair-correlation function, the static structure function and the ground state energy in the thermodynamic limit. These results are in good agreement with the expected behavior at $\nu=\frac12$.

Transverse Ising model at zero temperature

The method of correlated basis functions is applied at the variational level to the Ising model consisting of Pauli spins arranged on a simple cubic lattice, experiencing nearest-neighbor interactions through their $x$ components and subject to a transverse field in the $z$ direction of strength $\ensuremath{\lambda}$. Full optimization of a Hartree-Jastrow trial wave function is performed by solving two Euler-Lagrange equations: a renormalized Hartree equation for the order parameter characterizing the ferromagnetic phase and a paired-magnon equation for the optimal two-spin spatial distribution function. The optimized trial wave function yields a second-order transition with a numerically determined critical coupling of ${\ensuremath{\lambda}}_{c}=5.10$. Explicit results are presented for (i) the magnetization order parameter, (ii) the energy per spin and its potential component, (iii) the static structure function at zero wave number, (iv) the spin-exchange strength, and (v) the magnon energy gap corresponding to a Feynman description of the elementary excitations.

Hypernetted-chain treatment and the extended shadow wave functions for fractional quantum Hall hierarchical states

The hypernetted-chain theory is applied to study hierarchical states in the fractional quantum Hall effect. It is noted that a class of wave functions introduced by Girvin [Phys. Rev. B 29, 6012 (1984)] and MacDonald, Aers, and Dharma-wardana [Phys. Rev. B 31, 5529 (1985)], based on charge-conjugation procedures, is of the extended shadow wave-function type. The correlation energy, pair distribution function, and static structure function have been calculated in the thermodynamic limit at various filling factors. The results obtained agree with those of previous calculations performed with a finite number of electrons.

Thermodynamics of boson quantum films

Theoretical studies of films of liquid $^{4}\mathrm{He}$ adsorbed to strongly attractive plane substrates indicate that the growth of such films occurs through a sequence of first-order phase transitions --- ``layering transitions'' --- which are a direct consequence of the short-range, hard-core-like interaction between individual helium atoms. The present work examines the effects of temperature on these transitions. At given temperatures, the spinodal points and phase coexistence boundaries are determined for the transitions. Increasing the temperature tends to decrease the coverage span of the transition regions, signaling the possible existence of a critical point terminating the two-phase equilibrium. The layering transitions depend strongly on the helium-substrate potential; the longer-range helium-magnesium potential yields fewer transitions and noticeably lower transition temperatures than the helium-graphite potential. The temperature dependence of the chemical potential, third sound, static structure function, heat capacities, and superfluid densities are reported. The heat capacities are compared to those measured by Greywall and Busch [Phys Rev. Lett. 67, 3535 (1991)]. The thermal broadening of the film's density profile is also discussed. We find that below 1.2 K, thermal broadening is quite weak for coverages away from the layering transitions. The monolayer film experiences the least broadening whereas double-layer and triple-layer films broaden by increasing the local density in the outer tail of their density profiles, while depleting the local density in the inner portion of the outermost layer.

Structure function of polymer nematic liquid crystals:mA Monte Carlo simulation

We present a Monte Carlo simulation of a polymer nematic liquid crystal for varying volume fractions, concentrating on the structure function of the sample. We achieve nematic ordering with stiff polymers made of spherical monomers that would otherwise not form a nematic state. Our results are in good qualitative agreement with theoretical and experimental predictions, most notably the bowtie pattern in the static structure function.