Correlation Hole Research Articles

Exchange-enhanced energy shifts in the polarized photoluminescence of a two-dimensional hole system in the integer quantum Hall regime

Polarized photoluminescence spectroscopy studies have been performed on two-dimensional hole systems in GaAs-(Al,Ga)As one-side modulation-doped quantum wells in the integer quantum Hall effect regime. Energy shifts of the photoluminescence are observed at integer filling factors. For v≥2, the energies of the photoluminescence in the right- and left-circular polarizations are almost equal near even filling factors and maximally separated near odd filling factors. This behavior is attributed to a combination of many-body effects in the screening of the correlation hole of the photoexcited electrons and an exchange-enhanced Zeeman splitting at odd filling factors. At v= 1 upward energy shifts are seen in both polarizations: in contrast to the behavior at other odd filling factors, the transition energies in the two polarizations are almost equal instead of being maximally separated. This is attributed to the occurrence of filling factor v= 1 in a region of magnetic field where there is strong mixing of the heavy-hole and light-hole states.

Two interacting electrons confined within a sphere: An accurate solution

We present highly accurate configuration interaction results for two nonrelativistic electrons confined within a sphere and interacting via a Coulomb force. In such a system, the radius of the sphere R can be considered as a measure of the strenght of the electronic repulsion. So, distinct correlation regimes, from the noninteracting limit to a high correlated regime, can be achieved by varying R. The results clearly show how very high correlation effects might appear in the system. Energies, density distributions, conditional probabilities and the exchange–correlation hole have been evaluated for different values of R. The essentially exact results here presented can be used as benchmarks for new exchange–correlation functionals and/or other approximate methods.

Small-Angle Neutron Scattering Analysis of Blends with Very Strong Intermolecular Interactions: Polyamide/Ionomer Blends

Partially miscible blends of the lithium salt of sulfonated polystyrene ionomer (Li−SPS) and a methylated polyamide (mPA) were studied using small-angle neutron scattering. The blends exhibit lower critical solution temperature behavior (LCST), and the LCST increases with increasing sulfonation level of the ionomer. When the sulfonation level of the ionomer was below 20 mol %, a peak was observed in the scattering structure factor. The position of the peak moved to lower wavevector with increasing sulfonation level and with increasing temperature. The origin of the peak was a correlation hole due to the essential formation of a graft copolymer by the formation of an ion−dipole complex between the amide and sulfonate groups. The tendency of the unsulfonated polystyrene to phase separate from the polyamide was suppressed by the complexation, but it also produced large concentration fluctuations in the blends. The size and intensity of the concentration fluctuations increased with increasing temperature, i.e...

Exactly solvable model of three interacting particles in an external magnetic field

The quantum mechanical problem of three identical particles, moving in a plane and interacting pairwise via a spring potential, is solved exactly in the presence of a magnetic field. Calculations of the pair--correlation function, mean distance and the cluster area show a quantization of these parameters. Especially the pair-correlation function exhibits a certain number of maxima given by a quantum number. We obtain Jastrow pre-factors which lead to an exchange correlation hole of liquid type, even in the presence of the attractive interaction between the identical electrons.

Dynamical properties of the slithering-snake algorithm: a numerical test of the activated-reptation hypothesis.

Correlations in the motion of reptating polymers in a melt are investigated by means of Monte Carlo simulations of the three-dimensional slithering-snake version of the bond-fluctuation model. Surprisingly, the slithering-snake dynamics becomes inconsistent with classical reptation predictions at high chain overlap (created either by chain length N or by the volume fraction phi of occupied lattice sites), where the relaxation times increase much faster than expected. This is due to the anomalous curvilinear diffusion in a finite time window whose upper bound tau+(N) is set by the density of chain ends phi/N. Density fluctuations created by passing chain ends allow a reference polymer to break out of the local cage of immobile obstacles created by neighboring chains. The dynamics of dense solutions of "snakes" at t<<tau+ is identical to that of a benchmark system where all chains but one are frozen. We demonstrate that the subdiffusive dynamical regime is caused by the slow creeping of a chain out of its correlation hole. Our results are in good qualitative agreement with the activated-reptation scheme proposed recently by Semenov and Rubinstein (Eur. Phys. J. B, 1 (1998) 87). Additionally, we briefly comment on the relevance of local relaxation pathways within a slithering-snake scheme. Our preliminary results suggest that a judicious choice of the ratio of local to slithering-snake moves is crucial to equilibrate a melt of long chains efficiently.

A new correlation functional based on a transcorrelated Hamiltonian

We propose a new correlation functional based on a transcorrelated Hamiltonian that uses an exponential correlation factor. In our approach, electron–electron correlation effects are not calculated directly but are incorporated into an effective kinetic contribution. Our new functional reproduces accurate correlation energies for H–Ar atoms reasonably well. In order to investigate the behavior of this functional, we have also studied the correlation holes of He and Hooke atoms in detail.

Two interacting electrons in a spherical box: An exact diagonalization study

We study a system of two electrons interacting with a Coulomb potential in a sphere of radius R, bounded by an infinite wall using exact diagonalization. We have also investigated the influence of an additional parabolic potential (of strength $k)$ arising from a uniform background smeared throughout the sphere. The convergence of the ground state energy of the singlet spin state of the system is investigated as a function of sphere size (essentially ${r}_{s},$ the Wigner--Seitz density parameter) for cases where there is no background potential $(k=0)$ and for when $k\ensuremath{\ne}0.$ With $k=0$ and small ${r}_{s},$ we observe a maximum in the ground state density at the origin of the sphere. At ${r}_{s}\ensuremath{\approx}8\mathrm{a}.\mathrm{u}.,$ the ground state density acquires a minimum at the origin. For this and larger systems we identify the formation of a ``Wigner'' molecule state. We further investigate the ground state density as a function of k and also the correlation hole density as a function of ${r}_{s}$ and k. We invert the Kohn--Sham equation for a two electron system and calculate the local effective potential and correlation potential (to within an additive constant) as functions of the radial coordinate for a number of values of ${r}_{s}$ and k.

Relaxation of entangled model H-shaped polymers: a SANS investigation

This study is related to the understanding of rheology of long-chain branched polymers. A model compound for long-chain branching (H-shaped architecture) was investigated in elongational flow as a function of time after a step strain to λ=2. The experiments were performed in a strain rig with temperature and strain-rate control. The structure factor was measured after specific relaxation times intimately connected to the microscopic hierarchy of the polymer structure. The correlation hole effect and the quenched disorder in the scattering were described in a random phase approximation approach. This approach, already used for permanent rubber-elastic networks, has been modified to permit the observation of strain locally along the faster-relaxing arms. The data roughly follow the time scale of linear-shear rheology from which shift factors were derived. They confirm that bridge and arm relaxations can be treated in a decoupled, hierarchical way in time, although details of the analysis remain unsolved.

Exchange‐correlation energies and correlation holes for some two‐ and four‐electron atoms along a nonlinear adiabatic connection in density functional theory

AbstractThe adiabatic connection procedure of density functional theory has been applied to two‐ and four‐electron atomic systems by following a nonlinear path that leads from the noninteracting Kohn–Sham reference system to the physical one. We have calculated the exchange and correlation energies as the interaction strength is increased, as well as the densities of the corresponding correlation holes. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Kinetic energy as functional of the correlation hole

Using the marginal decomposition of the many-body probability distribution the electronic kinetic energy is expressed as the functional of the electron density and correlation hole. The analysis covers both the molecule as a whole and its constituent subsystems. The importance of the Fisher information for locality is emphasized.

Evolution ofν=1bilayer quantum Hall ferromagnet

The natures of the ground state in a ${\ensuremath{\nu}}_{T}=1$ bilayer quantum Hall system at a variety of layer spacing are investigated. At small layer separations the system exhibits spontaneous interlayer phase coherence. It is claimed that the Halperin's (1,1,1) state is not relevant in the incompressible regime near the incompressible to compressible transition point in which the Josephson-like effect was observed. The two-particle correlation function shows the deflated correlation hole at this regime. An effective model that can give a good approximation to the ground state is proposed. A connection to the modified composite fermion theory is discussed.

An in situ rheological and SANS investigation of the crosslinking reaction of polyisoprene and dicumyl peroxide

The crosslinking reaction of polyisoprene with the radical forming dicumyl peroxide (DCP) is studied in an in situ small angle neutron scattering study and a transient dynamical mechanical experiment in shear on an isotopic HDH triblock copolymer. Both experiments are closely identical in time as well as temperature profile which was chosen to simulate typical conditions of peroxide crosslinking. Oscillatory shear data provided typical, easily amenable parameters which were physically probed at the molecular level by the parallel SANS experiment. A scissioning side reaction as proposed earlier was confirmed in detail. No sign of this chain degradation could be detected in the rheological response except for times exceeding the typical reaction time. The data agree with a theoretical description in the random phase approximation for the formed networks, necessary to describe the quenched correlation hole effect due to the crosslinking reaction of the triblock copolymer.

Particle-Flux Separation and Quasi-excitations in Quantum Hall Systems

The quasiexcitations of quantum Hall systems at the filling factor $\nu = p/(2pq \pm 1)$ are studied in terms of chargeon and fluxon introduced previously as constituents of an electron at $\nu = 1/2$. At temperatures $T < T_{\rm PFS}(\nu)$, the phenomenon so-called particle-flux separation takes place, and chargeons and fluxons are deconfined to behave as quasiparticles. Bose condensation of fluxons justify the (partial) cancellation of external magnetic field. Fluxons describe correlation holes, while chargeons describe composite fermions. They contribute to the resistivity $\rho_{xy} = h/(\nu e^2)$ additively.

Self-Assembly in the Bulk Complexes of Poly(ethylene oxide) with Amphiphilic Dodecylbenzenesulfonic Acid

We studied the self-assembly behavior in the bulk complexes of poly(ethylene oxide) (PEO) with an amphiphilic dodecylbenzenesulfonic acid (DBSA) formed through hydrogen bonding. In the hydrate state, PEO−DBSA complexes self-organized into a lamellar morphology consisting of alternating stacks of polar and nonpolar layers. The interlamellar distance increased with decreasing binding fraction of DBSA due to increasing inclusion of unbound monomer units into the polar layers. In the disordered state the comblike structure persisted and a “correlation hole” peak was present in the corresponding small-angle X-ray scattering (SAXS) profile. Complexation with PEO greatly promoted the thermal stability of the mesophase and the dynamics of mesophase formation as compared with those in pure DBSA. The faster mesophase formation in the complexes was proposed to stem from the higher isotropization temperature as well as the existence of comblike structure in the disordered melt.

Chain conformations and correlations in thin polymer films: A Monte Carlo study

Using Monte Carlo simulations of a coarse grained lattice model, we study conformations and concentration fluctuations of polymers confined into thin films. We vary the chain length from N=32 to 512. As we reduce the film thickness to the unperturbed radius of gyration Rg, the chain extension parallel to the surface increase only by about 5% for the largest chain length. Confinement has, however, a much more pronounced effect on intra- and intermolecular correlations: the surfaces make the chain fold back into the volume it occupies and squeeze out neighboring chains. Decreasing the film thickness, we reduce the interdigitation of chains. This gives rise to deviations from the ideal Gaussian chain structure for wave vectors qRg&amp;gt;1, which are qualitatively similar to corrections observed in semidilute (bulk) solutions. Fitting the structure factor with a Debye function in this Kratky regime, we systematically overestimate the chain extension by up to 15%. Additional (minor) deviations from the incompressible random phase approximation at large wave vectors are found. As we reduce the film thickness the correlation function of the centers of mass develops a very strong correlation hole and resembles in thin films that of a two-dimensional fluid of soft particles.

A new correlation functional based on analysis of the Colle–Salvetti functional

The behavior of the Colle–Salvetti (CS) correlation functional based on the Hartree–Fock (HF) second-order density matrix is investigated in the case of the He atom. The analysis of the correlation hole and energy contributions show that correlation effects are not taken into account appropriately due to the missing kinetic correlation. The CS final simplified energy expression also has some problems. To address these problems, we have constructed a new correlation functional based on the HF second-order density matrix including the effects of not only electron–electron interaction but also the kinetic energy by using an adiabatic connection formula. In addition, correlation effects for opposite and parallel spins are treated independently. This functional reproduces accurate correlation energies for H–Ar atoms. Combining it with the Becke 1988 exchange functional, we get reasonable atomization energies for the G2 set.

A dynamical correlation functional

The purpose of this work is to search for a justifiable form for a molecular dynamic correlation functional. A detailed examination of Colle and Salvetti’s derivation of the LYP functional is presented. It is argued that the leading term is all important, and furthermore that it should account for αβ correlation. This term only depends upon the densities, and it has a truncation factor which is obtained from the size of the correlation hole. It is −c∫ραρβ/(ρ(1+dρ−1/3))dr. It reproduces the αβ correlation energies of (He–Ar) to a very high accuracy. The correlation functional which represents σσ correlation is more complex, because the two particle Hartree–Fock density matrix is zero at electron coalescence. The functional must therefore depend upon (∇ρ)2. Using these and related arguments we have found a four parameter generalized gradient functional which appears to perform nearly as well as the LYP functional. However unlike the LYP functional, it has two identifiable terms for αβ correlation, and two identifiable terms for σσ correlation. Together with our previously derived exchange functional, we have therefore obtained an exchange-correlation functional for molecular studies, the form for which can be more understandably justified. The performance of this new Generalized Gradient Approximation functional for molecular predictions is reported. It is a considerable improvement on the BLYP functional, and is in the category of an optimum Generalized Gradient functional. Finally the present status of the science of searching for exchange-correlation functions is reviewed. It is suggested that it may not be possible to find a local functional which is significantly more accurate for chemistry than the presently used Generalized Gradient Approximation functionals.

Signatures of the correlation hole in total and partial cross sections.

In a complex scattering system with few open channels, say a quantum dot with leads, the correlation properties of the poles of the scattering matrix are most directly related to the internal dynamics of the system. We may ask how to extract these properties from an analysis of cross sections. In general this is very difficult, if we leave the domain of isolated resonances. We propose to consider the cross correlation function of two different elastic or total cross sections. For these we can show numerically and to some extent also analytically a significant dependence on the correlations between the scattering poles. The difference between uncorrelated and strongly correlated poles is clearly visible, even for strongly overlapping resonances.

Ordering at Two Length Scales in Comb−Coil Diblock Copolymers Consisting of Only Two Different Monomers

The microphase-separated morphology of a melt of a specific class of comb−coil diblock copolymers, consisting of an AB comb block and a linear homopolymer A block, is analyzed in the weak segregation limit. On increasing the length of the homopolymer A block, the systems go through a characteristic series of structural transitions. Starting from the pure comb copolymer, the first series of structures involve a short length scale followed by structures involving a large length scale. A maximum of two critical points exists. Furthermore, in the two parameter space characterizing the comb−coil diblock copolymer molecules considered, a nontrivial bifurcation point exists beyond which the structure factor can have two maxima (two correlation hole peaks).

Role of electron–electron coalescence density in density functional theory

AbstractAn expression for the evaluation of electron–electron coalescence density as a functional of the density for any electron system is proposed. The formula, clarifies previously advanced upper bounds for this quantity and provides a method to independently estimate the system‐averaged on‐top exchange–correlation hole. The relationship with the on‐top pair density shows that producing the true electron–electron coalescense should be considered as a leading physical requirement for trial wave functions in any energy minimization scheme. © 2002 John Wiley &amp; Sons, Inc. Int J Quantum Chem, 2001