Correlation Hole Research Articles

Observation and Control of Laser-Enabled Auger Decay.

Single-photon laser-enabled Auger decay (spLEAD) is predicted theoretically [B. Cooper and V.Averbukh, Phys. Rev. Lett. 111, 083004 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.083004] and here we report its first experimental observation in neon. Using coherent, bichromatic free-electron laser pulses, we detect the process and coherently control the angular distribution of the emitted electrons by varying the phase difference between the two laser fields. Since spLEAD is highly sensitive to electron correlation, this is a promising method for probing both correlation and ultrafast hole migration in more complex systems.

Dynamic cross-correlations between entangled biofilaments as they diffuse

Entanglement in polymer and biological physics involves a state in which linear interthreaded macromolecules in isotropic liquids diffuse in a spatially anisotropic manner beyond a characteristic mesoscopic time and length scale (tube diameter). The physical reason is that linear macromolecules become transiently localized in directions transverse to their backbone but diffuse with relative ease parallel to it. Within the resulting broad spectrum of relaxation times there is an extended period before the longest relaxation time when filaments occupy a time-averaged cylindrical space of near-constant density. Here we show its implication with experiments based on fluorescence tracking of dilutely labeled macromolecules. The entangled pairs of aqueous F-actin biofilaments diffuse with separation-dependent dynamic cross-correlations that exceed those expected from continuum hydrodynamics up to strikingly large spatial distances of ≈15 µm, which is more than 104 times the size of the solvent water molecules in which they are dissolved, and is more than 50 times the dynamic tube diameter, but is almost equal to the filament length. Modeling this entangled system as a collection of rigid rods, we present a statistical mechanical theory that predicts these long-range dynamic correlations as an emergent consequence of an effective long-range interpolymer repulsion due to the de Gennes correlation hole, which is a combined consequence of chain connectivity and uncrossability. The key physical assumption needed to make theory and experiment agree is that solutions of entangled biofilaments localized in tubes that are effectively dynamically incompressible over the relevant intermediate time and length scales.

Determination of the local density of polydisperse nanoparticle assemblies.

Quantitative characterization of the average structure of dense nanoparticle assemblies and aggregates is a common problem in nanoscience. Small-angle scattering is a suitable technique, but it is usually limited to not too big assemblies due to the limited experimental range, low concentrations to avoid interactions, and monodispersity to keep calculations tractable. In the present paper, a straightforward analysis of the generally available scattered intensity - even for large assemblies, at high concentrations - is detailed, providing information on the local volume fraction of polydisperse particles with hard sphere interactions. It is based on the identical local structure of infinite homogeneous nanoparticle assemblies and their subsets forming finite-sized clusters. This approach is extended to polydispersity, using Monte-Carlo simulations of hard and moderately sticky hard spheres. As a result, a simple relationship between the observed structure factor minimum - termed the correlation hole - and the average local volume fraction κ on the scale of neighboring particles is proposed and validated through independent aggregate simulations. This relationship shall be useful as an efficient tool for the structural analysis of arbitrarily aggregated colloidal systems.

Observation of spatial charge and spin correlations in the 2D Fermi-Hubbard model.

Strong electron correlations lie at the origin of high-temperature superconductivity. Its essence is believed to be captured by the Fermi-Hubbard model of repulsively interacting fermions on a lattice. Here we report on the site-resolved observation of charge and spin correlations in the two-dimensional (2D) Fermi-Hubbard model realized with ultracold atoms. Antiferromagnetic spin correlations are maximal at half-filling and weaken monotonically upon doping. At large doping, nearest-neighbor correlations between singly charged sites are negative, revealing the formation of a correlation hole, the suppressed probability of finding two fermions near each other. As the doping is reduced, the correlations become positive, signaling strong bunching of doublons and holes, in agreement with numerical calculations. The dynamics of the doublon-hole correlations should play an important role for transport in the Fermi-Hubbard model.

Many electron correlations in stage-1 graphene intercalation compounds

Many electron correlations in stage-1 graphene intercalation compounds are studied in generalized random-phase approximation. With this approximation, we are able to study short-range exchange and correlation effects in graphene intercalation compounds. These exchange correlations lead to BCS superconducting states in which one electron correlates with another via its correlation hole to form a stable pair of electrons known as Cooper pair. Cooper pair energies are calculated as the excitations in S(q ,ω) following a method similar to exciton energy calculations. Short-range effects governing local field correction G(q ,ω) are studied for all wave vectors and frequencies. We have found a reasonable agreement between our results and the earlier reported theoretical results.

Coupling strength in Coulomb and Yukawa one-component plasmas

In a non-ideal classical Coulomb one-component plasma (OCP), all thermodynamic properties are known to depend only on a single parameter—the coupling parameter Γ. In contrast, if the pair interaction is screened by background charges (Yukawa OCP) the thermodynamic state depends, in addition, on the range of the interaction via the screening parameter κ. How to determine in this case an effective coupling parameter has been a matter of intensive debate. Here we propose a consistent approach for defining and measuring the coupling strength in Coulomb and Yukawa OCPs based on a fundamental structural quantity, the radial pair distribution function (RPDF). The RPDF is often accessible in experiments by direct observation or indirectly through the static structure factor. Alternatively, it is directly computed in theoretical models or simulations. Our approach is based on the observation that the build-up of correlation from a weakly coupled system proceeds in two steps: First, a monotonically increasing volume around each particle becomes devoid of other particles (correlation hole), and second (upon further increase of the coupling), a shell structure emerges around each particle giving rise to growing peaks of the RPDF. Using molecular dynamics simulation, we present a systematic study for the dependence of these features of the RPDF on Γ and κ and derive a simple expression for the effective coupling parameter.

On the simulation of indistinguishable fermions in the many-body Wigner formalism

The simulation of quantum systems consisting of interacting, indistinguishable fermions is an incredible mathematical problem which poses formidable numerical challenges. Many sophisticated methods addressing this problem are available which are based on the many-body Schrödinger formalism. Recently a Monte Carlo technique for the resolution of the many-body Wigner equation has been introduced and successfully applied to the simulation of distinguishable, spinless particles. This numerical approach presents several advantages over other methods. Indeed, it is based on an intuitive formalism in which quantum systems are described in terms of a quasi-distribution function, and highly scalable due to its Monte Carlo nature. In this work, we extend the many-body Wigner Monte Carlo method to the simulation of indistinguishable fermions. To this end, we first show how fermions are incorporated into the Wigner formalism. Then we demonstrate that the Pauli exclusion principle is intrinsic to the formalism. As a matter of fact, a numerical simulation of two strongly interacting fermions (electrons) is performed which clearly shows the appearance of a Fermi (or exchange–correlation) hole in the phase-space, a clear signature of the presence of the Pauli principle. To conclude, we simulate 4, 8 and 16 non-interacting fermions, isolated in a closed box, and show that, as the number of fermions increases, we gradually recover the Fermi–Dirac statistics, a clear proof of the reliability of our proposed method for the treatment of indistinguishable particles.

Multi-blob coarse graining for ring polymer solutions.

We present a multi-scale molecular modeling of concentrated solutions of unknotted and non-concatenated ring polymers under good solvent conditions. The approach is based on a multi-blob representation of each ring polymer, which is capable of overcoming the shortcomings of single-blob approaches that lose their validity at concentrations exceeding the overlap density of the solution [A. Narros, A. J. Moreno, and C. N. Likos, Soft Matter, 2010, 6, 2435]. By means of a first principles coarse-graining strategy based on analytically determined effective pair potentials between the blobs, computed at zero density, we quantitatively reproduce the single molecule and solution properties of a system with well-defined topological constraints. Detailed comparisons with the underlying, monomer-resolved model demonstrate the validity of our approach, which employs fully transferable pair potentials between connected and unconnected blobs. We demonstrate that the pair structure between the centers of mass of the rings is accurately reproduced by the multi-blob approach, thus opening the way for simulation of arbitrarily long polymers. Finally, we show the importance of the topological constraint of non-concatenation on the structure of the concentrated solution and in particular on the size of the correlation hole and the shrinkage of the rings as melt concentrations are approached.

Electron correlation effects in diamond: A wave-function quantum-chemistry study of the quasiparticle band structure

The quasiparticle bands of diamond, a prototype covalent insulator, are herein studied by means of wave-function electronic-structure theory, with emphasis on the nature of the correlation hole around a bare particle. Short-range correlations are in such a system conveniently described by using a real-space representation and many-body techniques from {\it ab initio} quantum chemistry. To account for long-range polarization effects, on the other hand, we adopt the approximation of a dielectric continuum. Having as "uncorrelated" reference the Hartree-Fock band structure, the post-Hartree-Fock treatment is carried out in terms of localized Wannier functions derived from the Hartree-Fock solution. The computed correlation-induced corrections to the relevant real-space matrix elements are important and give rise to a strong reduction, in the range of $50\%$, of the initial Hartree-Fock gap. While our final results for the indirect and direct gaps, 5.4 and 6.9 eV, respectively, compare very well with the experimental data, the width of the valence band comes out by $10$ to $15\%$ too large as compared to experiment. This overestimation of the valence-band width appears to be related to size-consistency effects in the configuration-interaction correlation treatment.

Accurate Ground-State Energies of Solids and Molecules from Time-Dependent Density-Functional Theory

We demonstrate that ground-state energies approaching chemical accuracy can be obtained by combining the adiabatic-connection fluctuation-dissipation theorem with time-dependent density-functional theory. The key ingredient is a renormalization scheme, which eliminates the divergence of the correlation hole characteristic of any local kernel. This new class of renormalized kernels gives a significantly better description of the short-range correlations in covalent bonds compared to the random phase approximation (RPA) and yields a fourfold improvement of RPA binding energies in both molecules and solids. We also consider examples of barrier heights in chemical reactions, molecular adsorption, and graphene interacting with metal surfaces, which are three examples where the RPA has been successful. In these cases, the renormalized kernel provides results that are of equal quality or even slightly better than the RPA, with a similar computational cost.

UNIVERSALITY OF NUCLEON–NUCLEON SHORT-RANGE CORRELATIONS AND NUCLEON MOMENTUM DISTRIBUTIONS

By analyzing recent microscopic many-body calculations of few-nucleon systems and complex nuclei performed by different groups in terms of realistic nucleon–nucleon (NN) interactions, it is shown that NN short-range correlations (SRCs) have a universal character, in that the correlation hole that they produce in nuclei appears to be almost A-independent and similar to the correlation hole in the deuteron. The correlation hole creates high-momentum components, missing in a mean-field (MF) description and exhibiting several scaling properties and a peculiar spin–isospin structure. In particular, the momentum distribution of a pair of nucleons in spin–isospin state (ST) = (10), depending upon the pair relative (k rel ) and center-of-mass (c.m.) (K c.m. ) momenta, as well as upon the angle Θ between them, exhibits a remarkable property: in the region k rel ≳2 fm -1 and K c.m. ≲1 fm -1, the relative and c.m. motions are decoupled and the two-nucleon momentum distribution factorizes into the deuteron momentum distribution and an A-dependent momentum distribution describing the c.m. motion of the pair in the medium. The impact of these and other properties of one- and two-nucleon momentum distributions on various nuclear phenomena, on ab initio calculations in terms of low-momentum interactions, as well as on ongoing experimental investigations of SRCs, are briefly commented.

Structure of amplitude correlations in open chaotic systems

The Verbaarschot-Weidenmüller-Zirnbauer (VWZ) model is believed to correctly represent the correlations of two S-matrix elements for an open quantum chaotic system, but the solution has considerable complexity and is presently only accessed numerically. Here a procedure is developed to deduce its features over the full range of the parameter space in a transparent and simple analytical form preserving accuracy to a considerable degree. The bulk of the VWZ correlations are described by the Gorin-Seligman expression for the two-amplitude correlations of the Ericson-Gorin-Seligman model. The structure of the remaining correction factors for correlation functions is discussed with special emphasis of the rôle of the level correlation hole both for inelastic and elastic correlations.

A first-principles-based correlation functional for harmonious connection of short-range correlation and long-range dispersion

We present a physically motivated correlation functional belonging to the meta-generalized gradient approximation (meta-GGA) rung, which can be supplemented with long-range dispersion corrections without introducing double-counting of correlation contributions. The functional is derived by the method of constraint satisfaction, starting from an analytical expression for a real-space spin-resolved correlation hole. The model contains a position-dependent function that controls the range of the interelectronic correlations described by the semilocal functional. With minimal empiricism, this function may be adjusted so that the correlation model blends with a specific dispersion correction describing long-range contributions. For a preliminary assessment, our functional has been combined with an atom-pairwise dispersion correction and full Hartree-Fock (HF)-like exchange. Despite the HF-exchange approximation, its predictions compare favorably with reference interaction energies in an extensive set of non-covalently bound dimers.

Predictions of elastic-plastic crack driving force and redistribution under combined primary and secondary stresses – Part 2: Experimental application

Engineering components may contain small crack-like defects that experience combinations of primary and secondary stresses during service. A new function, g, was introduced in the accompanying Part 1 paper to quantify the influence of plasticity interaction under combined primary and secondary loading. This paper reports new experiments to examine the interaction of primary and secondary loads with plasticity. These experiments were performed on three point bend specimens that had experienced a pre-compression to induce a residual stress field before being tested to failure at −150, −90 and −50 °C to correspond to varying levels of plasticity, and hence Lr, at fracture. Both 2D and 3D finite element analyses have been considered that show excelled agreement with experimental measures of the residual stress field from digital image correlation, neutron diffraction and surface hole drilling when adopting an incremental kinematic hardening model. On applying the existing R6 and the g plasticity interaction parameters to these experiments it was found that the accuracy of the methods diverged with increasing plasticity, with the g approach providing the more accurate result. However, since both the existing R6 and the g plasticity interaction parameters were shown to provide conservative results, the experiments provide useful validation for both methods.

Multiple-scattering model for the coherent reflection and transmission of light from a disordered monolayer of particles

Using a multiple-scattering formalism, we derive closed-form expressions for the coherent reflection and transmission coefficients of monochromatic electromagnetic plane waves incident upon a two-dimensional array of randomly located spherical particles. The calculation is performed within the quasi-crystalline approximation, and the statistical correlation among the particles is assumed to be given simply by a correlation hole. In the resulting model, the size of the spheres and the angle of incidence are both unrestricted. The final formulas are relatively simple, making the model suitable for a straightforward interpretation of optical-sensing measurements.

Mode-coupling approach to polymer diffusion in an unentangled melt. I. The effect of density fluctuations

We quantitatively assess the effect of density fluctuation modes on the dynamics of a tagged polymer in an unentangled melt. To this end, we develop a density-based mode-coupling theory (dMCT) using the Mori-Zwanzig approach and projecting the fluctuating force onto pair-density fluctuation modes. The effect of dynamical density fluctuations on the center-of-mass (c.m.) dynamics is also analyzed based on a perturbative approach and we show that dMCT and perturbation techniques yield identical results. The c.m. velocity autocorrelation function (c.m. VAF) exhibits a slow power law relaxation in the time range between the monomer time t_{1} and the Rouse relaxation time t_{N}. We obtain an analytical expression for the c.m. VAF in terms of molecular parameters. In particular, the c.m. VAF scales as -N^{-1}t^{-5/4} (where N is the number of monomer units per chain) in the relevant time regime. The results are qualitatively accounted for by the dynamical correlation hole effect. The predicted -t^{-5/4} dependence of the c.m. VAF is supported by data of non-momentum-conserving computer simulations. However, the comparison shows that the theory significantly underestimates the amplitude of the effect. This issue is discussed and an alternative approach is addressed in the second part of this series [Farago et al., Phys. Rev. E 85, 051807 (2012), the following paper].

Scaling properties of exchange and correlation holes of the valence shell of second-row atoms

We study the exchange and correlation hole of the valence shell of second row atoms using variational Monte Carlo techniques, especially correlated estimates, and norm-conserving pseudopotentials. The well-known scaling of the valence shell provides a tool to probe the behavior of exchange and correlation as a functional of the density and thus test models of density functional theory. The exchange hole shows an interesting competition between two scaling forms -- one caused by self-interaction and another that is approximately invariant under particle number, related to the known invariance of exchange under uniform scaling to high density and constant particle number. The correlation hole shows a scaling trend that is marked by the finite size of the atom relative to the radius of the hole. Both trends are well captured in the main by the Perdew-Burke-Ernzerhof generalized-gradient approximation model for the exchange-correlation hole and energy.

Order–Disorder Transition in Supramolecular Polymers

In supramolecular polymers, directional interactions control the constituting units connectivity, but dispersion forces may conspire to make complex organizations. Here we report on the long-range order and order-disorder transition (ODT) of main-chain supramolecular polymers based on poly(propylene oxide) (PPO) spacers functionalized on both ends with thymine. Below the ODT temperature (T(ODT)), these compounds are semicrystalline with a lamellar structure, showing nanophase separation between crystallized thymine planes and amorphous PPO layers. Above T(ODT), they are amorphous and homogeneous even though their X-ray scattering spectrum reveals a peak. This peak is due to correlation hole effect resulting from contrast between end-functional groups and spacer. Macroscopically, the transition is accompanied by dramatic flow and mechanical properties changes.

Spin-dependent two-electron emission from ferromagnetic Fe(001)

We present a joint experimental and theoretical study of correlated electron pair emission from a ferromagnetic Fe(001) surface induced by spin-polarized low-energy electrons. Spin-dependent angular and energy distributions of the emitted pairs have been measured and calculated. They are analyzed with the aid of the spin-, momentum-, symmetry-, and layer-resolved valence electron density of states, which we obtained by an ab initio density-functional theory calculation. The observed spectra are found to arise almost completely from only three surface-parallel atomic layers. Momentum distributions for parallel spins of the emitted electrons exhibit an exchange-correlation hole, which is larger than the correlation hole in the antiparallel spin case. By comparing experimental antiparallel-spin pair spectra with their theoretical counterparts we determine an effective screening strength of the Coulomb interaction in the surface region.

Explicitly correlated coupled cluster methods with pair-specific geminals

Explicitly correlated MP2-F12 and CCSD(T)-F12 methods with orbital-pair-specific Slater-type geminals are proposed. The fixed amplitude ansatz of Ten-no is used, and different exponents of the Slater geminal functions can be chosen for core–core, core–valence, and valence–valence pairs. This takes care of the different sizes of the correlation hole and leads to improved results when inner-shell orbitals are correlated. The complications and the extra computational cost as compared to corresponding calculations with a single geminal are minor. The improved accuracy of the method is demonstrated for spectroscopic properties of Br2, As2, Ga2, Cu2, GaCl, CuCl, and CuBr, where the d-orbitals are treated as core.