Short-range Pair Research Articles

On Justification of the Asymptotics of Eigenfunctions of the Absolutely Continuous Spectrum in the Problem of Three One-Dimensional Short-Range Quantum Particles with Repulsion

The present paper offers a new approach to the construction of the coordinate asymptotics of the kernel of the resolvent of the Schrodinger operator in the scattering problem of three onedimensional quantum particles with short-range pair potentials. Within the framework of this approach, the asymptotics of eigenfunctions of the absolutely continuous spectrum of the Schrodinger operator can be constructed. In the paper, the possibility of a generalization of the suggested approach to the case of the scattering problem of N particles with arbitrary masses is discussed.

The effect of short-range interaction and correlations on the charge and electric field distribution in a model solid electrolyte

A simple lattice model of a solid electrolyte presented as a xy-slab geometry system of mobile cations on a background of energetic landscape of the host system and a compensating field of uniformly distributed anions is studied. The system is confined in the z-direction between two oppositely charged walls, which are in parallel to xy-plane. Besides the long-range Coulomb interactions appearing in the system, the short-range attractive potential between cations is considered in our study. We propose the mean field description of this model and extend it by taking into account correlation effects at short distances. Using the free energy minimization at each of z-coordinates, the corresponding set of non-linear equations for the chemical potential is derived. The set of equations was solved numerically with respect to the charge density distribution in order to calculate the cations distribution profile and the electrostatic potential in the system along z-direction under different conditions. An asymmetry of charge distribution profile with respect to the midplane of the system is observed. The effects of the short-range interactions and pair correlations on the charge and electric field distributions are demonstrated.

Isostructural solid–solid coexistence of colloid–polymer mixtures

Hard spheres mixed with penetrable hard spheres display an isostructural solid–solid transition. This phase transition is fully driven by the entropy gain of the depletants without invoking explicit pair potentials between the colloidal particles. The solid–solid phase coexistence terminates at a critical endpoint with a size ratio q≈0.09. Colloid–polymer mixtures are an excellent candidate for the experimental realization of this intricate solid–solid transition, first predicted by Bolhuis and Frenkel for hard spheres with short range pair attractions [PRL 72, 2211–2214 (1994)].

Existence of bound states of N-body problem in an optical lattice

We provide sufficient conditions to have at least one N-particle bound state below the essential spectrum of a large class of N-particle discrete Schrödinger operators associated with the Hamiltonian of (not necessarily identical) N particles, moving on a lattice and interacting via short-range pair potentials. We also describe the essential spectrum of

Structure Formation in 2D Assemblies Comprising Functional Tripod Molecules with Reduced Symmetry

Surface-confined self-assembly of organic building blocks is a versatile method of creation of low dimensional structures with potential applications in nanotechnology and material engineering. A key factor which often determines morphology of such 2D supramolecular assemblies is the geometry and functionality of a molecular tecton at play. In this contribution, we use theoretical modeling to predict the structure of adsorbed systems in which tripod molecules with reduced symmetry interact via a short-range anisotropic pair potential. To that end the self-assembly of a tripod molecule with one shortened/elongated arm, adsorbed on a triangular lattice, is modeled using the Monte Carlo simulation method. The probe asymmetric molecule consists of a few interconnected segments, and it is equipped with terminal interaction centers (active segments) with differently assigned interaction directions. Our study focuses on the effect of directionality of intermolecular interactions on the morphology of the resulting supramolecular 2D assemblies. It is demonstrated that a suitable encoding of the interaction directions allows for the creation of largely diversified adsorbed structures including aperiodic porous networks, molecular ladders, strings, ribbons and dispersed aggregates. Main differences and similarities between the findings reported for the asymmetric molecules and their C3-symmetric counterparts are also discussed. The obtained results can be helpful in designing new molecular tectons for controlled on-surface self-assembly and coupling reactions, as they provide useful information on the molecule–superstructure relation. This preliminary information can, for example, facilitate screening of molecular libraries to select an optimal molecule able to create low-dimensional structures with predefined properties.

Self-Assembly of Mesophases from Nanoparticles.

A growing number of crystalline and quasi-crystalline structures have been formed by coating nanoparticles with ligands, polymers, and DNA. The design of nanoparticles that assemble into mesophases, such as those formed by block copolymers, would combine the order, mobility, and stimuli responsive properties of mesophases with the electronic, magnetic, and optical properties of nanoparticles. Here we use molecular simulations to demonstrate that binary mixtures of unbound particles with simple short-ranged pair interactions produce the same mesophases as block copolymers and surfactants, including lamellar, hexagonal, gyroid, body-centered cubic, face-centered cubic, perforated lamellar, and semicrystalline phases. The key to forming the mesophases is the frustrated attraction between particles of different types, achieved through control over interparticle size and over strength and softness of the interaction. Experimental design of nanoparticles with effective interactions described by the potentials of this work would provide a distinct, robust route to produce ordered tunable liquid crystalline mesophases from nanoparticles.

Uncertainties in constraining low-energy constants from 3H $ \beta$β decay

We discuss the uncertainties in constraining low-energy constants of chiral effective field theory from $^3$H $\beta$ decay. The half-life is very precisely known, so that the Gamow-Teller matrix element has been used to fit the coupling $c_D$ of the axial-vector current to a short-range two-nucleon pair. Because the same coupling also describes the leading one-pion-exchange three-nucleon force, this in principle provides a very constraining fit, uncorrelated with the $^3$H binding energy fit used to constrain another low-energy coupling in three-nucleon forces. However, so far such $^3$H half-life fits have only been performed at a fixed cutoff value. We show that the cutoff dependence due to the regulators in the axial-vector two-body current can significantly affect the Gamow-Teller matrix elements and consequently also the extracted values for the $c_D$ coupling constant. The degree of the cutoff dependence is correlated with the softness of the employed NN interaction. As a result, present three-nucleon forces based on a fit to $^3$H $\beta$ decay underestimate the uncertainty in $c_D$. We explore a range of $c_D$ values that is compatible within cutoff variation with the experimental $^3$H half-life and estimate the resulting uncertainties for many-body systems by performing calculations of symmetric nuclear matter.

Theory of model electrolyte solutions: Assessing the short- and long-ranged contributions by molecular simulations

In this work, we conduct a comprehensive simulation study on Helmholtz energies for non-primitive model electrolyte solutions in order to assess fluid theories. Simulation data is obtained with two different methods. Using a new thermodynamic integration path, we calculate Helmholtz energy contributions arising from damped, short-ranged electrostatic pair potentials. The division of the potential into a damped, short-ranged and a long-ranged part using a complementary error function corresponds to the division of a standard Ewald sum. Additionally, we applied a standard thermodynamic integration method to obtain the full electrostatic contribution to the Helmholtz energy. We evaluate the analytical long-range contribution developed by Rodgers and Weeks [J. M. Rodgers and J. D. Weeks, J. Chem. Phys. 131, 244108 (2009)] and find excellent agreement to our simulation data for any damping parameter α*≥1.5 for liquid-like densities. Further, the simulation data is compared to a third order perturbation theory we recently presented. By analyzing the theory against results of molecular simulations we were able to introduce refinements to our theory, such as a rearranged Padé approximation. We show, however, that third order perturbation theory, despite these improvements, is only reliable for strongly damped potentials (α*<1) for ion-dipole as well as for purely dipolar fluids. This study shows that a perturbation theory of third order is insufficient for such systems.

Ballistic quench-induced correlation waves in ultracold gases

We investigate the wave packet dynamics of a pair of particles that undergoes a rapid change of scattering length. The short-range interactions are modeled in the zero-range limit, where the quench is accomplished by switching the boundary condition of the wave function at vanishing particle separation. This generates a correlation wave that propagates rapidly to nonzero particle separations. We have derived universal, analytic results for this process that lead to a simple phase-space picture of the quench-induced scattering. Intuitively, the strength of the correlation wave relates to the initial contact of the system. We find that, in one spatial dimension, the $k^{-4}$ tail of the momentum distribution contains a ballistic contribution that does not originate from short-range pair correlations, and a similar conclusion can hold in other dimensionalities depending on the quench protocol. We examine the resultant quench-induced transport in an optical lattice in 1D, and a semiclassical treatment is found to give quantitatively accurate estimates for the transport probabilities.

Correlated fermions in nuclei and ultracold atomic gases

Background: The high momentum distribution of atoms in two spin-state ultra-cold atomic gases with strong short-range interactions between atoms with different spins, which can be described using Tan's contact, are dominated by short range pairs of different fermions and decreases as $k^{-4}$. In atomic nuclei the momentum distribution of nucleons above the Fermi momentum ($k>k_F \approx 250$ Mev/c) is also dominated by short rangecorrelated different-fermion (neutron-proton) pairs. Purpose: Compare high-momentum unlike-fermion momentum distributions in atomic and nuclear systems. Methods: We show that, for $k>k_F$ MeV/c, nuclear momentum distributions are proportional to that of the deuteron. We then examine the deuteron momentum distributions derived from a wide variety of modern nucleon-nucleon potentials that are consistent with $NN$-scattering data. Results: The high momentum tail of the deuteron momentum distribution, and hence of the nuclear momentum distributions appears to decrease as $k^{-4}$. This behavior is shown to arise from the effects of the tensor part of the nucleon-nucleon potential. In addition, when the dimensionless interaction strength for the atomic system is chosen to be similar to that of atomic nuclei, the probability for finding a short range different-fermion pair in both systems is the same. Conclusions: Although nuclei do not satisfy all of the conditions for Tan's contact, the observed similarity of the magnitude and $k^{-4}$ shape of nuclear and atomic momentum distributions is remarkable because these systems differ by about $20$ orders of magnitude in density. This similarity may lead to a greater understanding of nuclei and the density dependence of nuclear systems.

Extracting the mass dependence and quantum numbers of short-range correlated pairs fromA(e,e′p)andA(e,e′pp)scattering

The nuclear mass dependence of the number of short-range correlated (SRC) proton-proton (pp) and proton-neutron (pn) pairs in nuclei is a sensitive probe of the dynamics of short-range pairs in the ground state of atomic nuclei. This work presents an analysis of electroinduced single-proton and two-proton knockout measurements off 12C, 27Al, 56Fe, and 208Pb in kinematics dominated by scattering off SRC pairs. The nuclear mass dependence of the observed A(e,e'pp)/12C(e,e'pp) cross-section ratios and the extracted number of pp- and pn-SRC pairs are much softer than the mass dependence of the total number of possible pairs. This is in agreement with a physical picture of SRC affecting predominantly nucleon-nucleon pairs in a nodeless relative-S state of the mean-field basis.

Strong scaling of general-purpose molecular dynamics simulations on GPUs

We describe a highly optimized implementation of MPI domain decomposition in a GPU-enabled, general-purpose molecular dynamics code, HOOMD-blue (Anderson and Glotzer, 2013). Our approach is inspired by a traditional CPU-based code, LAMMPS (Plimpton, 1995), but is implemented within a code that was designed for execution on GPUs from the start (Anderson et al., 2008). The software supports short-ranged pair force and bond force fields and achieves optimal GPU performance using an autotuning algorithm. We are able to demonstrate equivalent or superior scaling on up to 3375 GPUs in Lennard-Jones and dissipative particle dynamics (DPD) simulations of up to 108 million particles. GPUDirect RDMA capabilities in recent GPU generations provide better performance in full double precision calculations. For a representative polymer physics application, HOOMD-blue 1.0 provides an effective GPU vs. CPU node speed-up of 12.5×.

Colloidal clusters from a global optimization perspective

Modern microscopy techniques opened new perspectives to look at colloidal clusters. It is now possible to visualize the colloidal particles forming the cluster, which provides relevant experimental data that can be combined with detailed information resulting from structural optimization to understand phenomena at the mesoscale. From the theoretical view point, short-ranged Morse pair potentials have been successfully applied to model interactions between colloidal particles, while the development of efficient global optimization methods has allowed one to face the difficult task of searching for the geometry of the cluster that minimizes energy. In this work, we have carried out a thorough review concerning the global optimization methods proposed in the literature. The optimization of the title systems relies on the methods especially designed to deal with atomic clusters. Studies involving the global optimization of colloidal clusters were also surveyed.We employ the evolutionary algorithm developed in our group to search low-energy structures of colloidal clusters that are modeled with short-ranged Morse potentials. To the best of our knowledge, this is the first time that such kind of global optimization algorithms are applied to colloidal clusters. The method shows to be efficient for discovering the putative global minima in the cluster size-range N≤38. The results appear to indicate that, for colloidal clusters, significant structural changes due to the variation in the range of the interaction are unlikely to occur. Also the quasi-degeneracy of both global and local minima, that is usually present in these aggregates, is not raised up by modifying the composition of the cluster or decreasing the range of the interaction between the colloidal particles. In contrast, charged particles have shown a great influence on the stable structure of the clusters.

Optimized Force Fields for Simulations of Intrinsically Disordered Proteins

Some frequently encountered deficiencies in all-atom molecular simulations, such as nonspecific protein-protein interactions being too strong, and unfolded or disordered states being too collapsed, suggest that proteins are insufficiently well solvated in simulations using current state-of-the-art force fields. In order to address these issues, we make the simplest possible change, by modifying the short-range protein-water pair interactions, and leaving all the water-water and protein-protein parameters unchanged. We find that a modest strengthening of protein-water interactions is sufficient to recover the correct dimensions of intrinsically disordered or unfolded proteins, as determined by direct comparison with small-angle X-ray scattering (SAXS) and Forster resonance energy transfer (FRET) data. The modification also results in more realistic protein:protein affinities, and average solvation free energies of model compounds which are more consistent with experiment. Most importantly, we show that this scaling is small enough not to affect adversely the stability of the folded state, with only a modest effect on the stability of model peptides forming alpha-helix and beta-sheet structures. The proposed adjustment opens the way to more accurate atomistic simulations of proteins, particularly for intrinsically disordered proteins, protein:protein association, and crowded cellular environments.

Balanced Protein-Water Interactions Improve Properties of Disordered Proteins and Non-Specific Protein Association.

Some frequently encountered deficiencies in all-atom molecular simulations, such as nonspecific protein–protein interactions being too strong, and unfolded or disordered states being too collapsed, suggest that proteins are insufficiently well solvated in simulations using current state-of-the-art force fields. To address these issues, we make the simplest possible change, by modifying the short-range protein–water pair interactions, and leaving all the water–water and protein–protein parameters unchanged. We find that a modest strengthening of protein–water interactions is sufficient to recover the correct dimensions of intrinsically disordered or unfolded proteins, as determined by direct comparison with small-angle X-ray scattering (SAXS) and Förster resonance energy transfer (FRET) data. The modification also results in more realistic protein-protein affinities, and average solvation free energies of model compounds which are more consistent with experiment. Most importantly, we show that this scaling is small enough not to affect adversely the stability of the folded state, with only a modest effect on the stability of model peptides forming α-helix and β-sheet structures. The proposed adjustment opens the way to more accurate atomistic simulations of proteins, particularly for intrinsically disordered proteins, protein–protein association, and crowded cellular environments.

Origin of polar distortion inLiNbO3-type “ferroelectric” metals: Role ofA-site instability and short-range interactions

Since conduction electrons of a metal screen effectively the local electric dipole moments, it was widely believed that the ferroelectric-like distortion cannot occur in metals. Recently, metallic LiOsO3, was discovered to be the first clear-cut example of an Anderson-Blount "ferroelectric" metal, which at 140 K undergoes a ferroelectric-like structural transition similar to insulating LiNbO3. This is very surprising because the mechanisms for structural phase transitions are usually quite distinct in metals and insulators. Through performing first principles calculations, here we reveal that the local polar distortion in LiOsO3 is solely due to the instability of the A-site Li atom, in contrast to the LiNbO3 case where the second order Jahn-Teller effect of the B-site Nb ion also plays an additional role. More importantly, the "ferroelectric"-like long range order of the local polar distortion is found to be due to the predominantly ferroelectric short-range pair interactions between the local polar modes which are not screened by conduction electrons. Furthermore, we predict that LiNbO3-type MgReO3 is also a "ferroelectric" metal, but with a much higher structural transition temperature by 391 K than LiOsO3. Our work not only unravels the origin of FE-like distortion in LiNbO3-type "ferroelectric" metals, but also provides clue for designing other multi-functional "ferroelectric" metals.

Cross-slip process in model Ni(Al) solid solution: An embedded-atom method study

The cross-slip process of a screw dislocation in model Ni(Al) random solid solution is studied using the climbing image nudged elastic band method with an embedded-atom method potential. The average stacking fault energy of model Ni(Al) solid solution decreases with increasing Al concentration from 0 to 10 at.%. However, the average activation energy under zero stress shows an initial increase and then plateaus with increasing concentration of Al. The excess activation energy is determined by comparing with results from linear-elastic continuum theory. The short-range repulsive solute atom pair and its interaction with the dislocation provide the excess activation energy in the cross-slip process of model Ni(Al) solid solution.

Microscopic observation of superconducting fluctuations inκ-(BEDT-TTF)2Cu[N(CN)2]Br byC13NMR spectroscopy

We performed $^{13}$C-NMR experiment and measured spin-lattice relaxation rate divided by temperature $1/T_{1}T$ near the superconducting (SC) transition temperature $T_{c}$ in $\kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Br ($\kappa$-Br salt), and $\kappa$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$ ($\kappa$-NCS salt). We observed the reduction of $1/T_{1}T$ starting at the temperature higher than $T_c$ in $\kappa$-Br salt. Microscopic observation of quasi-particle density of states in the fluctuating SC state revealed the effects of short-range Cooper pairs induced in the normal state to the quasi-particle density of states. We also performed systematic measurements in the fields both parallel and perpendicular to the conduction plane in $\kappa$-Br and $\kappa$-NCS salts, and confirmed that the reduction of $1/T_{1}T$ above $T_{c}$ is observed only in $\kappa$-Br salt regardless of the external field orientation.

Positivity of eigenvalues of the two-particle Schrödinger operator on a lattice

We consider the family H(k) of two-particle discrete Schrodinger operators depending on the quasimomentum of a two-particle system k ∈ \(\mathbb{T}^d \), where \(\mathbb{T}^d \) is a d-dimensional torus. This family of operators is associated with the Hamiltonian of a system of two arbitrary particles on the d-dimensional lattice ℤd, d ≥ 3, interacting via a short-range attractive pair potential. We prove that the eigenvalues of the Schrodinger operator H(k) below the essential spectrum are positive for all nonzero values of the quasimomentum k ∈ \(\mathbb{T}^d \) if the operator H(0) is nonnegative. We establish a similar result for the eigenvalues of the Schrodinger operator H+(k), k ∈ \(\mathbb{T}^d \), corresponding to a two-particle system with repulsive interaction.

Bridging interactions of proteins with silica nanoparticles: the influence of pH, ionic strength and protein concentration.

Charge-driven bridging of nanoparticles by macromolecules represents a promising route for engineering functional structures, but the strong electrostatic interactions involved when using conventional polyelectrolytes impart irreversible complexation and ill-defined structures. Recently it was found that the electrostatic interaction of silica nanoparticles with small globular proteins leads to aggregate structures that can be controlled by pH. Here we study the combined influence of pH and electrolyte concentration on the bridging aggregation of silica nanoparticles with lysozyme in dilute aqueous dispersions. We find that protein binding to the silica particles is determined by pH irrespective of the ionic strength. The hetero-aggregate structures formed by the silica particles with the protein were studied by small-angle X-ray scattering (SAXS) and the structure factor data were analyzed on the basis of a short-range square-well attractive pair potential (close to the sticky-hard-sphere limit). It is found that the electrolyte concentration has a strong influence on the stickiness near pH 5, where the weakly charged silica particles are bridged by the strongly charged protein. An even stronger influence of the electrolyte is found in the vicinity of the isoelectric point of the protein (pI = 10.7) and is attributed to shielding of the repulsion between the highly charged silica particles and hydrophobic interactions between the bridging protein molecules.