Local Density Fluctuations Research Articles

A combined first principles study of the structural, magnetic, and phonon properties of monolayer CrI3.

The first magnetic 2D material discovered, monolayer (ML) CrI3, is particularly fascinating due to its ground state ferromagnetism. However, because ML materials are difficult to probe experimentally, much remains unresolved about ML CrI3's structural, electronic, and magnetic properties. Here, we leverage Density Functional Theory (DFT) and high-accuracy Diffusion Monte Carlo (DMC) simulations to predict lattice parameters, magnetic moments, and spin-phonon and spin-lattice coupling of ML CrI3. We exploit a recently developed surrogate Hessian DMC line search technique to determine CrI3's ML geometry with DMC accuracy, yielding lattice parameters in good agreement with recently published STM measurements-an accomplishment given the ∼10% variability in previous DFT-derived estimates depending upon the functional. Strikingly, we find that previous DFT predictions of ML CrI3's magnetic spin moments are correct on average across a unit cell but miss critical local spatial fluctuations in the spin density revealed by more accurate DMC. DMC predicts that magnetic moments in ML CrI3 are 3.62 μB per chromium and -0.145 μB per iodine, both larger than previous DFT predictions. The large disparate moments together with the large spin-orbit coupling of CrI3's I-p orbital suggest a ligand superexchange-dominated magnetic anisotropy in ML CrI3, corroborating recent observations of magnons in its 2D limit. We also find that ML CrI3 exhibits a substantial spin-phonon coupling of ∼3.32 cm-1. Our work, thus, establishes many of ML CrI3's key properties, while also continuing to demonstrate the pivotal role that DMC can assume in the study of magnetic and other 2D materials.

Partial structure factors derived from coarse-grained phase-separation dynamics on a disordered lattice with density fluctuations

The simplest and most time-efficient phase-separation dynamics simulations are carried out on a disordered lattice to calculate the partial structure factors of coarse-grained A-B binary mixtures. The typical coarse-grained phase-separation models use regular lattices and can describe the local concentrations but cannot describe both local density and concentration fluctuations. To introduce fluctuation for local density in the model, the particle positions from a hard sphere fluid model are determined as disordered lattice points for the model. Then we place the local order parameter as the difference of the concentrations of A and B components on each lattice point. The concentration at each lattice point is time-evolved by discrete equations derived from the Cahn-Hilliard equation. From both fluctuations, Bhatia and Thornton’s structure factor can be accurately calculated. The structure factor for concentration fluctuations at the large wavenumber region gives us the correct mean concentrations of the components. Using the mean concentrations, partial structure factors can be converted from three of Bhatia and Thornton’s structure factors. The present model and procedures can provide a means of analysing the structural properties of many materials that exhibit complex morphological changes.

Intermittency analysis of proton numbers in heavy-ion collisions at energies available at the BNL Relativistic Heavy Ion Collider

Local density fluctuations near the QCD critical point has been suggested to exhibit a power-law behavior which can be probed by an intermittency analysis on scaled factorial moment (SFM) in relativistic heavy-ion collisions. The collision energy and centrality dependence of the second-order SFMs are systematically investigated in Au $+$ Au collisions at $\sqrt{s_{NN}}$ = 7.7, 11.5, 19.6, 27, 39, 62.4, and 200 GeV within the UrQMD model. We estimate the noncritical background in the measurement of intermittency and propose a cumulative variable method to effectively remove the background contributions. We further study the effect of particle detection efficiency by implementing the RHIC (STAR) experimental tracking efficiencies in the UrQMD events. A cell-by-cell method is proposed for experimental application of efficiency corrections on SFM. This work can provide a guidance of background subtraction and efficiency correction for the experimental measurement of intermittency in the search of the QCD critical point in heavy-ion collisions.

Gravitational cracking of general relativistic polytropes: A generalized scheme

We discuss the effect that small fluctuations of both local anisotropy and energy density, may have on the occurrence of cracking in spherical compact objects satisfying a polytropic equation of state. A systematic scheme to bring the fluid configurations out of hydrostatic equilibrium is revisited. Various models of polytropes are considered and it is shown that departures from equilibrium may lead to the appearance of cracking for a wide range of values of the parameters involved. Prospective applications of the obtained results to some astrophysical scenarios are pointed out.

Hidden Order Beyond Hyperuniformity in Critical Absorbing States.

Disordered hyperuniformity is a description of hidden correlations in point distributions revealed by an anomalous suppression in fluctuations of local density at various coarse-graining length scales. In the absorbing phase of models exhibiting an active-absorbing state transition, this suppression extends up to a hyperuniform length scale that diverges at the critical point. Here, we demonstrate the existence of additional many-body correlations beyond hyperuniformity. These correlations are hidden in the higher moments of the probability distribution of the local density and extend up to a longer length scale with a faster divergence than the hyperuniform length on approaching the critical point. Our results suggest that a hidden order beyond hyperuniformity may generically be present in complex disordered systems.

Doublon-Hole Correlations and Fluctuation Thermometry in a Fermi-Hubbard Gas.

We report on the single atom and single site-resolved detection of the total density in a cold atom realization of the 2D Fermi-Hubbard model. Fluorescence imaging of doublons is achieved by splitting each lattice site into a double well, thereby separating atom pairs. Full density readout yields a direct measurement of the equation of state, including direct thermometry via the fluctuation-dissipation theorem. Site-resolved density correlations reveal the Pauli hole at low filling, and strong doublon-hole correlations near half filling. These are shown to account for the difference between local and nonlocal density fluctuations in the Mott insulator. Our technique enables the study of atom-resolved charge transport in the Fermi-Hubbard model, the site-resolved observation of molecules, and the creation of bilayer Fermi-Hubbard systems.

The Difference in Molecular Orientation and Interphase Structure of SiO2/Shape Memory Polyurethane in Original, Programmed and Recovered States during Shape Memory Process.

In order to further understand the shape memory mechanism of a silicon dioxide/shape memory polyurethane (SiO2/SMPU) composite, the thermodynamic properties and shape memory behaviors of prepared SiO2/SMPU were characterized. Dynamic changes in the molecular orientation and interphase structures of SiO2/SMPU during a shape memory cycle were then discussed according to the small angle X-ray scattering theory, Guinier’s law, Porod approximation, and fractal dimension theorem. In this paper, a dynamic mechanical analyzer (DMA) helped to determine the glass transition start temperature (Tg) by taking the onset point of the sigmoidal change in the storage modulus, while transition temperature (Ttrans) was defined by the peak of tan δ, then the test and the calculated results indicated that the Tg of SiO2/SMPU was 50.4 °C, and the Ttrans of SiO2/SMPU was 72.18 °C. SiO2/SMPU showed good shape memory performance. The programmed SiO2/SMPU showed quite obvious microphase separation and molecular orientation. Large-size sheets and long-period structures were formed in the programmed SiO2/SMPU, which increases the electron density difference. Furthermore, some hard segments had been rearranged, and their gyration radii decreased. In addition, several defects formed at the interfaces of SiO2/SMPU, which caused the generation of space charges, thus leading to local electron density fluctuations. The blurred interphase structure and the intermediate layer formed in the programmed SiO2/SMPU and there was evident crystal damage and chemical bond breakage in the recovered SiO2/SMPU. Finally, the original and recovered SiO2/SMPU samples belong to the surface fractal system, but the programmed sample belongs to the mass fractal and reforms two-phase structures. This study provides an insight into the shape memory mechanism of the SiO2/SMPU composite.

Local relative density fluctuation in the early stage of a sintered glass sphere compact determined by X-ray computed tomography

The relative density of a sintered glass-powder compact varies at the local level due to its heterogeneous nature, which makes its characterization essential. In this work, high-resolution X-ray computed tomography (XCT) was used to quantitatively characterize the local relative density fluctuation of a sintered glass compact in its initial stage. The degree of heterogeneity of the microstructure was calculated taking into account the coarseness parameter. With a basis of 23,500 particles scanned in the representative volume element (RVE), the local environment was subdivided into three different groups of particles, represented by a cubic cell with a volume equivalent to that of approximately 600, 80 and 10 spherical particles with a diameter of 80 μm. Independent of the particle group analysed, we found that the maximum of the local relative density distributions, which could be described by a normal distribution function, always occurs around the relative density of the RVE. However, the fluctuation of the data showed a considerable change regarding the width, which increases as the volume of the analysed group of particles decreases, suggesting that particle packing is more heterogeneous on a small scale. In particular, we observed that the heterogeneity of the microstructure for the RVE under consideration becomes pronounced for groups of approximately 10 to 80 particles.

Probing the QCD phase structure using event-by-event fluctuations

Heavy-ion collisions at relativistic energies probe matter at extreme conditions of temperatures and energy densities. The study of event-by-event fluctuations of experimental observables is crucial to probe the QCD phase transition, locate the critical point, and learn about the associated critical phenomena. At the critical point, all thermodynamic quantities behave anomalously. Fluctuation measurements provide access to thermodynamic response functions. We discuss the methods for obtaining the isothermal compressibility using particle multiplicity fluctuation, and specific heat using fluctuations in mean transverse momentum, temperature, and energy. Lattice QCD calculations have predicted non-monotonic behavior in the higher-order cumulants of conserved quantities at the critical point. Fluctuations in the multiplicity of charged to neutral particles have been measured to understand the formation of domains of disoriented chiral condensates. We review the recent fluctuation results as a function of collision centrality and energy from experiments at SPS, RHIC, and LHC. In addition, we propose to map the temperature fluctuations in η-φ plane to probe local fluctuations of temperature and energy density.

Statistical properties of cold bosons in a ring trap

A study of an interacting system of bosons in a ring trap at a finite temperature is presented. We consider a gas with contact and long-range dipolar interactions within a framework of the classical fields approximation. For a repulsive gas we have obtained coherence length, population of the ground state and its fluctuations as a function of temperature. In the case of an attractive gas we study local density fluctuations. Additionally, we exactly calculate the partition function for the ideal gas in the canonical ensemble and derive several other macroscopic state functions.

A collective elastic fluctuation mechanism for decoupling and stretched relaxation in glassy colloidal and molecular liquids.

We propose a microscopic theory for the decoupling of self-diffusion and structural relaxation in glass-forming liquids within the Elastically Collective Nonlinear Langevin Equation (ECNLE) activated dynamics framework. Our central hypothesis is that the heterogeneity relevant to this problem is static fluctuations of local density on the scale of 3-4 particle diameters and how this changes local packing correlations. These fluctuations modify the degree of dynamical cage expansion that mechanistically couples intracage large amplitude hopping and longer range collective elasticity in ECNLE theory. Decoupling only emerges in the deeply supercooled regime where the strongly temperature dependent elastic barrier becomes non-negligible relative to its noncooperative local analog. The theory makes predictions for various aspects of the decoupling phenomenon, including apparent fractional power law Stokes-Einstein behavior, that appear to be consistent with experiments and simulations on hard sphere fluids and molecular liquids. Of central importance is a microscopic connection between the barrier fluctuation variance and most probable barrier height. Sensible results are also obtained for the nonexponential stretching of a generic relaxation time correlation function and its temperature evolution. Nonuniversality can arise from the relative importance of the local and collective barriers (related to fragility) and the precise magnitude of the length scale that defines the transition from local cage to elastic physics. Comparison is made with a traplike model based on a Gaussian distribution of barriers.

Molecular origins of bulk viscosity in liquid water.

The rapid equilibrium fluctuations of water molecules are intimately connected to the rheological response; molecular motions resetting the local structure and stresses seen as flow and volume changes. In the case of water or hydrogen bonding liquids generally, the relationship is a non-trivial consideration due to strong directional interactions complicating theoretical models and necessitating clear observation of the timescale and nautre of the associated equilibrium motions. Recent work has illustrated a coincidence of timescales for short range sub-picosecond motions and the implied timescale for the shear viscosity response in liquid water. Here, neutron and light scattering methods are used to experimentally illustrate the timescale of bulk viscosity and provide a description of the associated molecular relaxation. Brillouin scattering has been used to establish the timescale of bulk viscosity; and borrowing the Maxwell approach, the ratio of the bulk viscosity, ζ, to the bulk modulus, K, yields a relaxation time, τB, which emerges on the order of 1-2 ps in the 280 K to 303 K temperature range. Inelastic neutron scattering is subsequently used to describe the motions of water and heavy water at the molecular scale, providing both coherent and incoherent scattering data. A rotational (alternatively described as localized) motion of water protons on the 1-2 ps timescale is apparent in the incoherent scattering spectra of water, while the coherent spectra from D2O on the length scale of the first sharp diffraction peak, describing the microscopic density fluctuations of water, confirms the relaxation of water structure at a comparable timescale of 1-2 ps. The coincidence of these three timescales provides a mechanistic description of the bulk viscous response, with the local structure resetting due to rotational/localized motions on the order of 1-2 ps, approximately three times slower than the relaxations associated with shear viscosity. In this way we show that the shear viscous response is most closely associated with changes in water network connectivity, while the bulk viscous response is associated with local density fluctuations.

Searching for the Critical Point of Strongly Interacting Matter in Nucleus–Nucleus Collisions at CERN SPS

The search for experimental signatures of the critical point (CP) of strongly interacting matter is one of the main objectives of the NA61/SHINE experiment at CERN SPS. In the course of the experiment, a beam momentum and system size scan is performed. Local proton density fluctuations in transverse momentum space represent an order parameter of the chiral phase transition and are expected to scale according to a universal power-law in the vicinity of the CP; we probe their behavior through an intermittency analysis of the proton second scaled factorial moments (SSFMs) in transverse momentum space. Previous such analyses revealed power-law behavior in NA49 Si+Si collisions at 158$A$ GeV/$c$, with no intermittency observed in lighter or heavier NA49 & NA61/SHINE systems at the same energy. We now extend the analysis to NA61/SHINE Ar+Sc collisions at 150$A$ GeV/$c$, similar in size and baryochemical potential to NA49 Si+Si. We employ statistical techniques to subtract non-critical background and estimate statistical and systematic uncertainties. Subsequently, we use Monte Carlo simulations to assess the statistical significance of the observed intermittency effect.

Local Density Fluctuation Governs the Divergence of Viscosity Underlying Elastic and Hydrodynamic Anomalies in a 2D Glass-Forming Liquid.

If a liquid is cooled rapidly to form a glass, its structural relaxation becomes retarded, producing a drastic increase in viscosity. In two dimensions, strong long-wavelength fluctuations persist, even at low temperature, making it difficult to evaluate the microscopic structural relaxation time. This Letter shows that, in a 2D glass-forming liquid, relative displacement between neighbor particles yields a relaxation time that grows in proportion to the viscosity. In addition to thermal elastic vibrations, hydrodynamic fluctuations are found to affect the long-wavelength dynamics, yielding a logarithmically diverging diffusivity in the long-time limit.

Reaction coordinates and rate constants for liquid droplet nucleation: Quantifying the interplay between driving force and memory

In this work, we revisit the classic problem of homogeneous nucleation of a liquid droplet in a supersaturated vapor phase. We consider this at different extents of the driving force, or equivalently the supersaturation, and calculate a reaction coordinate (RC) for nucleation as the driving force is varied. The RC is constructed as a linear combination of three order parameters, where one accounts for the number of liquidlike atoms and the other two for local density fluctuations. The RC is calculated from biased and unbiased molecular dynamics (MD) simulations using the spectral gap optimization approach "SGOOP" [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)]. Our key finding is that as the supersaturation decreases, the RC ceases to simply be the number of liquidlike atoms, and instead, it becomes important to explicitly consider local density fluctuations that correlate with shape and density variations in the nucleus. All three order parameters are found to have similar barriers in their respective potentials of mean force; however, as the supersaturation decreases, the density fluctuations decorrelate slower and thus carry longer memory. Thus, at lower supersaturations, density fluctuations are non-Markovian and cannot be simply ignored from the RC by virtue of being noise. Finally, we use this optimized RC to calculate nucleation rates in the infrequent metadynamics framework and show that it leads to a more accurate estimate of the nucleation rate with four orders of magnitude acceleration relative to unbiased MD.

Scintillation Arc Brightness and Electron Density for an Analytical Noodle Model

Abstract We show that narrow filaments or sheets of over- or under-dense plasma, or “noodles,” with fluctuations of scattering phase of less than a radian, can form the scintillation arcs seen for many pulsars. The required local fluctuations of electron density are indefinitely small. We assume a cosine profile for the electron column and find the scattered field by analytic Kirchhoff integration. For a large electron column, corresponding to large amplitude of phase variation, the stationary-phase approximation is accurate; we call this regime “ray optics”. For smaller-amplitude phase variation, the stationary-phase approximation is inaccurate or inapplicable; we call this regime “wave optics”. We show that scattering is most efficient when the width of the strip equals that of one pair of Fresnel zones, and in the wave-optics regime. We show that the resolution of present observations is about 100 Fresnel zones on the scattering screen. Incoherent superposition of strips within a resolution element tends to increase the scattered field. We find that observations match a single noodle per resolution element with phase of up to 12 radians; or many noodles per resolution element with arbitrarily small phase variation each, for net phase of less than a radian. Observations suggest a minimum radius for noodles of about 650 km, comparable to the ion inertial scale or the ion cyclotron radius in the scattering plasma.

Poloidally localized edge density fluctuation with applied and spontaneous 3-D fields in experimental advanced superconducting tokamak (EAST)

Poloidally localized density fluctuation with applied and spontaneous 3-D fields in high-confinement mode (H-mode) plasma is observed by using poloidally distributed multichannel interferometer diagnostics in the experimental advanced superconducting tokamak. With the application of an n = 1 rotating nonaxisymmetric magnetic perturbation (NAMP) field, a density fluctuation appears on different interferometer channels sequentially. Evidence shows that this fluctuation is located at the plasma edge. When an n = 1 static NAMP field is applied, the density fluctuation amplitude increases in parts of channels but decreases in other channels, implying a poloidal localization. This localization is enhanced with the increase in the NAMP field. In addition, when a spontaneous n = 1 external kink mode with a frequency of ∼3.5 kHz appears in the plasma edge, the amplitude of density fluctuation is modulated by the n = 1 kink. This modulation could be attributed to the localization effect on fluctuation by the 3-D fields of the spontaneous kink mode.

Hyperuniformity on spherical surfaces.

We study and characterize local density fluctuations of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to date few works have dealt with the problem of hyperuniformity in curved spaces. Indeed, some systems that display disordered hyperuniformity, like the spatial distribution of photoreceptors in avian retina, actually occur on curved surfaces. Here we will focus on the local particle number variance and its dependence on the size of the sampling window (which we take to be a spherical cap) for regular and uniform point distributions, as well as for equilibrium configurations of fluid particles interacting through Lennard-Jones, dipole-dipole, and charge-charge potentials. We show that the scaling of the local number variance as a function of the window size enables one to characterize hyperuniform and nonhyperuniform point patterns also on spherical surfaces.

Destabilization of field-line localized density fluctuation with a 1/1 internal kink mode in the EAST tokamak

A high frequency (HF) density fluctuation, ranging from 100 kHz to 400 kHz, is locally destabilized with an m/n = 1/1 internal kink mode before a sawtooth crash in the experimental advanced superconducting tokamak (EAST). The location is just around the region with a high electron pressure gradient due to the flux compression from the 1/1 mode. And this HF fluctuation can be triggered at both the low field side and high field side. This fluctuation has a poloidal wave number (kθ) from 3 to 5 cm−1, corresponding to a poloidal mode number (m) of 36–60. A threshold of the local electron pressure gradient (|∇p e|) exists for the stimulation of the HF fluctuation, and its amplitude increases with |∇p e|. The results could be beneficial for the understanding of a sawtooth crash, and also physics in 3D equilibrium.

Heterogeneity at multiple length scales in halide perovskite semiconductors

Materials with highly crystalline lattice structures and low defect concentrations have classically been considered essential for high-performance optoelectronic devices. However, the emergence of high-efficiency devices based on halide perovskites is provoking researchers to rethink this traditional picture, as the heterogeneity in several properties within these materials occurs on a series of length scales. Perovskites are typically fabricated crudely through simple processing techniques, which leads to large local fluctuations in defect density, lattice structure, chemistry and bandgap that appear on short length scales ( 10 μm). Despite these variable and complex non-uniformities, perovskites maintain exceptional device efficiencies and are, as of 2018, the best-performing polycrystalline thin-film solar cell material. In this Review, we highlight the multiple layers of heterogeneity ascertained using high-spatial-resolution methods that provide access to the relevant length scales. We discuss the impact that the optoelectronic variations have on halide perovskite devices, including the prospect that it is this very disorder that leads to their remarkable power-conversion efficiencies. Despite their excellent macroscopic operational parameters, halide perovskites exhibit heterogeneity in materials properties at all lateral and vertical length scales. In this Review, we discuss the nature of heterogeneity in halide perovskites and assess the impact of these non-uniformities on their optoelectronic properties and how the heterogeneity may even be beneficial for device properties.