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In this work, we investigate thermodynamic properties of the one-dimensional (1D) spin-crossover molecular chain being a subject of a constant external pressure. Effective compressible degenerate Ising model is used as a theoretical framework. Using transfer matrix formalism analytic results for the low spin -- high spin crossover were obtained. We derive the exact expressions for the fraction of molecules in the high spin state, correlation function and heat capacity. We provide analysis of parameters region where the spin crossover takes place and demonstrate how pressure changes location of the crossover., 9 pages, 5 figures, submitted to Low Temperature Physics

The paper contributes by developing computational and reviewing theoretical methods to propagate electromagnetic fields in free space, while taking account of the fact that the sources are typicall...

In the present work, Cu-doped indium sulfide thin films (In2S3:Cu) have been produced by chemical bath deposition (CBD) method on the glass substrates. The deposited films have been post-annealed at 300 °C temperature for about one hour. The morphological properties of produced thin films have been investigated analytically before and after the Cu doping process. To this end, the atomic force microscopy analysis has been used to study the height fluctuations of these rough thin films. By the monofractal analysis, the height distribution, and the higher-order moments (skewness and kurtosis) of the surface height have been studied. The deviation from the Gaussian distribution has been shown by the results. Also, the correlation function and therefore the correlation length of the produced surfaces have been investigated. The numerical calculations revealed that the morphology and the statistical properties of thin films depend on the growth method. The power spectral density has been evaluated, and the achieved results of higher-order moments of the surface height have been confirmed. The skewness values of thin films heights are nonzero; moreover, the obtained kurtosis values illustrate the mild peak respect to Gaussian distribution. The Hurst exponent and thus the fractal dimensions of surfaces have been estimated.

The structure of the planar surface of colloidal solutions of amorphous 27-nm silica sol particles enriched with heavy K+, Rb+, and Cs+ alkali ions is studied by the methods of reflectometry and diffuse (nonspecular) scattering of synchrotron radiation. For liquid-phase systems, we have used a self-consistent approach that makes it possible to reconstruct from experimental data the electron density profiles perpendicular to the hydrosol surface, as well as the spectra of the height–height correlation function in the plane of the surface without using any a priori information about the near-surface structure. Analysis represented here shows that for high values of pH, alkali cations with a large radius and a surface concentration of (5 ± 1) × 1018 m–2 replace Na+ ions with a smaller radius. This result is in qualitative agreement with the dependence of the Kharkats–Ukstrup single-ion electrostatic free energy on the ion radius and in good quantitative agreement with the results obtained by other authors using the capillary-wave approach. The integrated value of the effective height of interface roughness (3.2 ± 0.5 A) coincides to within the measuring error with the prediction of the capillary-wave theory; however, the experimental spectra of the height-to-height correlation function basically differ from the theoretical spectra in the range of low spatial frequencies ν < 10–3 nm–1. The approximation of the spectra by the sum of two K-correlation distributions indicates a transition from the natural roughness of the compact layer of alkali metal ions to the capillary roughness of the liquid surface in the correlation length range of about 1 μm. In our opinion, the aggregate of available data indicates the dispersion of this layer into 2D clusters (Wigner islands).

We explain how the axioms of Conformal Field Theory are used to make predictions about critical exponents of continuous phase transitions in three dimensions, via a procedure called the conformal bootstrap. The method assumes conformal invariance of correlation functions, and imposes some relations between correlation functions of different orders. Numerical analysis shows that these conditions are incompatible unless the critical exponents take particular values, or more precisely that they must belong to a small island in the parameter space., Comment: 16 pages, 3 figures, accepted for publication by C.R.Physique

One of the standard methods used to measure the hydrodynamic diameter of nanoparticles is photon correlation spectroscopy, especially dynamic light scattering (DLS). In principle, this technique is to analyze correlation function of the scattered light from the nanoparticles undergoing Brownian motion in solution and to calculate the diffusion coefficient from the correlation function which is converted into the hydrodynamic diameter. However, when using this technique, one needs to pay careful attention to interaction effects (i.e., particle-particle and particle-solvent interactions) on the diffusion coefficient of the particles in solution. If not, then incorrect information can be obtained on the self-diffusion coefficients of nanoparticles. In order to facilitate a strict procedure for obtaining real size of the nanoparticles in solution, we used 20 nm, 50 nm and 100 nm-nominal polystyrene latex (PSL) nanoparticle solutions for DLS measurement. We represented that a rigorous scrutinizing the concentration dependence of the diffusion coefficient of the PSL nanoparticles made it possible to separate the interaction effect from the diffusion phenomena of the PSL nanoparticles suspended in water and to give real size of the PSL nanoparticles.

Systematic expressions of the cluster expansion for one and two-body terms of elastic form factors and charge densities for 1g-2d shell nuclei with N≠Z (such as: 42 92 Mo , 46 104 Pd , 50 118 Sn , 60 142 Nd , 62 152 Sm and 64 154 Gd ) are derived. Using the harmonic oscillator size parameter b and the correlation parameter β which creates from the Jastrow correlation function. Here, the parameters b and β are determined via the fitting to the experimental elastic form factors. The inserting of short-range correlations imitates the measured elastic form factors at the high momentum transfers (q ≥ 2 fm−1). It is seen that embedding this effect is important for obtaining an adjustment in the calculated elastic form factors which leads to defining the data of electron scattering well through all range of considered momentum transfers.

We present a new partially coherent source with spatiotemporal coupling. The stochastic light, which we call a spatiotemporal (ST) non-uniformly correlated (NUC) beam, combines space and time in an inhomogeneous (shift- or space-variant) correlation function. This results in a source that self-focuses at a controllable location in space-time, making these beams potentially useful in applications such as optical trapping, optical tweezing, and particle manipulation. We begin by developing the mutual coherence function for an ST NUC beam. We then examine its free-space propagation characteristics by deriving an expression for the mean intensity at any plane $$z \ge 0$$ z ≥ 0 . To validate the theoretical work, we perform Monte Carlo simulations, in which we generate statistically independent ST NUC beam realizations and compare the sample statistical moments to the corresponding theory. We observe excellent agreement amongst the results.

The electrostatic screening length predicted by Debye-H\"uckel theory decreases with increasing ionic strength, but recent experiments have found that the screening length can instead increase in concentrated electrolytes. This phenomenon, referred to as underscreening, is believed to result from ion-ion correlations and short-range forces such as excluded volume interactions among ions. We use Brownian Dynamics to simulate a version of the Restrictive Primitive Model for electrolytes over a wide range of ion concentrations, ionic strengths, and ion excluded volume radii for binary electrolytes. We measure the decay of the charge-charge correlation among ions in the bulk, and compare it against scaling trends found experimentally and determined in certain weak coupling theories of ion-ion correlation. Moreover, we find that additional large scale ion structures emerge at high concentrations. In this regime, the frequency of oscillations computed from the charge-charge correlation function is not dominated by electrostatic interactions but rather by excluded volume interactions and with oscillation periods on the order of the ion diameter. We also find that the nearest neighbor correlation of ions sharing the same charge transitions from negative at small concentrations to positive at high concentrations, representing the formation of small, like-charge ion clusters. We conclude that the increase in local charge density due to the formation of these clusters and the topological constraints of macroscopic charged surfaces can help explain the degree of underscreening observed experimentally., Comment: 17 pages, 10 figures

In this paper, some thermophysical properties at low pressure of sulphur hexafluoride ( $$\hbox {SF}_{6}$$ ) fluid are modelled and predicted. Also, by comparing the obtained results with experimental data, the correlation performance of virial coefficients to predict thermodynamic properties over a wide temperature range is evaluated. Studied properties consist of Joule–Thomson coefficient, enthalpy, deviation function, fugacity coefficient, thermal expansion, Boyle temperature and Boyle volume. The studied correlation function is the one suggested by Zarkova et al and compared with correlation of Meng et al. The obtained results show that the correlation equation presented has a good ability to predict the thermophysical properties of sulpur hexafluoride and its deviation from the ideal state over a wide range of temperatures. Average absolute deviations (AAD) of thermophysical properties of $$\hbox {SF}_{6}$$ calculated by this approach is mainly below $$5\%$$ .

We propose a systematic methodology to identify the topological phase transition through a self-supervised machine learning model, which is trained to correlate system parameters to the non-local observables in time-of-flight experiments of ultracold atoms. Different from the conventional supervised learning approach, where the predicted phase transition point is very sensitive to the training region and data labeling, our self-supervised learning approach identifies the phase transition point by the largest deviation of the predicted results from the known system parameters and by the highest confidence through a systematic shift of the training regions. We demonstrate the robust application of this approach results in various 1D and 2D exactly solvable models, using different input features (time-of-flight images, spatial correlation function or density-density correlation function). As a result, our self-supervised approach should be a very general and reliable method for many condensed matter or solid-state systems to observe new states of matters solely based on experimental measurements, even without a priori knowledge of the phase transition models., 13 pages and 7 figures

We study the emission of photons from germinating seeds using an experimental technique designed to detect light of extremely small intensity. We analyze the dark count signal without germinating seeds as well as the photon emission during the germination process. The technique of analysis adopted here, called diffusion entropy analysis (DEA) and originally designed to measure the temporal complexity of astrophysical, sociological and physiological processes, rests on Kolmogorov complexity. The updated version of DEA used in this paper is designed to determine if the signal complexity is generated either by non-ergodic crucial events with a non-stationary correlation function or by the infinite memory of a stationary but non-integrable correlation function or by a mixture of both processes. We find that dark count yields the ordinary scaling, thereby showing that no complexity of either kinds may occur without any seeds in the chamber. In the presence of seeds in the chamber anomalous scaling emerges, reminiscent of that found in neuro-physiological processes. However, this is a mixture of both processes and with the progress of germination the non-ergodic component tends to vanish and complexity becomes dominated by the stationary infinite memory. We illustrate some conjectures ranging from stress induced annihilation of crucial events to the emergence of quantum coherence.

Direct correlation functions (DCFs), linked to the second functional derivative of the free energy with respect to the one-particle density, play a fundamental role in a statistical mechanics description of matter. This holds, in particular, for the ordered phases: DCFs contain information about the local structure including defects and encode the thermodynamic properties of crystalline solids; they open a route to the elastic constants beyond low temperature expansions. Via a demanding numerical approach, we have explicitly calculated for the first time the DCF of a solid: based on the fundamental measure concept, we provide results for the DCF of a hard sphere crystal. We demonstrate that this function differs at coexistence significantly from its liquid counterpart—both in shape as well as in its order of magnitude—because it is dominated by vacancies. We provide evidence that the traditional use of liquid DCFs in functional Taylor expansions of the free energy is conceptually wrong and show that the emergent elastic constants are in good agreement with simulation-based results. published

The influence of two body short range correlations on elastic electron scattering charge form factors, charge densities as well as root mean square charge radii of some fp-shell nuclei (for example, 48Ca, 50Cr, 54Fe, 58Ni, 70Ge and 74Se) and some N50-shell nuclei (for example, 88Sr and 90Zr) is analyzed using the one- and two-body terms in the cluster expansion together with the single particle harmonic oscillator wave functions. The Jastrow-type correlation function is utilized to embed the effect of short range correlations into elastic charge form factors F(q) and charge densities ρ(r). Both F(q) and ρ(r) depend upon the harmonic oscillator parameter b and the correlation parameter β (which initiates from the Jastrow correlation function). Here, the parameters b and β are determined via the fitting to the measured charge form factors. The embedding of short range correlations imitates the measured charge form factors at the high momentum transfers (q ≥ 2 fm−1). It is noticed that the implanting of short range correlations is required for obtaining a remarkable alteration in the computed elastic charge form factors which in turn leads to explain the data of electron scattering astonishingly throughout the entire range of considered momentum transfers.

The self-diffusion coefficient (D) and the surface tension (γ) of the liquid alkali metals such as cesium (Cs) and rubidium (Rb) were calculated based on the Einstein's relation in a wide range of densities and temperatures. A developed mean spherical approximation (MSA) theory was applied to compute the direct correlation function using the effective square-well potential model for pair interaction in each temperature and density. The static structure factor, S(k), of the studied liquid species was evaluated by the proposed MSA theory in a wide range of wave vectors. The linear isothermal regularity equation of state was employed to determine the radial distribution function at a contact point at any thermodynamic state. A good agreement was obtained between the numerical results for both the D and γ values for the titled species and their available experimental data over the whole liquid range. For both liquids Cs and Rb, the temperature and density dependencies of the self-diffusion coefficient were investigated. Moreover, a correlation relation between the liquid surface tension and density and the temperature was found, in which the order of magnitude and sign of the coefficients were in good agreement with those obtained by experiment.

We analyze frustration properties of the Ising model for a 1D monatomic equidistant lattice in an external uniform magnetic field considering exchange interactions of atomic spins at the sites of the first (nearest) and second neighbors. Exact analytic expressions for thermodynamic and magnetic characteristics of the system, as well as for the Fourier transform of the pair spin–spin correlation function and magnetic diffused scattering wavevectors, were obtained by the method of the Kramers–Wannier transfer matrix considering the exchange interaction between spins at the nearest-neighbor sites in an external magnetic field, as well as the exchange interaction between spins at the second-neighbor sites in zero magnetic field. The criteria for the emergence of magnetic frustration in the presence of competition not only between exchange-interaction energies, but also between these energies and the external magnetic field energy are formulated. The frustration points and the values of frustration magnetic fields depending on the magnitudes and signs of the exchange interaction are determined. The distinguishing features of this model in the frustration regime and its vicinity are analyzed. The set of characteristic features inherent in observables for systems with magnetic frustrations is considered and analyzed. It is shown that the inclusion of competing exchange interactions at the first- and second-neighbor sites makes it possible to describe the behavior of the magnetic diffused scattering wavevector for commensurate, incommensurate, and lock-in structures.

A decaying 2D homogeneous and isotropic turbulent flow is considered in the self-similar limit, which is achieved with large values of the Reynolds number formed using the time and kinetic energy of the flow if the initial value of the averaged enstrophy tends to infinity with the viscosity tending to zero. In this case, the enstrophy-dissipation rate has a nonzero finite limit. The correlation function of the vorticity field and the enstrophy spectral density in the inertial range of distances and wave numbers, where these functions are free from the effect of viscosity and large-scale flow parameters, is investigated. It turns out that the inertial range exists in the decaying 2D self-similar turbulence in physical space but is absent in the space of wavenumbers. This means that the turbulent vortices of the appropriate size do not contribute to the spectral density, and the well-known law of the first degree is not satisfied. At large wave numbers, the spectral density of enstrophy behaves nonmonotonically - it first decreases faster than the law of the minus first degree and, then, in the dissipation region, it has a growth segment and a second peak. In this case, the enstrophy flow along the spectrum on the left boundary of the dissipation region is only a fraction of the enstrophy-dissipation rate.

Inelastic X-ray scattering was measured for copper/ethylene glycol nanofluid at 298 K. The collective excitation of the solvent was analyzed by a generalized Langevin equation. The thermal diffusion coefficient and μ(fast)- and α(structure)-relaxations of the solvent for the nanofluid are larger and faster than those of pure liquid, respectively. The high-frequency sound velocity obtained from momentum transfer dependence of a maximum in the longitudinal current-current correlation function increases with increasing the number of copper nanoparticles. The enhanced thermal conductivity of copper/ethylene glycol nanofluid could be related to the solvent dynamics.

The development of a molecular theory of inhomogeneous fluids and, in particular, of the liquid–gas interface has received enormous interest in recent years; however, long-standing attempts to extend the concept of surface tension in mesoscopic approaches by making it scale dependent, although apparently plausible, have failed to connect with simulation and experimental studies of the interface that probe the detailed properties of density correlations. Here, we show that a fully microscopic theory of correlations in the interfacial region can be developed that overcomes many of the problems associated with simpler mesoscopic ideas. This theory originates from recognizing that the correlation function displays, in addition to a Goldstone mode, an unexpected hierarchy of resonances that constrain severely its structural properties. Indeed, this approach allows us to identify new classes of fully integrable models for which, surprisingly, the tension, density profile and correlation function can all be determined analytically, revealing the microscopic structure of correlations in all generalized van der Waals theories. Accurately capturing both microscopic and mesoscopic properties of fluid–gas interfaces is a long-standing challenge. Now, a microscopic theory of correlation functions that can be scaled up to explain mesoscopic surface tension phenomena is put forward.

The mechanism of surfaces/interfaces and precise control of growth morphology is a key parameter for any specific device application. Herein, we report on a qualitative growth study of molecular beam epitaxy-grown polycrystalline InAs thin films on a lattice-mismatched Si(1 0 0) substrate using atomic force microscopy. The height-height correlation function (HHCF) and power spectral density function (PSDF) were employed to analyze the surface structures. Clear oscillatory behavior in the HHCF for sufficiently larger lateral distances suggests a mound-like morphology, which was confirmed by the existence of a characteristic frequency peak in the PSDF. The growth mechanism is described qualitatively by the Schwoebel barrier (roughening) effect coupled with the Mullins diffusion model (smoothing effect).

This study establishes an explicit relation between spatial two-point correlation function (TPCF) and volumetric (or three-dimensional) grain size distribution for aggregates of statistically equiaxed grains by extending a prior study (Sha, JASA, 2018). This relation is further validated by applying it to available TPCF and volumetric grain size distribution in the literature. Based on this relation, analytical attenuation coefficients for longitudinal and transverse waves, accounting for volumetric grain size distribution, are derived under Born approximation for macroscopically isotropic polycrystals of equiaxed triclinic grains. These attenuation models are applicable for whole frequency range except geometric region. Moreover, scattering coefficients for a polycrystal of equiaxed triclinic grains with a volumetric grain size distribution are obtained. Finally, the analytical attenuation model for the longitudinal wave is verified by comparison with existing 3D finite element simulation results in the literature. This theoretic study has practical applications to the inverse determination of volumetric grain size distribution from ultrasonic measurements.

A study of the one-dimensional molecular chain (MC) with two single-particle degenerate states is presented. We establish connection of the MC with the Ising model with phononic interactions and investigate properties of the model using a transfer matrix method. The transfer matrix method offers a promising pathway for simulating such materials properties. The role of degeneracy of states and phononic interaction being made explicit. We analyze regimes of the system and parameters of the occurring crossover. Here, we present exact results for the magnetization per spin, the correlation function and the effective volume of the system. We demonstrate possibility of existence of two peaks in the specific heat capacity thermal behavior., 9 pages, 6 figures

We examine the magnetic properties of the quasi 2D ferrimagnetic single crystal Mn3Si2Te6 (MST) through critical phenomena and magnetic entropy analysis in the easy axis (H || ab) as a function of proton irradiance. Employing a modified asymptotic analysis method, we find that upon proton irradiation the critical exponents do not fall into any particular universality class but lie close to mean field critical exponents ({\gamma} = 1, \b{eta} = 0.5). The presence of long-range interactions can be safely assumed for the pristine and irradiated cases of MST examined in this work. Further analysis on the effective spatial dimensionality reveal that MST remains at d = 3 under proton irradiation transitioning from an n = 1 spin dimensionality to n = 2 and n=3 for 1 x 10^15 and 5 x 10^15 H+/cm^2, indicating an XY interaction and a Heisenberg interaction, respectively. The pair (spin-spin) correlation function reveals an increase in magnetic correlations at the proton irradiance of 5 x 10^15 H+/cm^2. In conjunction, the maximum change in magnetic entropy obtained from isothermal magnetization at 3 T is the largest for 5 x 10^15 H+/cm^2 with a value of 2.45 J/kgK at T = 73.66 K, in comparison to 1.60 J/kgK for pristine MST at T = 73 K. Magnetic entropy derived from zero-field heat capacity does not show large deviations across the proton irradiated samples. This suggests that the antiferromagnetic coupling between the Mn sites is stable even after proton irradiation. Such result implies that magnetization is enhanced through a strengthening of the super-exchange interaction between Mn atoms mediated through Te rather than a weakening of the AFM component. Overall, our study finds that the magnetic interactions are manipulated the greatest when MST is irradiated at 5 x 10^15 H+/cm^2.

Heterogeneous materials such as rocks and composites are comprised of multiple material phases of different sizes and shapes that are randomly distributed through the medium. The random microstructure is typically described by using various statistical descriptors, which include volume fraction, two-point correlation function, and tortuosity, to name a few. Capturing different morphological features, a large number of statistical descriptors are proposed in different research fields, such as material science, geoscience and computational engineering. It is well known that these statistical descriptors are not independent from each other, but until recently it remains unclear what descriptors are more similar or more different. In particular, it is extremely difficult to look for quantified relations between various descriptors, since they are often defined in very different formats. The lack of quantified understanding of descriptors’ relations can cause uncertainties or even systematic errors in heterogeneous materials studies. To address this issue, we propose a novel and generic correlation analysis strategy and establish, for the first time, the quantified relations between various statistical descriptors for heterogeneous materials. Based on data science techniques, our approach consists of three operational steps: data regularization , dimension reduction and correlation analysis. A total of 41 statistical descriptors are collected and analysed in this study, which is readily extensible to include other new descriptors. The generic and quantified correlation results are compared with other established descriptor relations that are obtained from analytical analysis or physical intuition, and good agreements are observed in all cases. The quantified relations between various descriptors are summarized in a single correlation graph, which provides useful guiding information for the characterization, reconstruction and property prediction of heterogeneous materials.

Considering the large deviations of activity and current in the Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between the joint scaled cumulant generating functions of activity and current of two ASEPs with different parameters. This mapping is obtained by applying a similarity transform on the deformed Markov matrix of the source model in order to obtain the deformed Markov matrix of the target model. We first derive this correspondence for periodic boundary conditions, and show in the diffusive scaling limit (corresponding to the Weakly Asymmetric Simple Exclusion Processes, or WASEP) how the mapping is expressed in the language of Macroscopic Fluctuation Theory (MFT). As an interesting specific case, we map the large deviations of current in the ASEP to the large deviations of activity in the SSEP, thereby uncovering a regime of Kardar-Parisi-Zhang in the distribution of activity in the SSEP. At large activity, particle configurations exhibit hyperuniformity [Jack et al., PRL 114 060601 (2015)]. Using results from quantum spin chain theory, we characterize the hyperuniform regime by evaluating the small wavenumber asymptotic behavior of the structure factor at half-filling. Conversely, we formulate from the MFT results a conjecture for a correlation function in spin chains at any fixed total magnetization (in the thermodynamic limit). In addition, we generalize the mapping to the case of two open ASEPs with boundary reservoirs, and we apply it in the WASEP limit in the MFT formalism. This mapping also allows us to find a symmetry-breaking dynamical phase transition (DPT) in the WASEP conditioned by activity, from the prior knowledge of a DPT in the WASEP conditioned by the current., Comment: 30 pages. Updated references, conclusion

We investigate a two-dimensional system of active particles confined to a narrow annular domain. Despite the absence of explicit interactions among the velocities or the active forces of different particles, the system displays a transition from a disordered and stuck state to an ordered state of global collective motion where the particles rotate persistently clockwise or anticlockwise. We describe this behavior by introducing a suitable order parameter, the velocity polarization, measuring the global alignment of the particles' velocities along the tangential direction of the ring. We also measure the spatial velocity correlation function and its correlation length to characterize the two states. In the rotating phase, the velocity correlation displays an algebraic decay that is analytically predicted together with its correlation length, while in the stuck regime, the velocity correlation decays exponentially with a correlation length that increases with the persistence time. In the first case, the correlation (and, in particular, its correlation length) does not depend on the active force but the system size only. The global collective motion, an effect caused by the interplay between finite-size, periodicity, and persistent active forces, disappears as the size of the ring becomes infinite, suggesting that this phenomenon does not correspond to a phase transition in the usual thermodynamic sense.

We numerically study the structure of the interactions occurring in three-dimensional systems of hard spheres at jamming, focusing on the large-scale behavior. Given the fundamental role they play in the configuration of jammed packings, we analyze the propagation through the system of the weak forces and of the variation of the coordination number with respect to the isostaticity condition $\Delta Z$. We show that these correlations can be successfully probed by introducing a correlation function weighted on the density-density fluctuations. The results of this analysis can be further improved by introducing a representation of the system based on the contact points between particles. In particular, we find evidence that the weak forces and the $\Delta Z$ fluctuations support the hypothesis of randomly jammed packings of spherical particles being hyperuniform by exhibiting an anomalous long-range decay. Moreover, we find that the large-scale structure of the density-density correlation exhibits a complex behavior due to the superimposition of two exponentially damped oscillating signals propagating with linearly depending frequencies., Comment: Main: 5 pages, 4 figures; Supp. Info.: 2 pages, 1 figure

Dynamic heterogeneity, believed to be one of the hallmarks of the dynamics of supercooled liquids, is expected to affect the diffusion of the particles comprising the liquid. We have carried out extensive molecular dynamics simulations of two model glass-forming liquids in three dimensions to study the time scales at which Fick's law of diffusion starts to set in. We have identified two different Fickian timescales: one at which the mean squared displacement begins to show a linear dependence on time, and another one at which the distribution of particle displacements becomes Gaussian. These two times scales are found to be very different from each other and from the $\alpha$ relaxation time in both systems. An interesting connection is found between one of these Fickian time scales and the time scale obtained from the bond-breakage correlation function. We discuss the relationships between these different timescales and their connection to dynamic heterogeneity in the system.

Using a framework of partial differential equation-constrained optimization, we demonstrate that multiple constitutive relations can be extracted simultaneously from a small set of images of pattern formation. Examples include state-dependent properties in phase-field models, such as the diffusivity, kinetic prefactor, free energy, and direct correlation function, given only the general form of the Cahn-Hilliard equation, Allen-Cahn equation, or dynamical density functional theory (phase-field crystal model). Constraints can be added based on physical arguments to accelerate convergence and avoid spurious results. Reconstruction of the free energy functional, which contains nonlinear dependence on the state variable and differential or convolutional operators, opens the possibility of learning nonequilibrium thermodynamics from only a few snapshots of the dynamics.

We investigate the momentum distribution function of a single distinguishable impurity particle which formed a polaron state in a gas of either free fermions or Tonks-Girardeau bosons in one spatial dimension. We obtain a Fredholm determinant representation of the distribution function for the Bethe ansatz solvable model of an impurity-gas $\delta$-function interaction potential at zero temperature, in both repulsive and attractive regimes. We deduce from this representation the fourth power decay at a large momentum, and a weakly divergent (quasi-condensate) peak at a finite momentum. We also demonstrate that the momentum distribution function in the limiting case of infinitely strong interaction can be expressed through a correlation function of the one-dimensional impenetrable anyons., Comment: 39 pages, 10 figures; Restored overall phase factor in Eq. (66), references added

Tan’s contact is a quantity that unifies many different properties of a low-temperature gas with short-range interactions, from its momentum distribution to its spatial two-body correlation function. Here, we use a Ramsey interferometric method to realize experimentally the thermodynamic definition of the two-body contact, i.e., the change of the internal energy in a small modification of the scattering length. Our measurements are performed on a uniform two-dimensional Bose gas of 87Rb atoms across the Berezinskii–Kosterlitz–Thouless superfluid transition. They connect well to the theoretical predictions in the limiting cases of a strongly degenerate fluid and of a normal gas. They also provide the variation of this key quantity in the critical region, where further theoretical efforts are needed to account for our findings., Here the authors use Ramsey interferometry to study Tan’s contact in uniform two-dimensional Bose gas of 87Rb atoms across the Berezinskii–Kosterlitz–Thouless superfluid transition. They find that the two-body contact is continuous across the critical point.

Using atomistic computer simulations we determine the roughness and topographical features of melt-formed (MS) and fracture surfaces (FS) of oxide glasses. We find that the topography of the MS is described well by the frozen capillary wave theory. The FS are significant rougher than the MS and depend strongly on glass composition. The height-height correlation function for the FS shows an unexpected logarithmic dependence on distance, in contrast to the power law found in experiments. We unravel the crucial role of spatial resolution on surface measurements and conclude that on length scales less than 10 nm FS are not self-affine fractals.

We study the effect of heavy impurities on the dynamics of supercooled liquids. When a small fraction of particles in the supercooled liquid is made heavier, they exhibit slower dynamics than the original particles and also make the overall system slower. If one looks at the overlap correlation function to quantify dynamics in the system, it has different behavior for the heavy and the light particles. In particular, at the relaxation time of the overall system, the degree of relaxation achieved by the heavier particles is lesser on average than that achieved by the light particles. This difference in relaxation however, goes down drastically as a crossover temperature, $T_0$, is crossed. Below this crossover temperature, particles in the system have similar relaxation times irrespective of their masses. This crossover temperature depends on the fraction of the heavy particles and their masses. Next, we isolate the effect of mass heterogeneity on the dynamics of supercooled liquids and find that its effect increases monotonically with temperature. We also see that the development of dynamical heterogeneity with decreasing temperature is less dramatic for the system with impurities than for the pure system. Finally, the introduction of heavy impurities can be seen as a way of reducing the kinetic fragility of a supercooled liquid., Comment: accepted in J. Chem. Phys

The Journal of Chemical Physics, 153 (19), ISSN:0021-9606, ISSN:1089-7690

We report a quantum Monte Carlo study of the phase transition between antiferromagnetic and valence-bond solid ground states in the square-lattice $S=1/2$ $J$-$Q$ model. The critical correlation function of the $Q$ terms gives a scaling dimension corresponding to the value $\nu = 0.455 \pm 0.002$ of the correlation-length exponent. This value agrees with previous (less precise) results from conventional methods, e.g., finite-size scaling of the near-critical order parameters. We also study the $Q$-derivatives of the Binder cumulants of the order parameters for $L^2$ lattices with $L$ up to $448$. The slope grows as $L^{1/\nu}$ with a value of $\nu$ consistent with the scaling dimension of the $Q$ term. There are no indications of runaway flow to a first-order phase transition. The mutually consistent estimates of $\nu$ provide compelling support for a continuous deconfined quantum-critical point., Comment: 6 pages, 4 figures. v2: minor changes only

We develop a fast multi-fidelity modeling method for very complex correlations between high- and low-fidelity data by working in modal space to extract the proper correlation function. We apply this method to infer the amplitude of motion of a flexible marine riser in cross-flow, subject to vortex-induced vibrations (VIV). VIV are driven by an absolute instability in the flow, which imposes a frequency (Strouhal) law that requires a matching with the impedance of the structure; this matching is easily achieved because of the rapid parametric variation of the added mass force. As a result, the wavenumber of the riser spatial response is within narrow bands of uncertainty. Hence, an error in wavenumber prediction can cause significant phase-related errors in the shape of the amplitude of response along the riser, rendering correlation between low- and high-fidelity data very complex. Working in modal space as outlined herein, dense data from low-fidelity data, provided by the semi-empirical computer code VIVA, can correlate in modal space with few high-fidelity data, obtained from experiments or fully-resolved CFD simulations, to correct both phase and amplitude and provide predictions that agree very well overall with the correct shape of the amplitude response. We also quantify the uncertainty in the prediction using Bayesian modeling and exploit this uncertainty to formulate an active learning strategy for the best possible location of the sensors providing the high fidelity measurements., Comment: 26 pages, 13 figures

Weakly interacting Fermi gases simulate spin-lattices in energy-space, offering a rich platform for investigating information spreading and spin coherence in a large many-body quantum system. We show that the collective spin vector can be determined as a function of energy from the measured spin density, enabling general energy-space resolved protocols. We measure an out-of-time-order correlation function in this system and observe the energy dependence of the many-body coherence., Comment: Note revised title and completely rewritten text

In this work, the order parameter and the two-site correlation functions are expressed properly using the decimation transformation process in the presence of an external field so that their applications lead to some significant physical results. Indeed, their applications produce or reproduce some relevant and important results which were included in cumbersome mathematics in the previous studies, if not in a form impossible to understand. The average magnetization or the order parameter $ $ is expressed as $= $. Here, $\kappa$ is the coupling strength, $z$ is the number of nearest neighbors. $\sigma_{0,i}$ denotes the central spin at the $i^{th}$ site, while $\sigma_{l,i}$, $l=1,2,\dots,z$ are the nearest neighbor spins around the central spin. $H$ is the normalized external magnetic field. We show that the application of this relation to the 1D Ising model reproduces readily the previously obtained exact results in the absence of an external field. Furthermore, the three-site correlation functions of square and honeycomb lattices of the form $$ are analytically obtained. One finds that the three-site correlation functions are equal to $f(\kappa)\!\!$. Here $f(\kappa)$ depends on the lattice types and is an analytic function of coupling constant. This result indicates that the critical properties of three-site correlation functions of those lattices are the same as the corresponding order parameters $$ of those lattices. This will mean that the uniqueness of the average magnetization as an order parameter is questionable. ..., Comment: 18 pages

The bulk viscosity determines dissipation during hydrodynamic expansion. It vanishes in scale invariant fluids, while a nonzero value quantifies the deviation from scale invariance. For the dilute Fermi gas the bulk viscosity is given exactly by the correlation function of the contact density of local pairs. As a consequence, scale invariance is broken purely by pair fluctuations. These fluctuations give rise also to logarithmic terms in the bulk viscosity of the high-temperature nondegenerate gas. For the quantum degenerate regime I report numerical Luttinger-Ward results for the contact correlator and the dynamical bulk viscosity throughout the BEC-BCS crossover. The ratio of bulk to shear viscosity $\zeta/\eta$ is found to exceed the kinetic theory prediction in the quantum degenerate regime. Near the superfluid phase transition the bulk viscosity is enhanced by critical fluctuations and has observable effects on dissipative heating, expansion dynamics and sound attenuation., Comment: 6+4 pages, 4 figures; published version

Neutron scattering is a powerful experimental technique for characterizing the structure and dynamics of materials on the atomic or molecular scale. However, the interpretation of experimental data from neutron scattering is oftentimes not trivial, partly because scattering methods probe ensemble-averaged information in the reciprocal space . Therefore, computer simulations, such as classical and ab initio molecular dynamics, are frequently used to unravel the time-dependent atomistic configurations that can reproduce the scattering patterns and thus assist in the understanding of the microscopic origin of certain properties of materials . LiquidLib is a post-processing package for analyzing the trajectory of atomistic simulations of liquids and liquid-like matter with application to neutron scattering experiments. From an atomistic simulation, LiquidLib provides the computation of various statistical quantities including the pair distribution function , the weighted and unweighted structure factors, the mean squared displacement, the non-Gaussian parameter, the four-point correlation function, the velocity auto correlation function, the self and collective van Hove correlation functions, the self and collective intermediate scattering functions, and the bond orientational order parameter. LiquidLib analyzes atomistic trajectories generated from packages such as LAMMPS, GROMACS, and VASP. It also offers an extendable platform to conveniently integrate new quantities into the library and integrate simulation trajectories of other file formats for analysis. Weighting the quantities by element-specific neutron-scattering lengths provides results directly comparable to neutron scattering measurements. Lastly, LiquidLib is independent of dimensionality , which allows analysis of trajectories in two, three, and higher dimensions. The code is beginning to find worldwide use. Program summary Program Title: LiquidLib Program Files doi: http://dx.doi.org/10.17632/tyggwp7656.1 Licensing provisions: GNU Lesser General Public License v3.0 Programming language: C++ Supplementary material: User manual of the package. External routines/libraries: BOOST (optional), GSL (optional), xdrfilelib (optional, available at ftp.gromacs.org/pub/contrib/xdrfile-1.1.1.tar.gz ) Nature of problem: LiquidLib is a post-processing package for analyzing the trajectory of atomistic simulations of liquids and liquid-like matter with application to neutron scattering experiments. Solution method: We provide a collection of executables to compute statistical quantities relevant to the structure and dynamics of liquids and liquid-like matter from the simulation trajectories. Furthermore, the option to weigh the quantities by element-specific neutron-scattering lengths provides results comparable to neutron scattering measurements. The quantities computable by LiquidLib include the pair distribution function, the weighted and unweighted structure factors, the mean squared displacement, the non-Gaussian parameter, the four-point correlation function, the velocity auto correlation function, the self and collective van Hove correlation functions, the self and collective intermediate scattering functions, and the bond orientational order parameter. LiquidLib can directly read trajectories of file types .xyz, .xtc, .trr, .atom, .dump, .gro, and XDATCAR. Additional comments: Each computable quantity in LiquidLib is defined as a derived class, and has its own respective executable. Thus, LiquidLib is extendable to compute other quantities not already offered in the current version. Similarly, LiquidLib is extendable to handle simulation trajectory files with formats not already offered in the current version. Restrictions: LiquidLib reads in the complete simulation trajectory into the memory at the start of runtime. Thus, if the trajectory size is larger than the available memory of the computer, LiquidLib will fail to execute properly. In this case, the user must reduce the size of the trajectory to be read in before LiquidLib can analyze the trajectory successfully. Unusual features: We provide the option to weigh the computed quantities by the element-specific respective coherent or incoherent scattering lengths. Therefore, LiquidLib allows direct comparisons of the computed quantities to neutron scattering experiments. In addition, the dimension of the simulation trajectories can be any positive integer.

In this paper I present an interesting analysis focused on the hypothesis of relativistic velocities and quantum aspects inside a nanostructure. A new analytical model is considered, able to well describe the conductors in nanostructured form. Considering appropriate scattering times, it is possible to mimic the infrared properties of oxides and semiconductors in the nano-form. The new presented result concerns the analytical form of the quantum-relativistic velocities correlation function, and how it works with experimental data of carbon nanotube films.

The 2D scaling properties of GaN surfaces have been studied by means of the 2D height–height correlation function (HHCF). The GaN layers under investigation presented exemplar morphologies, generated by distinct growth methods: a molecular beam epitaxy (MBE) grown surface decorated by hillocks and a metal organic vapor phase epitaxy (MOVPE) grown surface with terraced structure. The 2D statistical analysis of these surfaces has allowed assessing quantitatively the degree of morphological variability along all the different directions across each surface, their corresponding roughness exponents and correlation lengths. A scaling anisotropy as well as correlation length anisotropy has been detected for both hillocked and terraced surfaces. Especially, a marked dependence of correlation length from the direction across the terraced surface has been observed. Additionally, the terraced surfaces showed the lower root mean square (RMS) roughness value and at the same time, the lower roughness exponent value. This could appear as a contradiction, given that a low RMS value is associated to a smooth surface, and usually the roughness exponent is interpreted as a “measure” of the smoothness of the surface, the smoother the surface, the higher (approaching the unity) is the roughness exponent. Our case study is an experimental demonstration in which the roughness exponent should be, more appropriately, interpreted as a quantification of how the roughness changes with length scale.

We explore the feasibility of using machine learning methods to obtain an analytic form of the classical free energy functional for two model fluids, hard rods and Lennard--Jones, in one dimension . The Equation Learning Network proposed in Ref. 1 is suitably modified to construct free energy densities which are functions of a set of weighted densities and which are built from a small number of basis functions with flexible combination rules. This setup considerably enlarges the functional space used in the machine learning optimization as compared to previous work 2 where the functional is limited to a simple polynomial form. As a result, we find a good approximation for the exact hard rod functional and its direct correlation function. For the Lennard--Jones fluid, we let the network learn (i) the full excess free energy functional and (ii) the excess free energy functional related to interparticle attractions. Both functionals show a good agreement with simulated density profiles for thermodynamic parameters inside and outside the training region., Update figures and SI. Some explanations and clarifications are added

We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's functions grow linearly with rate $\alpha$ in generic systems, with an extra logarithmic correction in 1d. The rate $\alpha$ --- an experimental observable --- governs the exponential growth of operator complexity in a sense we make precise. This exponential growth even prevails beyond semiclassical or large-$N$ limits. Moreover, $\alpha$ upper bounds a large class of operator complexity measures, including the out-of-time-order correlator. As a result, we obtain a sharp bound on Lyapunov exponents $\lambda_L \leq 2 \alpha$, which complements and improves the known universal low-temperature bound $\lambda_L \leq 2 \pi T$. We illustrate our results in paradigmatic examples such as non-integrable spin chains, the Sachdev-Ye-Kitaev model, and classical models. Finally we use the hypothesis in conjunction with the recursion method to develop a technique for computing diffusion constants., Comment: 18+9 pages, 10 figures, 1 table; accepted version

Fractional Ornstein–Uhlenbeck noise is considered and investigated. The fractional Ornstein–Uhlenbeck noise may be linked with a supercapacitor driven by the white noise, and its correlation function for the stationary state shows monotonic and oscillatory decays. In the case of the oscillatory behavior the correlation function presents behaviors similar to those of the harmonic noise (harmonic oscillator driven by the white noise). For application, the Langevin equation with the harmonic potential driven by the fractional Ornstein–Uhlenbeck noise is considered; the first two moments and mean energy are investigated.

In previous work, the direct correlation functions of hard spheres and hard ellipsoidal fluids were calculated. In the present work, using Marko variational method and Pynn–Wulf approximation, the three-body direct correlation function of hard ellipsoid fluid is calculated. In these calculations, the triplet direct correlation function of hard spheres is required. The new expressions for the direct correlation function of hard spheres and hard ellipsoids and triplet correlation of hard spheres, introduced by Muller and coworker, are used. The Fourier transform of new triplet direct correlation of hard sphere fluid is compared with the simulation data. As mentioned in previous work, the expansion coefficients of two-body correlations of hard ellipsoids (components of three-body correlations) are fairly in agreement with the Monte Carlo simulation and the other theories. The Fourier transform of new triplet direct correlation of hard spheres and hard ellipsoid fluids is calculated. These Fourier transforms can be used for calculation of triplet structure factor of hard spheres and hard ellipsoid fluids. The Fourier transforms of triplet correlation of hard ellipsoids with elongations $$x = 1.50,\,\,1.20,\,\,1.10$$ as limited cases are compared with exact result of hard spheres of unit diameter. There is qualitative agreement between hard ellipsoids and hard spheres results of triplet correlations.

The susceptibility of the Ising model on a kagome lattice has never been obtained. We investigate the properties of the kagome-lattice Ising model by using the Wang-Landau sampling method. We estimate both the magnetic scaling exponent yh = 1.90(1) and the thermal scaling exponent yt = 1.04(2) only from the susceptibility. From the estimated values of yh and yt, we obtain all the critical exponents, the specific-heat critical exponent α = 0.08(4), the spontaneous-magnetization critical exponent β = 0.10(1), the susceptibility critical exponent γ = 1.73(5), the isothermalmagnetization critical exponent δ = 16(4), the correlation-length critical exponent ν = 0.96(2), and the correlation-function critical exponent η = 0.20(4), without using any other thermodynamic function, such as the specific heat, magnetization, correlation length, and correlation function. One should note that the evaluation of all the critical exponents only from information on the susceptibility is an innovative approach.

Accurately modeling and reconstructing three-dimensional (3D) microstructure of heterogeneous media from limited morphological information obtained from a single two-dimensional (2D) section remains an outstanding problem. Specially, based on simulated annealing (SA) procedure, two-point correlation function S2 is widely used to reconstruct various 3D microstructures in many different cases. However, two-point correlation function is a lower-order statistical descriptor and is generally not sufficient to accurately characterize a microstructure. From the perspective of texture description, a co-occurrence correlation function (CCF) based on gray-level co-occurrence matrix is presented, and four feature functions are derived from it and used as objective function in SA procedure. Moreover, the CCF can be both manageably measured from a single 2D image and embody non-trivial higher-order morphological information. Furthermore, to avoid completely re-computing the CCF in the reconstruction, a fast updating method for CCF is proposed, and thus accelerating the reconstruction process. The four feature functions are utilized to reconstruct different types of media, including square array of nonoverlapping disks, anode microstructure of solid oxide fuel cell and sandstone core. Meanwhile, the two-point correlation function reconstructions are used for comparison. Unconstrained functions including lineal-path function and two-point cluster function are used to quantitatively ascertain the accuracy of the reconstructions, and the comparison of run time is also demonstrated. The results indicate that the proposed method can accurately reconstruct the microstructures with correlation functions being in good agreement with those of the target.

In this work, the structural and dynamical properties of two imidazolium-based geminal dicationic ionic liquids (GDILs), i.e. [Cn(mim)2][NTf2]2 with n = 3 and 5, have been studied to obtain a fundamental understanding of the molecular basis of the macroscopic and microscopic properties of the bulk liquid phase. To achieve this purpose, molecular dynamics (MD) simulation, density functional theory (DFT) and atoms in molecule (AIM) methods were used. Interaction energies, charge transfers and hydrogen bonds between the cation and anions of each studied GDIL were investigated by DFT calculations and also AIM. The mean square displacement (MSD), self-diffusion coefficient, and transference number of the cation and anions, and also the density, viscosity and electrical conductivity of the studied GDILs, were computed at 333.15 K and at 1 atm. The simulated values were in good agreement with the experimental data. The effect of linkage alkyl chain length on the thermodynamic, transport and structural properties of these GDILs has been investigated. The structural features of these GDILs were characterized by calculating the partial site–site radial distribution functions (RDFs) and spatial distribution functions (SDFs). The heterogeneity order parameter (HOP) has been used to describe the spatial structures of these GDILs and the distribution of the angles formed between two cation heads and the middle carbon atom of the linkage alkyl chain was analyzed in these ILs. To investigate the temporal heterogeneity of the studied GDILs, the deviation of the self-part of the van Hove correlation function, Gs(,t), from the Gaussian distribution of particle displacement and also the second-order non-Gaussian parameter, α2(t), were used. Since, the transport and interfacial properties and ionic characteristics of these GDILs were studied experimentally in our previous studies as a function of linkage chain length and temperature, in this work, we try to give a better perspective of the structure and dynamics of these systems at a molecular level.

The ridge signal, which is long-ranged in rapidity, in di-hadron correlations in high-multiplicity p-p and p-A collisions opened up a whole new research area in high-energy QCD. Although the ridge had been observed in A-A collisions and interpreted as a result of the radial flow of quark-gluon plasma, it had not appeared until recently in the data of small collision systems such as p-p and p-A, nor had it been predicted theoretically or seen in event generators. There are two competing approaches that attempt to explain the systematics of the di-hadron ridge signal: hydrodynamics and gluon saturation physics (color glass condensate/glasma). In this work, we present predictions for the transverse momentum and rapidity dependence of the three-particle correlation function within gluon saturation physics. Tri-hadron correlations can be measured, and the data can possibly rule out one of the two alternative approaches.