Long-range Behavior Research Articles

Product-State Distributions of Three-Body Recombination in Zero-Collision-Energy 4He2-Alkaline-Earth-Metal Systems.

The distributions of product states after three-body recombination (TBR) of zero-collision-energy 4He2X systems, with X being 9Be, 24Mg, 40Ca, 88Sr, or 138Ba, are investigated in the hyperspherical representation by quantum mechanically solving the Schrödinger equation. It is found that the weakly bound (dimer) product states are preferentially populated for all of these cases, which could be understood from the joint effects of the lowest incident channel and the relatively long-range behavior of the corresponding nonadiabatic couplings among these lowest incident and shallow recombination channels. For the strongly bound products, since the flow is accessible in the small hyperradial region, their distributions are closely related to the behavior of the nonadiabatic couplings among the corresponding deep recombination channels. Particularly, our results indicate that the products are not always formed exclusively in the most weakly bound state when the scattering lengths among the reactants are relatively large and that there may exist a large fluctuation of the strongly bound products versus their binding energies in the universal region. In addition, the total TBR rates of these nonuniversal systems are also accounted for by the joint effects of the main adiabatic potentials and nonadiabatic couplings.

Continuously varying critical exponents in long-range quantum spin ladders

We investigate the quantum-critical behavior between the rung-singlet phase with hidden string order and the Néel phase with broken SU(2)-symmetry in quantum spin ladders with algebraically decaying unfrustrated long-range Heisenberg interactions. To this end, we determine high-order series expansions of energies and observables in the thermodynamic limit about the isolated rung-dimer limit. This is achieved by extending the method of perturbative continuous unitary transformations (pCUT) to long-range Heisenberg interactions and to the calculation of generic observables. The quantum-critical breakdown of the rung-singlet phase then allows us to determine the critical phase transition line and the entire set of critical exponents as a function of the decay exponent of the long-range interaction. We demonstrate long-range mean-field behavior as well as a non-trivial regime of continuously varying critical exponents implying the absence of deconfined criticality contrary to a recent suggestion in the literature.

Structure and Properties of Metallosupramolecular Polymers with a Nitrogen-Based Bidentate Ligand.

The solid-state properties of supramolecular polymers that feature metal-ligand (ML) complexes are, in addition to the general nature of the monomer, significantly affected by the choice of ligand and metal salt. Indeed, the variation of these components can be used to alter the structural, thermal, mechanical, and viscoelastic properties over a wide ranges. Moreover, the dynamic nature of certain ML complexes can render the resulting metallosupramolecular polymers (MSPs) stimuli-responsive, enabling functions such as healing, reversible adhesion, and mechanotransduction. We here report MSPs based on the bidentate ligand 6-(1'-methylbenzimidazolyl) pyridine (MBP), which is easily accessible and forms threefold coordination complexes with various transition metal ions. Thus, a poly(ethylene-co-butylene) telechelic was end-functionalized with two MBP ligands and the resulting macromonomer was assembled with the triflate salts of either Zn2+, Fe2+, or Ni2+. All three MSPs microphase separate and adopt, depending on the metal ion and thermal history, lamellar or hexagonal morphologies with crystalline domains formed by the ML complexes. The melting transitions are well below 200 °C, and this permits facile (re)processing. Furthermore, defects can be readily and fully healed upon exposure to UV-light. While the three MSPs display similar moduli in the rubbery regime, their extensibility and tensile strength depend on the nature of the ML complex, which similarly affects the long-range order and dynamic behavior.

Chemical Mapping of Excitons in Halide Double Perovskites.

Halide double perovskites comprise an emerging class of semiconductors with tremendous chemical and electronic diversity. While their band structure features can be understood from frontier-orbital models, chemical intuition for optical excitations remains incomplete. Here, we use ab initio many-body perturbation theory within the GW and the Bethe-Salpeter equation approach to calculate excited-state properties of a representative range of Cs2BB'Cl6 double perovskites. Our calculations reveal that double perovskites with different combinations of B and B' cations display a broad variety of electronic band structures and dielectric properties and form excitons with binding energies ranging over several orders of magnitude. We correlate these properties with the orbital-induced anisotropy of charge-carrier effective masses and the long-range behavior of the dielectric function by comparing them with the canonical conditions of the Wannier-Mott model. Furthermore, we derive chemically intuitive rules for predicting the nature of excitons in halide double perovskites using computationally inexpensive density functional theory calculations.

Geometrically constrained kink-like configurations engendering long-range, double-exponential, half-compact and compact behavior

Geometrically constrained kink-like configurations engendering long-range, double-exponential, half-compact and compact behavior

Quantifying the Impact of Halogenation on Intermolecular Interactions and Binding Modes of Aromatic Molecules.

Halogenation of aromatic molecules is frequently used to modulate intermolecular interactions with ramifications for optoelectronic and mechanical properties. In this work, we accurately quantify and understand the nature of intermolecular interactions in perhalogenated benzene (PHB) clusters. Using benchmark binding energies from the fixed-node diffusion Monte Carlo (FN-DMC) method, we show that generalized Kohn-Sham semicanonical projected random phase approximation (GKS-spRPA) plus approximate exchange kernel (AKX) provides reliable interaction energies with mean absolute error (MAE) of 0.23 kcal/mol. Using the GKS-spRPA+AXK method, we quantify the interaction energies of several binding modes of PHB clusters ((C6X6)n; X = F, Cl, Br, I; n = 2, 3). For a given binding mode, the interaction energies increase 3-4 times from X = F to X = I; the X-X binding modes have energies in the range of 2-4 kcal/mol, while the π-π binding mode has interaction energies in the range of 4-12 kcal/mol. SAPT-DFT-based energy decomposition analysis is then used to show that the equilibrium geometries are dictated primarily by the dispersion and exchange interactions. Finally, we test the accuracy of several dispersion-corrected density functional approximations and show that only the r2SCAN-D4 method has a low MAE and correct long-range behavior, which makes it suitable for large-scale simulations and for developing structure-function relationships of halogenated aromatic systems.

Extrapolation properties of the Morse-Long Range potential at large internuclear distances

The accuracy of the potential energy curves for diatomic molecules determined from experimental data is confirmed empirically with numerous examples in the literature. Usually PECs are determined from a limited set of experimental data and this in turns limits the range of internuclear distances where the shape of the potential is unambiguously fixed. While the uncertainty for interpolation could be assessed, the extrapolation is usually questionable and needs careful analyses. The Morse/Long-Range potential (Le Roy and Henderson, 2007) has been reported to have a built in long-range asymptotic behavior and therefore it is plausible to expect that one can expect good extrapolation properties and even possibility to determine important molecular parameters like De or/and Cm from limited set of experimental data. In this contribution we undertake a systematic study which confirms these expectations in the case of Ca2 ground state.

Percolation in fractal spatial networks with long-range interactions

We study the emergence of a giant component in a spatial network where the nodes form a fractal set, and the interaction between the nodes has a long-range power-law behavior. The nodes are positioned in the metric space using a L\`evy flight procedure, with an associated scale-invariant step probability density function, that is then followed by a process of connecting each pair of nodes with a probability that depends on the distance between them. Since the nodes are positioned sequentially, we are able to calculate the probability for an edge between any two nodes in terms of their indexes and to map the model to the problem of percolation in a one-dimensional lattice with long-range interactions. This allows the identification of the conditions for which a percolation transition is possible. The system is characterized by two control parameters which determine the fractal dimension of the nodes and the power law decrease of the probability of a bond with the distance between the nodes. The competition between these two parameters forms an intricate phase diagram, which describes when the system has a stable giant component, and when percolation transitions occur. Understanding the structure of this class of spatial networks is important when analyzing real systems, which are frequently heterogeneous and include long-range interactions.

Hyperspherical Cluster Model for Bosons: Application to Sub-threshold Halo States in Helium Drops

To describe long-range behaviour of one particle removed from a few- or a many-body system, a hyperspherical cluster model has been developed. It has been applied to the ground and first excited states of helium drops with five, six, eight and ten atoms interacting via a two-body soft gaussian potential. Convergence of the hyperspherical cluster harmonics expansion is studied for binding energies, root-mean-squared radii and overlaps of the wave functions of two helium drops differing by one atom. It was shown that with increasing model space the functional form of such overlaps at large distances converges to the correct asymptotic behaviour. The asymptotic normalization coefficients that quantify the overlaps’ amplitudes in this region are calculated. It was also shown that in the first excited state one helium atom stays far apart from the rest forming a two-body molecule, or a halo. The probability of finding the halo atom in the classically-forbidden region of space depends on the definition of the latter and on the valence atom binding energy. The total norm of the overlap integrals, the spectroscopic factor, represents the number of partitions of a many-body state into a chosen state of the system with one particle removed. The spectroscopic factors have been calculated and their sum rules are discussed giving a further insight into the structure of helium drops.

Revisiting the DD* chiral interactions with the local momentum-space regularization up to the third order and the nature of Tcc+

We revisit the $DD^\ast$ interactions in chiral effective field theory up to the third order for the first time. We deal with the pion-exchanged interactions via local momentum-space regularization, in which we focus on their long-range behaviors through demanding their contributions vanish at the origin in the coordinate space. The short-range contact interactions and subleading pion-charmed meson couplings are estimated with the phenomenological resonance saturation model. The subleading pion-charmed meson couplings are much weaker than those in the pion-nucleon system, thus the $DD^\ast$ binding mechanism is very different with that of the $NN$ system. We also obtain the analytic structure of the two-pion exchange interactions in the coordinate space, and we find that its asymptotic behavior at long distance is similar to but slightly different with the $NN$ interactions. We get the same asymptotic behavior of the two-pion exchange interaction with that from HAL QCD method but appearing in the longer distance rather than $1 <r<2\text{ fm}$. The binding solution only exists in the isoscalar channel. Our calculation supports the molecular interpretation of $T_{cc}^+$.

Near-continuous isotropic – nematic transition in compressed rod-like liquid crystal based nanocolloid

Landau-de Gennes mean-field model predicts the discontinuous transition for the isotropic – nematic (I-N) transition, associated with uniaxial ordering and a quadrupolar order parameter in three dimensions. This report shows pressure-related dielectric studies for rod-like nematogenic pentylcyanobiphenyl (5CB) and its nanocolloids with BaTiO3 nanoparticles. The scan of the dielectric constant revealed the near-continuous I-N phase transition in the compressed nanocolloid with a tiny amount of nanoparticles (x = 0.1%).For the nematic phase in 5CB and its x = 1% nanocolloid the enormous values of the dielectric constant and the bending–type, long-range pretransitional behavior were detected. The impact of prenematic fluctuations was also noted for the ionic-related contribution to dielectric permittivity in the isotropic liquid phase. For the high-frequency relaxation domain, this impact was tested for the primary relaxation time pressure evolution and the translational–orientational decoupling.

Gapless Spin Liquid and Nonlocal Corner Excitation in the Spin-1/2 Heisenberg Antiferromagnet on Fractal

Motivated by the mathematical beauty and the recent experimental realizations of fractal systems, we study the spin-1/2 antiferromagnetic Heisenberg model on a Sierpiński gasket. The fractal porous feature generates new kinds of frustration to exhibit exotic quantum states. Using advanced tensor network techniques, we identify a quantum gapless-spin-liquid ground state in fractional spatial dimension. This fractal spin system also demonstrates nontrivial nonlocal properties. While the extremely short-range correlation causes a highly degenerate spin form factor, the entanglement in this fractal system suggests a long-range scaling behavior. We also study the dynamic structure factor and clearly identify the gapless excitation with a stable corner excitation emerged from the ground-state entanglement. Our results unambiguously point out multiple essential properties of this fractal spin system, and open a new route to explore spin liquid and frustrated magnetism.

Stochastic simulation of wind wave parameters for energy production

A combination of stochastic and deterministic models is applied for the study of ocean wind waves. Timeseries of significant wave height and mean zero up-crossing period, obtained from globally scattered floating buoys, are analyzed in order to construct a double periodic model, and select an optimal marginal distribution and dependence function for the description of the stochastic structure of wind waves. It is concluded that wind waves, in contrast to the atmospheric wind speed process, are mostly governed by the seasonal periodicity rather than the diurnal periodicity, which is often weak and can be neglected. Also, the Pareto-Burr-Feller distribution is found to be a fair selection among other common three-parameter marginal distributions. The dependence function is simulated through the Hurst-Kolmogorov (HK) dynamics using the climacogram (i.e., variance of the averaged process in the scale domain), a stochastic tool that can robustly estimate both the short-term fractal and long-range dependence behaviors both apparent at the wind wave process. To test the validity of the model, a stochastic synthesis of the wind wave process is performed through the Symmetric Moving Average scheme, focused on the explicit preservation of the probabilistic and the dependence structures. Finally, the stochastic model is applied for simulation to an offshore station southeast of Australia having one of the largest record lengths. The energy potential is also estimated through the significant wave height and the mean zero up-crossing period of both the synthetic and observed timeseries, and the effectiveness of the model is further discussed.

Cryptocurrencies and Long-Range Trends

In this study we investigate possible long-range trends in the cryptocurrency market. We employed the Hurst exponent in a sample covering the period from 1 January 2016 to 26 March 2021. We calculated the Hurst exponent in three non-overlapping consecutive windows and in the whole sample. Using these windows, we assessed the dynamic evolution in the structure and long-range trend behavior of the cryptocurrency market and evaluated possible changes in their behavior towards an efficient market. The innovation of this research is that we employ the Hurst exponent to identify the long-range properties, a tool that is seldomly used in analysis of this market. Furthermore, the use of both the R/S and the DFA analysis and the use of non-overlapping windows enhance our research’s novelty. Finally, we estimated the Hurst exponent for a wide sample of cryptocurrencies that covered more than 80% of the entire market for the last six years. The empirical results reveal that the returns follow a random walk making it difficult to accurately forecast them.

Occurrence, spatial distribution, and sources of PFASs in the water and sediment from lakes in the Tibetan Plateau.

Per-and polyfluoroalkyl substances (PFASs) are omnipresent globally and received increasing attention recently. However, there are limited data on PFASs in the Tibetan Plateau (TP), a remote high-altitude mountain region, which is regard as an important indicator region to study long-range transport behaviors of contaminants. This study investigates the occurrence, distribution, partitioning behavior, and sources of 26 PFASs in water and sediments from the four lakes of TP. The ΣPFAS concentrations ranged from 338 to 9766pgL-1 in water, and 12.2-414pgg-1 dry weight in sediments. Perfluorobutanonic acid (PFBA) and perfluorooctane sulfonate (PFOS) were detected in all samples. Qinghai Lake had the highest ΣPFAS concentrations in both water and sediments, while the Ranwu Lake had the lowest. The functional groups and CF2 moiety units were investigated as essential factors influencing the partition behavior. Principal component analysis (PCA) combined back-trajectory was used to infer possible sources of PFASs. The results suggested that the main source of PFASs in Yamdrok Lake, Namco Lake, and Ranwu Lake on southern TP were mainly originated from South Asia via long-range atmospheric transport (LRAT); while for the Qinghai Lake of northern TP, LRAT, local emissions, and tourism activities were the primary sources of PFASs.

Rethinking Generalized Beta family of distributions

We approach the Generalized Beta (GB) family of distributions using a mean-reverting stochastic differential equation (SDE) for a power of the variable, whose steady-state (stationary) probability density function (PDF) is a modified GB (mGB) distribution. The SDE approach allows for a lucid explanation of Generalized Beta Prime (GB2) and Generalized Beta (GB1) limits of GB distribution and, further down, of Generalized Inverse Gamma (GIGa) and Generalized Gamma (GGa) limits, as well as describe the transition between the latter two. We provide an alternative form to the "traditional" GB PDF to underscore that a great deal of usefulness of GB distribution lies in its allowing a long-range power-law behavior to be ultimately terminated at a finite value. We derive the cumulative distribution function (CDF) of the "traditional" GB, which belongs to the family generated by the regularized beta function and is crucial for analysis of the tails of the distribution. We analyze fifty years of historical data on realized market volatility, specifically for S\&P500, as a case study of the use of GB/mGB distributions and show that its behavior is consistent with that of negative Dragon Kings.

Electrically conductive [Fe4S4]-based organometallic polymers.

Tailoring the molecular components of hybrid organic-inorganic materials enables precise control over their electronic properties. Designing electrically conductive coordination materials, e.g. metal-organic frameworks (MOFs), has relied on single-metal nodes because the metal-oxo clusters present in the vast majority of MOFs are not suitable for electrical conduction due to their localized electron orbitals. Therefore, the development of metal-cluster nodes with delocalized bonding would greatly expand the structural and electrochemical tunability of conductive materials. Whereas the cuboidal [Fe4S4] cluster is a ubiquitous cofactor for electron transport in biological systems, few electrically conductive artificial materials employ the [Fe4S4] cluster as a building unit due to the lack of suitable bridging linkers. In this work, we bridge the [Fe4S4] clusters with ditopic N-heterocyclic carbene (NHC) linkers through charge-delocalized Fe-C bonds that enhance electronic communication between the clusters. [Fe4S4Cl2(ditopic NHC)] exhibits a high electrical conductivity of 1 mS cm-1 at 25 °C, surpassing the conductivity of related but less covalent materials. These results highlight that synthetic control over individual bonds is critical to the design of long-range behavior in semiconductors.

Universal van der Waals Force between Heavy Polarons in Superfluids.

We investigate the long-range behavior of the induced Casimir interaction between two spinless heavy impurities, or polarons, in superfluid cold atomic gases. With the help of effective field theory (EFT) of a Galilean invariant superfluid, we show that the induced impurity-impurity potential at long distance universally shows a relativistic van der Waals-like attraction (∼1/r^{7}) resulting from the exchange of two superfluid phonons. We also clarify finite temperature effects from the same two-phonon exchange process. The temperature T introduces the additional length scale c_{s}/T with the speed of sound c_{s}. Leading corrections at finite temperature scale as T^{6}/r for distances r≪c_{s}/T smaller than the thermal length. For larger distances the potential shows a nonrelativistic van der Waals behavior (∼T/r^{6}) instead of the relativistic one. Our EFT formulation applies not only to weakly coupled Bose or Fermi superfluids but also to those composed of strongly correlated unitary fermions with a weakly coupled impurity. The sound velocity controls the magnitude of the van der Waals potential, which we evaluate for the fermionic superfluid in the BCS-BEC crossover.

Thermochemistry of per- and polyfluoroalkyl substances.

The determination of gas phase thermochemical properties of per- and polyfluoroalkyl substances (PFAS) is central to understanding the long-range transport behavior of PFAS in the atmosphere. Prior gas-phase studies have reported the properties of perfluorinated sulfonic acid (PFOS) and perfluorinated octanoic acid (PFOA). Here, this study reports the gas phase enthalpies of formation of short- and long-chain PFAS and their precursor molecules determined using density functional theory (DFT) and ab initio approaches. Two density functionals, two ab initio methods and an empirical method were used to compute enthalpies of formation with the total atomization approach and an isogyric reaction. The performance of the computational methods employed in this work were validated against the experimental enthalpies of linear alkanoic acids and perfluoroalkanes. The gas-phase determinations will be useful for future studies of PFAS in the atmosphere, and the methodological choices will be helpful in the study of other PFAS.

Measuring Cross-Correlations, Contagion and Long-Range Behavior between Fires in Brazil and Some Time Series Related to Its Economic Growth

Fires bring up the debate about their impact on Brazil’s economic growth. Some processing tools such as cointegration and, especially, the correlation have been applied for identifying possible transmission or contagion mechanisms between distinct time series. This paper adopts the detrended cross-correlation analysis (DCCA) and rolling window approach to investigate the dynamic coupling between fires and the evolution of some key variables related to Brazil’s economic growth (e.g., agricultural planted area, ethanol production, rainfall in the midwest region and gross domestic product) covering two periods, namely from January 2012 to August 2016 (before the Brazilian presidential impeachment occurred in 2016) and from September 2016 to April 2021, covering the post-impeachment scenario, with the new government policies in the environmental sector. The results show a positive cross-correlation between the level of fires versus planted area of all cereals, leguminous and oleaginous in Brazil (mostly Soybean and Corn) and versus ethanol production (a renewable energy generation). It is also possible to verify some impact level on the Brazilian gross domestic product. Furthermore, we observed quantitatively, by means of the adopted methods that fires in Brazil have the potential to damage economic growth and some activities addressed in this study can also harm the environment in both mid and long-term.