Short-range Model Research Articles

Energy transmission in the forbidden band-gap of a nonlinear chain with global interactions

The phenomenon of supratransmission in nonlinear systems with global interactions is predicted analytically for the first time. The model considered is a physically significant extension of the classical β-Fermi–Pasta–Ulam–Tsingou (β-FPUT) chain, with power-law interaction of degree α ⩾ 0. Using a relatively simple analytical theory, we derive the threshold that triggers the supratransmission process. The threshold for the short-range model is a particular case of our predictions. Our theoretical derivation shows that supratransmission is present for any power α > 1. We confirm numerically the validity of these results. Moreover, the numerical simulations also confirm the presence of supratransmission in the case of long-range interactions, in spite that the theoretical arguments are not valid for that case. It is worth pointing out that the present approach may be applied to other systems with global interactions.

Long-range multi-scalar models at three loops

We compute the three-loop beta functions of long-range multi-scalar models with general quartic interactions. The long-range nature of the models is encoded in a kinetic term with a Laplacian to the power 0 < ζ < 1, rendering the computation of Feynman diagrams much harder than in the usual short-range case (ζ = 1). As a consequence, previous results stopped at two loops, while seven-loop results are available for short-range models. We push the renormalization group analysis to three loops, in an ϵ = 4ζ − d expansion at fixed dimension d < 4, extensively using the Mellin–Barnes representation of Feynman amplitudes in the Schwinger parametrization. We then specialize the beta functions to various models with different symmetry groups: O(N), , and O(N) × O(M). For such models, we compute the fixed points and critical exponents.

Changes in spatial patterns of ammonia dry deposition flux and deposition threshold exceedance according to dispersion model formalism and horizontal resolution.

Ammonia (NH3) emitted into the atmosphere from agricultural sources may affect nearby sensitive ecosystems due to high dry deposition fluxes on vegetation and soil surfaces, contributing to critical load exceedances. Ammonia fluxes near sources are simulated by either short-range atmospheric models or regional models using large grid cell sizes. However, studies are missing on the comparison of the results simulated by these two types of models. This paper presents the effect of model formalism, input factors, especially grid cell size and wind speed and the choice of deposition threshold on the spatial patterns of NH3 dry deposition fluxes and deposition threshold exceedances. We used the Eulerian chemistry-transport model CHIMERE and the Gaussian plume model OPS-ST on two study domains characterised by contrasting land use. We showed that the average annual NH3 dry deposition fluxes over each whole domain are similar for both models. By contrast, NH3 dry deposition fluxes near sources are higher when simulated with OPS-ST that provides analytical solutions that can be sampled with small grid cell sizes (i.e., from 25 to 1600m in this study), than with CHIMERE, which uses large grid cell sizes (i.e., 800 and 1600m). As a result, the spatial patterns of deposition threshold exceedance were very different between both models. These patterns depend mainly on grid cell size, the input factors and the choice of the deposition threshold value. We show that the model formalism has a relatively small effect on the results and that the differences result mainly from the spatial resolutions to which they can be applied. Simulation results must therefore be interpreted carefully, taking into account the simulation conditions.

Semiclassical dynamics of a disordered two-dimensional Hubbard model with long-range interactions

Quench dynamics in a two-dimensional system of interacting fermions is analyzed within the semiclassical truncated Wigner approximation (TWA). The models with short-range and long-range interactions are considered. We show that in the latter case, the TWA is very accurate, becoming asymptotically exact in the infinite-range limit, provided that the semiclassical Hamiltonian is correctly identified. Within the TWA, different dynamical timescales of charges and spins can be clearly distinguished. Interestingly, for a weak and moderate disorder strength, we observe subdiffusive behavior of charges, while spins exhibit diffusive dynamics. At strong disorder, the quantum Fisher information shows logarithmic growth in time with a slower increase for charges than for spins. It is shown that in contrast to the short-range model, strong inhomogeneities such as domain walls in the initial state can significantly slow down thermalization dynamics, especially at weak disorder. This behavior can put additional challenges in designing cold-atom experimental protocols aimed to analyze possible many-body localization in such systems. While within this approach we cannot make any definite statements about the existence of a many-body localized phase, we see a very fast crossover as a function of disorder strength from rapidly thermalizing to a slow glassy like regime both for the short-range and long-range models.

The Mechanism of Dynamic Strain Aging for Type a Serrations in Tensile Curves of a Medium-Mn Steel

The objective of the present study is to clarify the mechanism of dynamic strain aging (DSA) causing serrations in tensile flow curves of Fe-5.1Mn-0.15C (wt%) medium-Mn steel specimens with triple phases of retained austenite (γR ), ferrite (α) and tempered martensite (α'T ). For the purpose, many tensile tests were performed at various conditions of deformation temperature ( Td = 273 - 333 K) and initial strain rate ( έini = 5 × 10 -4 - 1 × 10 -2 s -1 ). The medium-Mn steel specimens revealed type A serrations after the propagation of the Luders band in their tensile curves. The serrations were not related to both α and α'T ; they were not caused by strain-induced martensitic transformation, but by DSA in γR . The DSA was not explained by the short-range diffusion model based on the interaction between partial dislocations and C-Mn complexes due to the absence of intersection between staying time and reorientation time. In a viewpoint of the dislocation arrest model involving long-range diffusion, critical strains of γR for serrations (ecγ ) were measured. They showed the normal Portevine-Le Châtelier behavior that the ecγ value decreases with increasing Td and with decreasing έini . The activation energy measured using the ecγ values was similar to the activation energy for the dislocation pipe diffusion of C atoms. This result indicates that the DSA occurring in the present medium-Mn steel is explained by the dislocation arrest model involving the long-range pipe diffusion of C atoms, not by the short-range diffusion model involving the reorientation of C-Mn complexes.

A study on the vibrational frequencies, elastic properties and sound velocities of vanadium spinel oxides AV2O4 (A = Mn, Fe and Zn) short-range non-Coulomb potential theoretical model

Owing to the fact of the AB2O4 spinel oxide’s chemical and thermal stability, and other intriguing properties make them suitable candidate materials for many applications, including chemical looping and catalytic reactions. To do our investigations, a short-range non-Coulomb potential theoretical model is used to calculate the zone-centre, elastic constants, infrared phonon mode frequencies, Raman phonon mode frequencies, velocities of the sound wave along the highly symmetric three crystallographic-axes and Debye temperature of the vanadium spinel oxides AV2O4 (A = Mn, Fe and Zn). The preliminary results of our calculations show that the interaction in the second neighbour (V–O) is much stronger than the interaction of the first neighbour (A–O). Moreover, from the analysis of the obtained results of elastic constants, the nature of the studied vanadium spinels are found to be ductile.

Projective symmetry group classifications of quantum spin liquids on the simple cubic, body centered cubic, and face centered cubic lattices

We perform extensive classifications of $\mathbb{Z}_2$ quantum spin liquids on the simple cubic, body centered cubic, and face centered cubic lattices using a spin-rotation invariant fermionic projective symmetry group approach. Taking into account that all three lattices share the same point group $O_h$, we apply an efficient gauge where the classification for the simple cubic lattice can be partially carried over to the other two lattices. We identify hundreds of projective representations for each of the three lattices, however, when constructing short-range mean-field models for the fermionic partons (spinons) these phases collapse to only very few relevant cases. We self-consistently calculate the corresponding mean-field parameters for frustrated Heisenberg models on all three lattices with up to third neighbor spin interactions and discuss the spinon dispersions, ground state energies and dynamical spin structure factors. Our results indicate that phases with non-uniform spinon hopping or pairing amplitudes are energetically favored. An unusual situation is identified for the fcc lattice where the spinon dispersion minimizing the mean-field energy features a network of symmetry protected line-like zero modes in reciprocal space. We further discuss characteristic fingerprints of these phases in the dynamical spin structure factor which may help to identify and distinguish them in future numerical or experimental studies.

Dynamic response functions of two-dimensional Dirac fermions with screened Coulomb and short-range interactions

We consider a screened Coulomb interaction between electrons in graphene and determine their dynamic response functions, such as a longitudinal and a transverse electric conductivity and a polarization function and compare them to the corresponding quantities in the short-range interaction model. The calculations are performed to all orders for short-range interaction by taking into account the self-energy renormalization of the electron velocity and using a ladder approximation to account for the vertex corrections, ensuring that the Ward identity (charge conservation law) is satisfied. Our findings predict a resonant response of interacting electron-hole pairs at a particular frequency below the threshold $qv=\omega$ and further predict an instability for sufficiently strong interactions.

Confinement in the spectrum of a Heisenberg–Ising spin ladder

The Heisenberg–Ising spin ladder is one of the few short-range models showing confinement of elementary excitations without the need of an external field, neither transverse nor longitudinal. This feature makes the model suitable for an experimental realization with ultracold atoms. In this paper, we combine analytic and numerical techniques to precisely characterize its spectrum in the regime of Hamiltonian parameters showing confinement. We find two kinds of particles, which we dub intrachain and interchain mesons, that correspond to bound states of kinks within the same chain or between different ones, respectively. The ultimate physical reasons leading to the existence of two families of mesons is a residual double degeneracy of the ground state: the two types of mesons interpolate either between the same vacuum (intrachain) or between the two different ones (interchain). While the intrachain mesons can also be qualitatively assessed through an effective mean field description and were previously known, the interchain ones are new and they represent general features of spin ladders with confinement.

Subsystem symmetry enriched topological order in three dimensions

We introduce a model of three-dimensional (3D) topological order enriched by planar subsystem symmetries. The model is constructed starting from the 3D toric code, whose ground state can be viewed as an equal-weight superposition of two-dimensional (2D) membrane coverings. We then decorate those membranes with 2D cluster states possessing symmetry-protected topological order under line-like subsystem symmetries. This endows the decorated model with planar subsystem symmetries under which the loop-like excitations of the toric code fractionalize, resulting in an extensive degeneracy per unit length of the excitation. We also show that the value of the topological entanglement entropy is larger than that of the toric code for certain bipartitions due to the subsystem symmetry enrichment. Our model can be obtained by gauging the global symmetry of a short-range entangled model which has symmetry-protected topological order coming from an interplay of global and subsystem symmetries. We study the non-trivial action of the symmetries on boundary of this model, uncovering a mixed boundary anomaly between global and subsystem symmetries. To further study this interplay, we consider gauging several different subgroups of the total symmetry. The resulting network of models, which includes models with fracton topological order, showcases more of the possible types of subsystem symmetry enrichment that can occur in 3D.

Quasideterministic dynamics, memory effects, and lack of self-averaging in the relaxation of quenched ferromagnets.

We discuss the interplay between the degree of dynamical stochasticity, memory persistence, and violation of the self-averaging property in the aging kinetics of quenched ferromagnets. We show that, in general, the longest possible memory effects, which correspond to the slowest possible temporal decay of the correlation function, are accompanied by the largest possible violation of self-averaging and a quasideterministic descent into the ergodic components. This phenomenon is observed in different systems, such as the Ising model with long-range interactions, including the mean-field, and the short-range random-field Ising model.

Nonlinear propagation of pulses in multimode fiber with strong linear coupling

Multimode fiber has a richer spatial dimension than single-mode fiber, and is an ideal platform for studying many novel nonlinear effects. We established a strong linear coupling and short-range fiber model to understand the interactive effects of linear coupling and nonlinear effects. We find that strong linear coupling can compensate for the group delay between eigenmodes and cause energy fluctuation between modes which weakens the nonlinear effects. In high energy pulses, the interaction of linear coupling and nonlinear effects can help producing weak dispersion waves when the spectrum is broadened. Since linear coupling in a mode group is common and unavoidable, these results may provide a certain theoretical explanation for multi-mode nonlinear phenomena.

Dielectric response with short-ranged electrostatics

The dielectric nature of polar liquids underpins much of their ability to act as useful solvents, but its description is complicated by the long-ranged nature of dipolar interactions. This is particularly pronounced under the periodic boundary conditions commonly used in molecular simulations. In this article, the dielectric properties of a water model whose intermolecular electrostatic interactions are entirely short-ranged are investigated. This is done within the framework of local molecular-field theory (LMFT), which provides a well-controlled mean-field treatment of long-ranged electrostatics. This short-ranged model gives a remarkably good performance on a number of counts, and its apparent shortcomings are readily accounted for. These results not only lend support to LMFT as an approach for understanding solvation behavior, but also are relevant to those developing interaction potentials based on local descriptions of liquid structure.

Statistics of geometric clusters in Potts model: statistical mechanics approach.

The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters' size distributions is developed. It allows full description of percolation transition when a giant cluster of equal-valued Potts spins appears. The method is applied to the short-ranged q-state ferromagnetic Potts model on the Bethe lattices with the arbitrary coordination number z. The analytical results for the field-temperature percolation phase diagram of geometric spin clusters and their size distribution are obtained. The last appears to be proportional to that of the classical non-correlated bond percolation with the bond probability, which depends on temperature and Potts model parameters.

Study of Fuel-Smoke Dynamics in a Prescribed Fire of Boreal Black Spruce Forest through Field-Deployable Micro Sensor Systems

Understanding the combustion dynamics of fuels, and the generation and propagation of smoke in a wildland fire, can inform short-range and long-range pollutant transport models, and help address and mitigate air quality concerns in communities. Smoldering smoke can cause health issues in nearby valley bottoms, and can create hazardous road conditions due to low-visibility. We studied near-field smoke dynamics in a prescribed fire of 3.4 hectares of land in a boreal black spruce forest in central Alberta. Smoke generated from the fire was monitored through a network of five field-deployable micro sensor systems. Sensors were placed within 500–1000 m of the fire area at various angles in downwind. Smoke generated from flaming and smoldering combustions showed distinct characteristics. The propagation rates of flaming and smoldering smoke, based on the fine particulate (PM2.5) component, were 0.8 and 0.2 m/s, respectively. The flaming smoke was characterized by sharp rise of PM2.5 in air with concentrations of up to 940 µg/m3, followed by an exponential decay with a half-life of ~10 min. Smoldering combustion related smoke contributed to PM2.5 concentrations above 1000 µg/m3 with slower decay half-life of ~18 min. PM2.5 emissions from the burn area during flaming and smoldering phases, integrated over the combustion duration of 2.5 h, were ~15 and ~16 kilograms, respectively, as estimated by our mass balance model.

A review on short-range dispersion modelling of gaseous pollutants released from stationary sources

The reliance on solid fuels for heat processing and power generation with low efficiency and inadequately control of gaseous pollutants is strongly related to health impacts and environmental pollution. Atmospheric dispersion modelling is an essential tool to assess the potential impacts of related stationary sources on local air quality. Advanced Gaussian plume models provide an up-to-date assemble of algorithms to estimate contaminant concentrations distributed at a variety of heights and distances. This review presented a comparative evaluation on ADMS and AERMOD performance in different validation scenarios considering SO2 emissions and the NOx chemistry scheme. Terrain, stack height and plume rise influence on emissions, along with modelling uncertainties and limitations were also discussed. Contour plots of maximum daily values and annual averages confirmed a remarkable similarity in patterns within simulations. By this approach, the study extended recent practical information and recommended a complementary instrument for the improvement of the reference model SYMOS´97 implemented in the Czech Republic.

Sextic tensor field theories in rank 3 and 5

We study bosonic tensor field theories with sextic interactions in d < 3 dimensions. We consider two models, with rank-3 and rank-5 tensors, and U(N)3 and O(N)5 symmetry, respectively. For both of them we consider two variations: one with standard short-range free propagator, and one with critical long-range propagator, such that the sextic interactions are marginal in any d < 3. We derive the set of beta functions at large N , compute them explicitly at four loops, and identify the respective fixed points. We find that only the rank-3 models admit melonic interacting fixed points, with real couplings and critical exponents: for the short-range model, we have a Wilson-Fisher fixed point with couplings of order sqrt{epsilon } , in d = 3 − ϵ; for the long-range model, instead we have for any d < 3 a line of fixed points, parametrized by a real coupling g1 (associated to the so-called wheel interaction). By standard conformal field theory methods, we then study the spectrum of bilinear operators associated to such interacting fixed points, and we find a real spectrum for small ϵ or small g1.

Assignment of optical phonons at the zone center of distorted orthorhombic RCrO3 (R = La, Pr, Nd, Sm, Eu) perovskites using force-field lattice dynamics model

The assignment of the optical phonons to the specific active modes of an arbitrary crystal structure provides important keys to establish a proper correlation between the structural changes, microstructural characterization and the properties of the material. A short-range force-field model is, therefore, applied to investigate the optical phonon distributions and complex behavior of atomic motions in distorted orthorhombic (space group: Pbnm) perovskites RCrO3 (R = La, Pr, Nd, Sm, Eu). The lattice dynamics calculations are performed taking account of the nine bond-stretching and seven angle-bending force constants within the framework of normal coordinate analysis. The model calculations provide good agreement between our theoretical and the previously observed Raman and infrared modes of orthochromites RCrO3. All of the total forty nine optical modes of these perovskites are assigned to the specific modes at Γ-point of the Brillouin zone simultaneously. The potential energy distribution (PED) coefficients have also been evaluated to investigate the contribution of each force constant to the calculated optical phonon modes. Depending on the bond strengths and PED of various coupling between ions forming bonds, complex behavior of several low-wave number Raman modes, namely, mode mixing and mode crossing, in the light of atomic movements are addressed for this series of orthochromites.

Universal regularity of higher-dimensional disorder and density of states under non-local interactions. I. Infinite smoothness and localization

It is shown that in a large class of disordered systems with singular alloy-type disorder and non-local media-particle interactions, the marginal measures of the induced random potential and the finite-volume integrated density of states (IDS) are infinitely differentiable in higher dimensions. The proposed approach complements the classical Wegner estimate which says that the IDS in the short-range models is at least as regular as the marginal distribution of the disorder. In the models with non-local interaction the finite-volume IDS is much more regular than the underlying disorder. In turn, smoothness of the finite-volume IDS is responsible for a mechanism complementing the Lifshitz tails phenomenon. The new eigenvalue concentration estimates give rise to relatively simple proofs of Anderson localization in several classes of discrete and continuous long-range models with arbitrarily singular disorder. The present paper addresses the model with power-law decay of the potential.

Many-body localization in a long-range model: Real-space renormalization-group study.

We develop a real-space renormalization-group (RSRG) scheme by appropriately inserting the long-range hopping t∼r^{-α} with nearest-neighbor interaction to study the entanglement entropy and maximum block size for the many-body localization (MBL) transition. We show that for α<2 there exists a localization transition with renormalized disorder that depends logarithmically on the finite size of the system. The transition observed for α>2 does not need a rescaling in disorder strength. Most important, we find that even though the MBL transition for α>2 falls in the same universality class as that of the short-range models, the transition for α<2 belongs to a different universality class. Because of the intrinsic nature of the RSRG flow toward delocalization, MBL phase for α>2 might suffer an instability in the thermodynamic limit while the underlying systems support algebraic localization. Moreover, we verify these findings by inserting microscopic details to the RSRG scheme where we additionally find a more appropriate rescaling function for disorder strength; we indeed uncover a power-law scaling with a logarithmic correction and a distinctly different stretched exponential scaling for α<2 and α>2, respectively, by analyzing system with finite size. This finding further suggests that microscopic RSRG scheme is able to give a hint of instability of the MBL phase for α>2 even considering systems of finite size.