Function Of Order Parameter Research Articles

Variational time reversal for free-energy estimation in nonequilibrium steady states.

Studying the structure of systems in nonequilibrium steady states necessitates tools that quantify population shifts and associated deformations of equilibrium free-energy landscapes under persistent currents. Within the framework of stochastic thermodynamics, we establish a variant of the Kawasaki-Crooks equality that relates nonequilibrium free-energy corrections in overdamped Langevin systems to heat dissipation statistics along time-reversed relaxation trajectories computable with molecular simulation. Using stochastic control theory, we arrive at a general variational approach to evaluate the Kawasaki-Crooks equality and use it to estimate distribution functions of order parameters in specific models of driven and active matter, attaining substantial improvement in accuracy over simple perturbative methods.

Certifying Ground-State Properties of Many-Body Systems

A ubiquitous problem in quantum physics is to understand the ground-state properties of many-body systems. Confronted with the fact that exact diagonalization quickly becomes impossible when increasing the system size, variational approaches are typically employed as a scalable alternative: Energy is minimized over a subset of all possible states and then different physical quantities are computed over the solution state. Despite remarkable success, rigorously speaking, all that variational methods offer are upper bounds on the ground-state energy. On the other hand, so-called relaxations of the ground-state problem based on semidefinite programming represent a complementary approach, providing lower bounds to the ground-state energy. However, in their current implementation, neither variational nor relaxation methods offer provable bound on other observables in the ground state beyond the energy. In this work, we show that the combination of the two classes of approaches can be used to derive certifiable bounds on the value of any observable in the ground state, such as correlation functions of arbitrary order, structure factors, or order parameters. We illustrate the power of this approach in paradigmatic examples of 1D and 2D spin-1/2 Heisenberg models. To improve the scalability of the method, we exploit the symmetries and sparsity of the considered systems to reach sizes of hundreds of particles at much higher precision than previous works. Our analysis therefore shows how to obtain certifiable bounds on many-body ground-state properties beyond energy in a scalable way. Published by the American Physical Society 2024

Interplay of superconductivity and magnetism in the Fe1+yTe1‐xSex iron‐based superconductor: A theoretical study

AbstractThe competition between superconductivity and magnetism has been studied for the ongoing investigation of mechanisms in unconventional superconductors. Fe1+yTe1−xSex is distinct among iron‐based superconductors due to its structural simplicity, comprising solely FeTe/Se layers that are favorable for probing the superconductivity mechanism. The main goal of this article is to focus on the computational investigation of the interplay of magnetism and superconductivity in the Fe1+yTe1−xSex multiband superconductor. From the electronic structure of the Fe1+yTe1−xSex superconductor, a two‐band Hamiltonian model was considered to examine the interplay of magnetism and superconductivity in the Fe1+yTe1‐xSex superconductor. Using Green's function formalism with the Hamiltonian model, the mathematical statements for the superconducting (Sc) gap parameter, spin density wave (SDW) ordering parameter, Sc and magnetic transitional temperatures have been obtained. Using these mathematical expressions, the phase diagram of transition temperatures versus the gap parameters for the Fe1+yTe1‐xSex superconductor has been plotted. The intersection region in the phase diagram of transition temperatures as a function of the SDW order parameter has been plotted to show the possible interplay of superconductivity and magnetism in a Fe1+yTe1‐xSex iron‐based superconductor.

Theoretical investigation of the Co-occurrence of superconductivity and antiferromagnetism in iron-based high-temperature superconductors

In this research work, the Co-occurrence of superconductivity and antiferromagnetism in Ca0.74 1 La0.26 1 Fe1−xCox As2 iron-based high-temperature superconductors have been investigated. Based on the multi-band nature of Ca0.74 1 La0.26 1 Fe1−xCox As2 iron-based superconductors, a two-band model Hamiltonian that contains intra- and inter-bands is developed. By employing the matrix form of the temperature-dependent Green’s function formalism with the two-band Hamiltonian, the mathematical expressions of superconducting transition temperature as functions of the superconducting order parameter and antiferromagnetism translational temperature as a function of the magnetic order parameter are obtained, respectively. The plotted graph of the superconducting and magnetic temperature as a function of the magnetic order parameter indicates a clear possibility of Co-occurrence of superconductivity and the antiferromagnetism order parameter in Ca0.74 1 La0.26 1 Fe1−xCox As2 iron-based superconductors in the range of magnetic order parameters between 2.3 meV and 6.07 meV, which is in good agreement with experimental observations. This research contributes to understanding the complex behavior of high-temperature superconductors and provides valuable technological applications for other fields.

Critical Opalescence and Its Impact on the Jet Quenching Parameter q^

Jet quenching parameter q^ is essential for characterizing the interaction strength between jet partons and nuclear matter. Based on the quark-meson model, we develop a new framework for calculating q^ at finite chemical potentials, in which q^ is related to the spectral function of the chiral order parameter. A mean field perturbative calculation up to the one-loop order indicates that the momentum broadening of jets is enhanced at both high temperature and high chemical potential, and approximately proportional to the parton number density in the partonic phase. We further investigate the behavior of q^ in the vicinity of the critical endpoint (CEP) by coupling our calculation with a recently developed equation of state that includes a CEP in the universality class of the Ising model, from which we discover the partonic critical opalescence, i.e., the divergence of scattering rate of jets and their momentum broadening at the CEP, contributed by scatterings via the σ exchange process. Hence, for the first time, jet quenching is connected with the search of CEP.

Statistical field theory of mechanical stresses in Coulomb fluids: general covariant approach vs Noether’s theorem

In this paper, we introduce a statistical field theory that describes the macroscopic mechanical forces in inhomogeneous Coulomb fluids. Our approach employs the generalization of Noether’s first theorem for the case of a fluctuating order parameter to calculate the stress tensor for Coulomb fluids. This tensor encompasses the mean-field stress tensor and fluctuation corrections derived through the one-loop approximation. The correction for fluctuations includes a term that accounts for the thermal fluctuations of the local electrostatic potential and field in the vicinity of the mean-field configuration. This correlation stress tensor determines how electrostatic correlation affects local stresses in a nonuniform Coulomb fluid. We also use a previously formulated general covariant methodology (Brandyshev and Budkov 2023 J. Chem. Phys. 158 174114) in conjunction with a functional Legendre transformation method and derive within it the same total stress tensor. We would like to emphasize that our general approaches are applicable not only to Coulomb fluids but also to nonionic simple or complex fluids, for which the field-theoretic Hamiltonian is known as a function of the relevant scalar order parameters.

Buckling critical pressures in collapsible tubes relevant for biomedical flows

The behaviour of collapsed or stenotic vessels in the human body can be studied by means of simplified geometries like a collapsible tube. The objective of this work is to determine the value of the buckling critical pressure of a collapsible tube by employing Landau’s theory of phase transition. The methodology is based on the implementation of an experimentally validated 3D numerical model of a collapsible tube. The buckling critical pressure is estimated for different values of geometric parameters of the system by treating the relation between the intramural pressure and the area of the central cross-section as the order parameter function of the system. The results show the dependence of the buckling critical pressures on the geometric parameters of a collapsible tube. General non-dimensional equations for the buckling critical pressures are derived. The advantage of this method is that it does not require any geometric assumption, but it is solely based on the observation that the buckling of a collapsible tube can be treated as a second-order phase transition. The investigated geometric and elastic parameters are sensible for biomedical application, with particular interest to the study of the bronchial tree under pathophysiological conditions like asthma.

Kinetic reconstruction of free energies as a function of multiple order parameters.

A vast array of phenomena, ranging from chemical reactions to phase transformations, are analyzed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used, especially in the presence of large free energy barriers, to estimate free energies using biasing protocols and sampling of transition paths. Kinetic reconstructions of free energy barriers of intermediate height have been performed, with respect to a single order parameter, employing the steady state properties of unconstrained simulation trajectories when barrier crossing is achievable with reasonable computational effort. Considering such cases, we describe a method to estimate free energy surfaces with respect to multiple order parameters from a steady state ensemble of trajectories. The approach applies to cases where the transition rates between pairs of order parameter values considered is not affected by the presence of an absorbing boundary, whereas the macroscopic fluxes and sampling probabilities are. We demonstrate the applicability of our prescription on different test cases of random walkers executing Brownian motion in order parameter space with an underlying (free) energy landscape and discuss strategies to improve numerical estimates of the fluxes and sampling. We next use this approach to reconstruct the free energy surface for supercooled liquid silicon with respect to the degree of crystallinity and density, from unconstrained molecular dynamics simulations, and obtain results quantitatively consistent with earlier results from umbrella sampling.

Coupling stress fields and vacancy diffusion in phase-field models of voids as pure vacancy phase

High vacancy concentrations in crystals may lead to formation and growth of voids, which is connected to swelling under irradiation and degradation of material properties. Recent experimental work suggests that vacancy condensation may also be involved in nucleation and evolution of porosity in early stages of ductile fracture. Mostly in the realm of irradiation effects, void formation and growth has been simulated with phase-field methods, where voids are treated as pure vacancy phases. Since vacancies induce an eigenstrain field, it is well-known that the evolution of vacancy concentrations is coupled to the elastic stress field. However, the few existing elastically coupled diffuse interface models of void growth seem to face a conceptual problem in the diffuse interface; in the center of which they predict the highest eigenstrains, which results in unrealistically high, fluctuating stresses. In the current work, we present a new model for coupling elastically driven vacancy diffusion with a diffuse interface model of void surfaces, which overcomes the named short-comings and closely reproduces the sharp interface solution. This is achieved by making the eigenstrain a function of the non-conserved order parameter used to distinguish the crystal and void phase. The model is verified for two-dimensional example problems by comparison to the analytical solution of the according sharp interface model. Eventually, the model is used to show the impact of elasto-diffusional coupling on void growth in mechanically loaded systems. We analyze the model with regard to the bi-stable energy landscape and discuss limitations and future prospects of the approach.

МАГНИТОЭЛЕКТРИЧЕСКИЕ ЭФФЕКТЫ И НОВЫЕ ЛОГИЧЕСКИЕ УСТРОЙСТВА СПИНТРОНИКИ

The paper discusses new logic spintronic devices and the prospects for the use of perovskite-type multiferroics as working elements of magnetoelectric components. The principle of operation of the considered logical devices is based on the use of two components - a magnetoelectric, in which the magnetic state is recorded due to energy-efficient magnetoelectric interaction, and a spin-orbital component, in which information is read out based on the conversion of spin into charge due to the spin-orbital interaction of electrons; both components are interconnected by a nanoelectrode. When designing new logic spintronic devices, it is necessary to take into account the effectiveness of the mechanisms of ME interactions; features of spin - polarized currents and associated torques influencing magnetic moments; as well as other factors affecting the speed of switching magnetic states and the sensitivity of the device to external agents. Multiferroic materials that are promising for use as elements of ME components of new logic devices must meet a number of requirements, the most significant of which are the magnitude of the magnetoelectric coupling coefficient and the temperature at which ME effects occur. The paper considers representatives of multiferroics with a perovskite structure that meet these conditions, to some extent partially, these are high-temperature multiferroic bismuth ferrite (BiFeO3) and Ruddlesden-Popper structures, in which high-temperature ferroelectric effects are already realized and under certain conditions an ME effect is possible. The crystal structure of these compounds is considered, and the role of crystallographic distortions responsible for the manifestation of magnetoelectric properties is analyzed. Expressions are obtained for the tensor of the magnetoelectric effect as functions of magnetic order parameters, and the fundamental possibility of realizing ME effects in Ruddlesden-Popper structures containing magnetic cations is shown.

Perturbation analysis of nonlinear partial reflected wave on a sloping bottom

In this paper, we use the perturbation method to develop a new mathematical derivation to describe nonlinear partial standing wave over uniformly sloping bottoms. In the Lagrangian coordinate system, the particle trajectories are obtained as a function of the nonlinear order parameter ɛ and the bottom slope α to the second order of the perturbation. The setups and mean return flow for an arbitrary bottom in the Lagrangian framework are also found as part of the solutions. The direct influences of reflection coefficient, wave steepness and bottom slope on the surface profiles of partially reflected waves are also derived. This nonlinear analytical solution is verified by reduction to the classical Stokes solution of progressive waves in both the deep water and constant depth limit. This solution allows to describe the successive deformation of partial reflected wave profiles and water particle trajectories prior to wave breaking to be described. The dynamic properties including mass transport, and Lagrangian mean level and radiation stress for nonlinear partially reflected waves on various sloping bottoms are investigated.

Effect of molecular aspect ratio on structure, dynamics and phase stability of thermotropic liquid crystals studied by molecular dynamics simulation

Due to the importance of liquid crystals in modern technology and food industry, understanding their structural and dynamical properties are scientifically important. In this study, we applied extensive molecular dynamics simulations to infer the effect of the molecular elongation on the formation, stability and dynamics of liquid crystal mesophases in a system of Gay-Berne model mesogens with parameters GB (k,k′=20,μ=1,ν=1). Four aspect ratio values, k=2,3,4.4 and 5, were studied at pressure P*=4. Thermodynamics properties, the order parameter and pair distribution functions (both translational and positional), helped to identify phases, hysteresis, and consequently phase diagrams. By increasing aspect ratio from 2 to 5, nematic and smectic phases were induced and all transition temperatures were shifted to higher values, hence, the range of stability of the nematic and smectic mesophases became wider. The analysis of the coordination numbers and angular distribution functions showed that the structure of the solid phase of system with k=2 at lowest temperatures was fcc which by increasing the aspect ratio changed to a complete hexagonal in-layer structure. Moreover, by increasing the axial ratio of particles, decoupling between the principal components of diffusion coefficients increased, where it reflects an increase in the molecular orientational order in the system with higher k. The effect of increasing aspect ratio was more pronounced on inter-layers diffusion rather than the in-layers. In all mesophases parallel components of diffusion coefficients were greater than the perpendicular components. We analyzed the results based on the existing theoretical descriptions and experimental observations.

Metastable hybridized structure transformation in amorphous carbon films during friction—A study combining experiments and MD simulation

Amorphous carbon films have attracted substantial interest due to their exceptional mechanical and tribological properties. Previous studies revealed that the amorphous carbon films exhibited lower coefficient of friction (COF) because of the transformation in bond structure from sp3-C to sp2-C during friction processes. However, the mechanism for such a transformation during friction is not well understood. This study is conducted to get an insight into the metastable transformation in amorphous carbon film during friction by means of experiments and molecular dynamics (MD) simulation. Relevant wear tests showed that wear of the film changed from an abrasive wear mode to a mixture of abrasion and adhesive wear, resulting in a decrease in growth rate of the wear rate after the running-in stage. It is worth noting that the sp3-C atoms were increased during the running-in stage when the films contained lower sp3/sp2 ratios. However, the formed sp3-C atoms could only be short-lived and gradually transformed to sp2-C atoms with the graphitization generated on the wearing surface of the films. The radial distribution function and translational order parameter indicated that the films’ high sp3/sp2 ratio led to an increased sp2-C proportion on the wear scar after friction, which caused an increased structural ordering.

Antiferromagnetic Ising model with frustration on Graphenylene lattice

Frustration effects due to competition between nearest-neighbor and next-nearest-neighbor spins interaction on the graphenylene lattice, also known as biphenylene carbon lattice, were investigated by Monte Carlo simulations. We identified two possible phases from our results of the entropy at zero temperature, namely an ordered spin glass and other an antiferromagnetic phase. Despite the complexity of the lattice, a finite size scaling analysis for the antiferromagnetic regime shows that it can be classified into the same universality class of the usual Ising model. The canonical probability distribution as a function of the spin glass order parameter was computed and the continuous spin glass phase transition confirmed.

Blume–Emery–Griffiths model on random graphs

The Blume–Emery–Griffiths model with a random crystal field is studied in a random graph architecture, in which the average connectivity is a controllable parameter. The disordered average over the graph realizations is treated by replica symmetry formalism of order parameter functions. A self consistent equation for the distribution of local fields is derived, and numerically solved by a population dynamics algorithm. The results show that the average connectivity amounts to changes in the topology of the phase diagrams. Phase diagrams for representative values of the model parameters are compared with those obtained for fully connected mean field and renormalization group approaches.

Kinetics of the Chiral Phase Transition in a Quark–Meson \(\sigma \) Model

Using the two-particle irreducible (2PI) $\Phi$-functional formalism for self-consistent approximations of a linear-$\sigma$ model for quarks and mesons in and out of equilibrium, the build-up of fluctuations of net-baryon number during the time evolution of an expanding fireball is studied within a kinetic theory for the order parameter ($\sigma$ field) and quark distribution functions. Initializing the system with purely Gaussian fluctuations a fourth-order cumulant is temporarily built up due to the evolution of the $\sigma$-field. This is counterbalanced, however, by the dissipative evolution due to collisions between quarks, anti-quarks, mesons, and the mean field, depending on the speed of the fireball expansion.

The hydrodynamic theory of dynamical correlation functions in the XX chain

By the hydrodynamic linear response theory, dynamical correlation functions decay as power laws along certain velocities, determined by the flux Jacobian. Such correlations are obtained by hydrodynamic projections, and physically, they are due to propagating ‘sound waves’ or generalisation thereof, transporting conserved quantities between the observables. However, some observables do not emit sound waves, such as order parameters associated to symmetry breaking. In these cases correlation functions decay exponentially everywhere, a behaviour not captured by the hydrodynamic linear response theory. Focussing on spin–spin correlation functions in the XX quantum chain, we first review how hydrodynamic linear response works, emphasising that the necessary fluid cell averaging washes out oscillatory effects. We then show how, beyond linear response, Euler hydrodynamics can still predict the exponential decay of correlation functions of order parameters. This is done by accounting for the large-scale fluctuations of domain walls, via the recently developed ballistic fluctuation theory. We use the framework of generalised hydrodynamics, which is particularly simple in this model due to its free fermion description. In particular, this reproduces, by elementary calculations, the exponential decay in the celebrated formulae by Its et al (1993) and by Jie (1998), which were originally obtained by intricate Fredholm determinant analysis; and gives a new formula in a parameter domain where no result was obtained before. We confirm the results by numerical simulations.

Dynamical Anomaly of Aqueous Amphiphilic Solutions: Connection to Solution H-Bond Fluctuation Dynamics?

We have investigated the possible connection between “dynamical anomaly” observed in time-resolved fluorescence measurements of reactive and nonreactive solute-centered relaxation dynamics in aqueous binary mixtures of different amphiphiles and the solution intra- and interspecies H-bond fluctuation dynamics. Earlier studies have connected the anomalous thermodynamic properties of binary mixtures at very low amphiphile concentrations to the structural distortion of water. This is termed as “structural anomaly.” Interestingly, the abrupt changes in the composition-dependent average rates of solute relaxation dynamics occur at amphiphile mole fractions approximately twice as large as those where structural anomalies appear. We have investigated this anomalous solution dynamical aspect by considering (water + tertiary butanol) as a model system and performed molecular dynamics simulations at several tertiary butanol (TBA) concentrations covering the extremely dilute to the moderately concentrated regimes. The “dynamical anomaly” has been followed via monitoring the composition dependence of the intra- and interspecies H-bond fluctuations and reorientational relaxations of TBA and water molecules. Solution structural aspects have been followed via examining the tetrahedral order parameter, radial and spatial distribution functions, numbers of H bonds per water and TBA molecules, and the respective populations participating in H-bond formation. Our simulations reveal abrupt changes in the H-bond fluctuations and reorientational dynamics and tetrahedral order parameter at amphiphile concentrations differing approximately by a factor of 2 and corroborates well with the steady-state and the time-resolved spectroscopic measurements. This work therefore explains, following a uniform and cogent manner, both the experimentally observed structural and dynamical anomalies in microscopic terms.

Exact dynamics of phase transitions in oscillator populations with nonlinear coupling

The Kuramoto model consisting of a population of coupled phase oscillators has served as an idealized tool for studying synchronization transitions in diverse self-sustained systems. It has been a common brief that the model exhibits a first-order discontinuous (hybrid) phase transition towards synchrony with the absence of partial locking by assuming that the natural frequencies are uniformly distributed. In this paper, we consider a variant of this model by modifying its global coupling to depend on a power law function of the macroscopic order parameter of the population via an exponent α. The generalization retains the uniform coupling and mean-field character of the system, where there is an interplay between the coupling and oscillator dynamics. Surprisingly, we show that the partial locking with the coexistence of the phase locked and drifting populations indeed exists for α<1, whereas it can never occur as long as α≥1. Through a remarkable ansatz of the frequency-dependent version of Ott–Antonsen manifold, we reveal that the long term macroscopic dynamics of the resulting model, as well as their corresponding critical properties can be analytically described. More importantly, we construct the characteristic function to give intuitive interpretations of a variety of dynamical phenomena occurring in the system, such as the emergence of the partial locking, vanishing synchronization onset, and the irreversibly abrupt desynchronization transition.

Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics.

Understanding the driving forces behind the nucleation of different polymorphs is of great importance for material sciences and the pharmaceutical industry. This includes understanding the reaction coordinate that governs the nucleation process and correctly calculating the relative free energies of different polymorphs. Here, we demonstrate, for the prototypical case of urea nucleation from the melt, how one can learn such a one-dimensional reaction coordinate as a function of prespecified order parameters and use it to perform efficient biased all-atom molecular dynamics simulations. The reaction coordinate is learnt as a function of the generic thermodynamic and structural order parameters using the "spectral gap optimization of order parameters (SGOOP)" approach [Tiwary, P. and Berne, B. J. Proc. Natl. Acad. Sci. U.S.A. (2016)] and is biased using well-tempered metadynamics simulations. The reaction coordinate gives insights into the role played by different structural and thermodynamics order parameters, and the biased simulations obtain accurate relative free energies for different polymorphs. This includes an accurate prediction of the approximate pressure at which urea undergoes a phase transition and one of the metastable polymorphs becomes the most stable conformation. We believe the ideas demonstrated in this work will facilitate efficient sampling of nucleation in complex, generic systems.