Nonequilibrium Phase Transition Research Articles

A comprehensive neural network study of the non-equilibrium phase transition of the two-dimensional Ising model on the square lattice

A comprehensive neural network study of the non-equilibrium phase transition of the two-dimensional Ising model on the square lattice

Origins of complexity in the rheology of Soft Earth suspensions.

When wet soil becomes fully saturated by intense rainfall, or is shaken by an earthquake, it may fluidize catastrophically. Sand-rich slurries are treated as granular suspensions, where the failure is related to an unjamming transition, and friction is controlled by particle concentration and pore pressure. Mud flows are modeled as gels, where yielding and shear-thinning behaviors arise from inter-particle attraction and clustering. Here we show that the full range of complex flow behaviors previously reported for natural debris flows can be reproduced with three ingredients: water, silica sand, and kaolin clay. Going from sand-rich to clay-rich suspensions, we observe continuous transition from brittle (Coulomb-like)to ductile (plastic)yielding. We propose a general constitutive relation for soil suspensions, with a particle rearrangement time that is controlled by yield stress and jamming distance. Our experimental results are supported by models for amorphous solids, suggesting that the paradigm of non-equilibrium phase transitions can help us understand and predict the complex behaviors of Soft Earth suspensions.

Nonequilibrium Phase Transition and Pattern Formation in Nematic Liquid Crystal

Nonequilibrium Phase Transition and Pattern Formation in Nematic Liquid Crystal

Nonequilibrium tricritical behavior in anisotropic XY ferromagnet driven by elliptically polarized propagating magnetic field wave

The three-dimensional anisotropic XY ferromagnet, driven by an elliptically polarized propagating magnetic field wave, has been extensively investigated by Monte Carlo simulation with the Metropolis single spin flip algorithm. Both the effects of the bilinear exchange type and the single-site anisotropies are thoroughly investigated. The time-averaged magnetization (over the complete cycle of the elliptically polarized propagating magnetic field wave) components play the role of the dynamic order parameter. For a fixed set of values of the strength of anisotropy and the field amplitudes, the system has been found to get dynamically ordered at a pseudocritical temperature. The pseudocritical temperature of such a dynamic nonequilibrium phase transition has been found to depend both on the strength of anisotropy and the amplitudes of the elliptically polarized propagating magnetic field wave. A comprehensive phase diagram is represented here in the form of an image plot of the pseudocritical temperature in the plane formed by the strength of anisotropy and field amplitudes. Interestingly, this nonequilibrium phase transition has been found to be discontinuous (first order) for higher values of the field amplitude. On the other hand, the continuous (second order) transition has been noticed for lower values of the field amplitude. Such an interesting nonequilibrium tricritical behavior has been observed in driven XY ferromagnet. The order of such a nonequilibrium phase transition has been confirmed by the thermal variation (near the transition) of the statistical distribution of the order parameter and by the thermal variation of the fourth-order Binder cumulant. In the plane formed by field amplitude and anisotropy, a tricritical line has been shown as the accompanying (and complementary) phase diagram. The dependence of the pseudocritical temperature, on the frequency and wavelength of the elliptically polarized propagating magnetic field wave, has also been reported.

Nanomechanically-induced nonequilibrium quantum phase transition to a self-organized density wave of a Bose-Einstein condensate

We report on a nonequilibrium quantum phase transition (NQPT) in a hybrid quantum many-body system consisting of a vibrational mode of a damped nanomembrane interacting optomechanically with a cavity, whose output light couples to two internal states of an ultracold Bose gas held in an external quasi-one-dimensional box potential. For small effective membrane-atom couplings, the system is in a homogeneous Bose-Einstein condensate (BEC) steady state, with no membrane displacement. Depending on the transition frequency between the two internal atomic states, either one or both internal states are occupied. By increasing the atom-membrane couplings, the system transitions to a symmetry-broken self-organized BEC phase, which is characterized by a considerably displaced membrane steady-state and density-wave-like BEC profiles. This NQPT can be both discontinuous and continuous for a certain interval of transition frequencies and is purely discontinuous outside of it. Published by the American Physical Society 2024

Unveiling the Phase Diagram and Reaction Paths of the Active Model B with the Deep Minimum Action Method.

Nonequilibrium phase transitions are notably difficult to analyze because their mechanisms depend on the system's dynamics in a complex way due to the lack of time-reversal symmetry. To complicate matters, the system's steady-state distribution is unknown in general. Here, the phase diagram of the active Model B is computed with a deep neural network implementation of the geometric minimum action method (gMAM). This approach unveils the unconventional reaction paths and nucleation mechanism in dimensions 1, 2, and 3, by which the system switches between the homogeneous and inhomogeneous phases in the binodal region. Our main findings are (i)the mean time to escape the phase-separated state is (exponentially) extensive in the system size L, but it increases nonmonotonically with L in dimension 1; (ii)the mean time to escape the homogeneous state is always finite, in line with the recent work of Cates and Nardini [Phys. Rev. Lett. 130, 098203 (2023)PRLTAO0031-900710.1103/PhysRevLett.130.098203]; (iii)at fixed L, the active term increases the stability of the homogeneous phase, eventually destroying the phase separation in the binodal for large but finite systems. Our results are particularly relevant for active matter systems in which the number of constituents hardly goes beyond 10^{7} and where finite-size effects matter.

Should we conserve entropy or energy when computing CAPE with mixed-phase precipitation physics?

Abstract The rapidly increasing resolution of global atmospheric reanalysis and climate model datasets necessitates finding methods for computing convective available potential energy (CAPE) both efficiently and accurately. To this end, this article compares two common methods for computing CAPE which conserve either energy or entropy. Inaccuracies in these computations arise from both physical and numerical errors. For instance, computing CAPE with entropy conserved results in physical errors from non-equilibrium phase transitions but minimizes numerical errors because solutions are analytic at each height. In contrast, computing CAPE with energy conserved avoids these physical errors, but accumulates numerical errors that are grid-resolution dependent because the numerical integration of a differential equation is required. Analysis of CAPE computed with large databases of soundings from the tropical Amazon and midlatitude storm environments shows that physical errors from the entropy method are typically 1-3 % as large as CAPE, which is comparable to the numerical errors from conserving energy with grid spacing of 25 m and 250 m using explicit first-order and second-order integration schemes respectively. Errors in entropy-based CAPE calculations are also insensitive to vertical grid spacing, in contrast with energy-based calculations whose error strongly scales with the grid spacing. It is shown that entropy-based methods are advantageous when intercomparing datasets with differing vertical resolution because they produce accurate and reasonably fast results that are insensitive to grid resolution. Whereas a second-order energy-based method is advantageous when analyzing data with a consistent vertical resolution because of its superior computational efficiency.

Quantum-inspired modeling of distributed intelligence systems with artificial intelligent agents self-organization

Distributed intelligence systems (DIS) containing natural and artificial intelligence agents (NIA and AIA) for decision making (DM) belong to promising interdisciplinary studies aimed at digitalization of routine processes in industry, economy, management, and everyday life. In this work, we suggest a novel quantum-inspired approach to investigate the crucial features of DIS consisting of NIAs (users) and AIAs (digital assistants, or avatars). We suppose that N users and their avatars are located in N nodes of a complex avatar - avatar network. The avatars can receive information from and transmit it to each other within this network, while the users obtain information from the outside. The users are associated with their digital assistants and cannot communicate with each other directly. Depending on the meaningfulness/uselessness of the information presented by avatars, users show their attitude making emotional binary “like”/“dislike” responses. To characterize NIA cognitive abilities in a simple DM process, we propose a mapping procedure for the Russell’s valence-arousal circumplex model onto an effective quantum-like two-level system. The DIS aims to maximize the average satisfaction of users via AIAs long-term adaptation to their users. In this regard, we examine the opinion formation and social impact as a result of the collective emotional state evolution occurring in the DIS. We show that generalized cooperativity parameters Gi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G_i$$\\end{document}, i=1,⋯,N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$i=1,\\dots,N$$\\end{document} introduced in this work play a significant role in DIS features reflecting the users activity in possible cooperation and responses to their avatar suggestions. These parameters reveal how frequently AIAs and NIAs communicate with each other accounting the cognitive abilities of NIAs and information losses within the network. We demonstrate that conditions for opinion formation and social impact in the DIS are relevant to the second-order non-equilibrium phase transition. The transition establishes a non-vanishing average information field inherent to information diffusion and long-term avatar adaptation to their users. It occurs above the phase transition threshold, i.e. at Gi>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G_i>1$$\\end{document}, which implies small (residual) social polarization of the NIAs community. Below the threshold, at weak AIA–NIA coupling (Gi≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G_i\\le 1$$\\end{document}), many uncertainties in the DIS inhibit opinion formation and social impact for the DM agents due to the information diffusion suppression; the AIAs self-organization within the avatar–avatar network is elucidated in this limit. To increase the users’ impact, we suggest an adaptive approach by establishing a network-dependent coupling rate with their digital assistants. In this case, the mechanism of AIA control helps resolve the DM process in the presence of some uncertainties resulting from the variety of users’ preferences. Our findings open new perspectives in different areas where AIAs become effective teammates for humans to solve common routine problems in network organizations.

Magnetically controlled bacterial turbulence

Concentrated active agents can exhibit turbulent-like flows reminiscent of hydrodynamic turbulence. Despite its importance, the influence of external fields on active turbulence remains largely unexplored. Here we demonstrate the ability to control the swimming direction and active turbulence of Bacillus subtilis bacteria using external magnetic fields. The control mechanism leverages the magnetic torque experienced by the non-magnetic, rod-shaped bacteria in a magnetizable medium containing superparamagnetic nanoparticles. This allows aligning individual bacteria with the magnetic field, leading to a nematically aligned state over millimetric scales with minute transverse undulations and flows. Turning off the field releases the alignment constraint, leading to directly observable hydrodynamic instability of the dipole pushers. Our theoretical model predicts the intrinsic length scale of this instability, independent of the magnetic field, and provides a quantitative control strategy. Our findings suggest that magnetic fields and torques can be excellent tools for controlling non-equilibrium phase transitions in active systems.

New approach to measuring topological phase transitions utilizing Floquet technology

Abstract The Floquet technique provides a novel anomalous topological phase for non-equilibrium phase transitions. Based on the high symmetry of Quantum Anomalous Hall model, the findings suggest a one-to-one correspondence between the average spin texture and the Floquet quasi-energy spectrum. A new approach is proposed to directly measure the quasi-energy spectrum, replacing previous measurements of the average spin texture. Finally, we proposed a reliable experimental scheme based on ion trap platforms. This scheme markedly reduces the measurement workload and improves measurement fidelity, and is applicable to multiple platforms such as cold atoms and nuclear magnetic resonance.

Lane formation in gravitationally driven colloid mixtures consisting of up to three different particle sizes.

Brownian dynamics simulations are utilized to study segregation phenomena far from thermodynamic equilibrium. In the present study, we expand upon the analysis of binary colloid mixtures and introduce a third particle species to further our understanding of colloidal systems. Gravitationally driven, spherical colloids immersed in an implicit solvent are confined in two-dimensional linear microchannels. The interaction between the colloids is modeled by the Weeks-Chandler-Andersen potential, and the confinement of the colloids is realized by hard walls based on the solution of the Smoluchowski equationin half space. In binary and ternary colloidal systems, a difference in the driving force is achieved by differing colloid sizes but fixed mass density. We observe for both the binary and ternary systems that a driving force difference induces a nonequilibrium phase transition to lanes. For ternary systems, we study the tendency of lane formation to depend on the diameter of the medium-sized colloids. Here we find a sweet spot for lane formation in ternary systems. Furthermore, we study the interaction of two differently sized colloids at the channel walls. Recently we observed that driven large colloids push smaller colloids to the walls. This results in small particle lanes at the walls at early simulation times. In this work we additionally find that thin lanes are unstable and dissolve over very long time frames. Furthermore, we observe a connection between lane formation and the nonuniform distribution of particles along the channel length. This nonuniform distribution occurs either alongside lane formation or in shared lanes (i.e., lanes consisting of two colloid types).

Nonequilibrium phase transitions and absorbing states in a model for the dynamics of religious affiliation

We propose a simple model to describe the dynamics of religious affiliation. For such purpose, we built a compartmental model with three distinct subpopulations, namely religious committed individuals, religious noncommitted individuals and not religious affiliated individuals. The transitions among the compartments are governed by probabilities, modeling social interactions among the groups and also spontaneous transitions among the compartments. First of all, we consider the model on a fully-connected network. Thus, we write a set of ordinary differential equations to study the evolution of the subpopulations. Our analytical and numerical results show that there is an absorbing state in the model where only one of the subpopulations survive in the long-time limit. There are also regions of parameters where some of the subpopulations coexist (two or three). We also verified the occurrence of two distinct critical points. In addition, we also present Monte Carlo simulations of the model on two-dimensional square lattices, in order to analyze the impact of the presence of a lattice structure on the critical behavior of the model. Comparison of the models’ results with data for religious affiliation in Northern Ireland shows a good qualitative agreement. Finally, we considered the presence of inflexible individuals in the population, i.e., individuals that never change their states. The impact of such special agents on the critical behavior of the model is also discussed.

Exploring the impact of fluctuation-induced criticality on non-Hermitian skin effect and quantum sensors

In this paper we present a concrete example comparing the results predicted by non-Hermitian quantum mechanics with those of a more comprehensive description that considers environment-induced fluctuations. Our results highlight inaccuracies in the non-Hermitian model. Specifically, we investigate the non-Hermitian skin effect and sensor in the Hatano-Nelson model, contrasting it with a more precise Lindblad description. Our analysis reveals that these phenomena can undergo breakdown when environmental fluctuations come to the forefront, resulting in a nonequilibrium phase transition from a localized skin phase to a delocalized phase. Beyond this specific case study, we engage in a broader discussion regarding the interpretations and implications of non-Hermitian quantum mechanics. This examination serves to broaden our understanding of these phenomena and their potential consequences. Published by the American Physical Society 2024

Numerical investigation of jet impingement on flat/concave cooling of CO2 with different phase states under high heat flux

The thermal load and high temperature brought by the increase in power of electronic devices or the increase in speed of supersonic aircraft limit the respective development. In this paper, a numerical model of CO2 jet impingement cooling of a constant heat flux plate/concave surface in different phase states was established. Secondly, the non-equilibrium phase transition and the real-thermophysical properties of CO2 was considered. The effects of different wall heat flux (0.7 MW/m2 ∼ 6.5 MW/m2) and initial phase states on the impact cooling performance of CO2 jet were studied.It is found that for SCO2 jet impingement, when the inlet temperature is lower than the pseudo-critical temperature, the heat transfer coefficient increases with the increase of inlet pressure, and the maximum increase is 24.7 %. For near-critical liquid CO2 (LCO2) jet impingement, low latent heat prevents temperature overshoot in the heat flux range studied. With the increase of the proportion of dry ice in the inlet, the heat transfer coefficient also increases. When q > 3 MW/m2, the heat transfer coefficient of dry ice jet impact is 2.5 ∼ 3 times and 1 ∼ 1.4 times of that of SCO2 and near-critical LCO2 jet impingement for the flat plate model, respectively. For concave surface with high heat flux, near-critical LCO2 jet impingement cooling effect is relatively good. In addition, concave surface will aggravate the uneven cooling surface temperature.The results can provide more references for the CO2 jet impingement technology in the design of stagnation cooling system of supersonic aircraft and thermal management of high-power electronic devices.

Inverted nucleation for photoinduced nonequilibrium melting.

Ultrafast photoinduced melting provides an essential platform for studying nonequilibrium phase transitions by linking the kinetics of electron dynamics to ionic motions. Knowledge of dynamic balance in their energetics is essential to understanding how the ionic reaction is influenced by femtosecond photoexcited electrons with notable time lag depending on reaction mechanisms. Here, by directly imaging fluctuating density distributions and evaluating the ionic pressure and Gibbs free energy from two-temperature molecular dynamics that verified experimental results, we uncovered that transient ionic pressure, triggered by photoexcited electrons, controls the overall melting kinetics. In particular, ultrafast nonequilibrium melting can be described by the reverse nucleation process with voids as nucleation seeds. The strongly driven solid-to-liquid transition of metallic gold is successfully explained by void nucleation facilitated by photoexcited electron-initiated ionic pressure, establishing a solid knowledge base for understanding ultrafast nonequilibrium kinetics.

Particle traps and stationary currents captured by an active 1D model

We investigate the onset of a non-equilibrium phase transition in a one-dimensional ring, constituted by two urns connected by two strands, called active and passive channels. A set of N particles move inside the ring with constant individual speeds; collisions against the channel entries produce reflections with certain probabilities, that differ between active and passive channels. The microscopic dynamics differs from a classical 1D billiard owing to the presence of an interaction mechanism acting inside the active channel, which potentially reverses velocities of its particles. We outline a general theory for the feedback-controlled system which describes quantitatively the phase diagram of the model, based on a mixing property, that is analytically predicted and numerically verified. The probability distributions we define and evolve in time are 1D projections of uniform distributions on d-dimensional spherical surfaces, with d≥1 and d=∞. Consequently results that apply to higher dimensional systems are recovered.

Nonequilibrium phase diagrams in a multilayer Ising ferrimagnet system: The Glauber type stochastic dynamics approach

Multilayer Ising ferrimagnet system is studied with nonequilibrium phase diagrams employing the Glauber stochastic dynamics approach. Firstly, nonequilibrium phase transition temperatures and their phase transition nature are investigated in detail. The study shows that the system displays both the second and first-phase transition behaviors. Then, it is determined that the essential phases of nonequilibrium phase diagrams consist of five phases (i1, i2, nm1, nm2, p), four mixed phases (i1+ p, nm1 +nm2, nm2 + p, i1 + nm2), and four special points (A, B, E, TP). Lastly, the study demonstrates that the dynamic magnetic characteristics of the system exhibit a significant dependence on the parameters of the Hamiltonian.

Self-propelled collective motion with multiplicative scalar noise

The emergence of order from initial disordered movement in self-propelled collective motion is an instance of nonequilibrium phase transition, which is known to be first order in the thermodynamic limit. Here, we introduce a multiplicative scalar noise model of collective motion as a modification of the original Vicsek model, which more closely mimics the particles’ behavior. We allow for more individual movement in sparsely populated neighborhoods, the mechanism of which is not incorporated in the original Vicsek model. This is especially important in the low velocity and density regime where the probability of a clear neighborhood is relatively high. The modification, thus, removes the shortcoming of the Vicsek model in predicting continuous phase transition in this regime. The onset of collective motion in the proposed model is numerically studied in detail, indicating a first-order phase transition in both high and low velocity/density regimes for systems with comparatively smaller size which is computationally desirable.

Lattice Boltzmann modeling of convective heat and solute transfer in additive manufacturing of multi-component alloys

Additive manufacturing (AM) is a remarkable breakthrough technology, allowing for the direct fabrication of three-dimensional components through the layer-by-layer stacking of materials. A novel free Surface lattice Boltzmann (LB) model is developed to simulate the heat and solute transfer in AM of multi-component alloys. The behavior liquid phase is described by using the free surface LB model, and the phase transitions between solid and liquid are modeled by using the LB-enthalpy method. A LB equation is directly constructed, which accounts for solute transfer in a certain multi-component alloys system. The thermodynamic information used in the calculation of phase transitions are determined by an extensive thermodynamic database. The model is validated via several benchmark examples of fluid flow and heat transfer. The characteristics of convective heat and solute transfer within various AM are investigated. Finally, the non-equilibrium convective heat transfer, phase transitions, and macroscopic segregation are discussed within the AM melt pools. The melt pool expands and convective heat transfer is enhanced by the Marangoni effect. Thus there is a consistent decrease in solute segregation. The solute segregation is more severe near the surface of the deposit layer. Additionally, the thermal convection experiences cyclic intensification attributed to the successive impact of multiple droplets in wire feeding and melting AM. This continuous impact serves to diminish the solute segregation. The results underscore the significant potential and advantages of LB method in accurately simulating the AM, which provides valuable insights for understanding the underlying mechanism of heat and solute transfer in materials and manufacturing.

Ergodicity breaking from Rydberg clusters in a driven-dissipative many-body system.

It is challenging to probe ergodicity breaking trends of a quantum many-body system when dissipation inevitably damages quantum coherence originated from coherent coupling and dispersive two-body interactions. Rydberg atoms provide a test bed to detect emergent exotic many-body phases and nonergodic dynamics where the strong Rydberg atom interaction competes with and overtakes dissipative effects even at room temperature. Here, we report experimental evidence of a transition from ergodic toward ergodic breaking dynamics in driven-dissipative Rydberg atomic gases. The broken ergodicity is featured by the long-time phase oscillation, which is attributed to the formation of Rydberg excitation clusters in limit cycle phases. The broken symmetry in the limit cycle is a direct manifestation of many-body collective effects, which is verified experimentally by tuning atomic densities. The reported result reveals that Rydberg many-body systems are a promising candidate to probe ergodicity breaking dynamics, such as limit cycles, and enable the benchmark of nonequilibrium phase transition.