Non-equilibrium Evolution Research Articles

Quantum turbulence, superfluidity, non-Markovian dynamics, and wave function thermalization

While quantum turbulence has been addressed both experimentally (predominantly for superfluid He4 and He3) and theoretically, the dynamics of various ensembles of quantized vortices has been followed in time only until the vortices have decayed into phonons. How this “thermalization” is achieved is still an unaddressed and thus an unelucidated question. The unitary Fermi gas (UFG) is a unique quantum system, which has no classical counterpart and is of relevance to neutron stars, cold atoms, condensed-matter and nuclear many-body systems. The non-Markovian evolution of an isolated UFG is put in evidence and its entire nonequilibrium evolution can be studied theoretically within a unified theoretical framework. The initial lattice of quantum vortices and antivortices evolves through a couple of vortex tangles and excitation of Kelvin waves, where vortices cross and reconnect, until very slowly thermalization sets in. Published by the American Physical Society 2024

Carbon Emission Effects of Spatially Connected Networks in the Digital Economy： Dynamic Evolution and Mechanism of Action

In the context of the "double carbon" goal and the construction of the "East Counts, West Counts" project, this study investigated the characteristics of the spatial and temporal evolution of the digital economy spatial correlation network, and the effects and mechanisms of carbon emission reduction and carbon rebound effects by selecting data at the level of 254 prefectural-level cities from 2011 to 2021 and using the UCINET software and empirical econometric modeling. The results indicated that： The spatial network of the digital economy represented the development pattern of multiple synergies and had the characteristics of non-equilibrium spatial evolution in geographic regions. Secondly, the spatial network of the digital economy in the sample selection period had a positive contribution to carbon emission reduction, and it led to the carbon rebound effect, which was still valid after the robustness test. Furthermore, the spatial correlation network of the digital economy could reduce carbon emissions by promoting the energy efficiency effect under technological progress and led to the carbon rebound effect. Finally, the empirical results were heterogeneous under the four dimensions of geographic region, administrative level, urban environmental governance objectives, and resource endowment.

Study on rapid prediction of flow field in a knudsen compressor based on multi-fidelity reduced-order models

The safe and stable operation of a hydrogen Knudsen compressor is essential for transporting hydrogen in microfluidic systems. This study uses proper orthogonal decomposition to identify the coherent structures within the hydrogen flow field during non-equilibrium evolution. A long short-term memory neural network is then used to create a multi-fidelity reduced-order model, connecting two-dimensional and three-dimensional data to uncover transient flow mechanisms and enable rapid flow field prediction. The results show that the coherent structures of hydrogen flow, representing the most energetic modes, retain 99% of the flow energy and significantly influence the evolution of Poiseuille and thermal transpiration flows during non-equilibrium processes. The multi-fidelity reduced-order model effectively captures hydrogen transient flow and instabilities at various stages, achieving a 99.4% reduction in computational time while maintaining a maximum relative error of 0.53%. This approach facilitates the rapid prediction and control of flow states during hydrogen transport.

Integrated crew organization and work zone scheduling for network-wide daily road pavement rehabilitation

This study develops a new integer-programming model to address the network-wide daily road pavement rehabilitation scheduling problem. In the model, the crew organization and work zone schedule are jointly optimized daily, with the objective of minimizing both the operational cost and user travel time. A day-to-day traffic dynamics model is applied to capture the non-equilibrium traffic evolution against network supply variation over the planning horizon, which leads to a simulation-based optimization problem. To solve this challenging problem, a two-stage hybrid heuristic solution method is proposed. In the first stage, hybrid tabu search (TS) meta-heuristics are comparatively developed to identify a group of active crew work routes without time slacks. The obtained crew routes are then fed to the second stage for work zone scheduling via a discrete compass search algorithm. Some important findings are obtained from numerical experiments. First, crew routing (or crew organization) is the dominant decision in the studied problem, and a desirable work zone schedule encourages a crew to execute the assigned tasks continually. The findings can be used to develop simplified and efficient solution algorithms. Second, the hybrid TS meta-heuristics developed for crew routing exhibit superior performance compared to other solution methods. Finally, a well-defined model for the current problem should consider both user travel time and operation cost. Our model enables decision-makers to make an effective trade-off between these two objectives. An effective measure is suggested to evaluate the cost-effectiveness of budget investment decisions when budgets are limited.

Uncovering the Nonequilibrium Evolution Mechanism between Na2+2 δFe2- δ(SO4)3 Cathode and Impurities in the Na2SO4-FeSO4·7H2O Binary System for High-Voltage Sodium-Ion Batteries.

Sodium-ion batteries are increasingly recognized as ideal for large-scale energy storage applications. Alluaudite Na2+2 δFe2- δ(SO4)3 has become one of the focused cathode materials in this field. However, previous studies employing aqueous-solution synthesis often overlooked the formation mechanism of the impurity phase. In this study, the nonequilibrium evolution mechanism between Na2+2 δFe2- δ(SO4)3 and impurities by adjusting ratios of the Na2SO4/FeSO4·7H2O in the binary system is investigated. Then an optimal ratio of 0.765 with reduced impurity content is confirmed. Compared to the poor electrochemical performance of the Na2.6Fe1.7(SO4)3 (0.765) cathode, the optimized Na2.6Fe1.7(SO4)3@CNTs (0.765@CNTs) cathode, with improved electronic and ionic conductivity, demonstrates an impressive discharge specific capacity of 93.8 mAh g-1 at 0.1 C and a high-rate capacity of 67.84 mAh g-1 at 20 C, maintaining capacity retention of 71.1% after 3000 cycles at 10 C. The Na2.6Fe1.7(SO4)3@CNTs//HC full cell reaches an unprecedented working potential of 3.71V at 0.1 C, and a remarkable mass-energy density exceeding 320Wh kg-1. This work not only provides comprehensive guidance for synthesizing high-voltage Na2+2 δFe2- δ(SO4)3 cathode materials with controllable impurity content but also lays the groundwork of sodium-ion batteries for large-scale energy storage applications.

Spatial non-equilibrium and distribution dynamic evolution of the development level of national physical fitness in China's provinces.

Physical health is fundamental to a country's socio-economic advancement. An in-depth exploration of the spatial distribution and dynamic evolution of national physical fitness across China is crucial for enhancing the country's overall physical health. This study aims to provide valuable insights into the geographical and temporal patterns of physical fitness, informing strategies for national physical fitness improvement. Employing data from China's national physical fitness monitoring of 31 provinces, cities, and districts for the years 2005, 2010, and 2015, this study utilizes the Gini coefficient, its decomposition, and nonparametric density estimation methods. These techniques are applied to analyze the spatial disparities and temporal trends in national physical fitness levels among different demographics, including the overall population, males, females, and urban and rural residents. The study reveals that the regional disparity in China's national physical fitness initially narrowed and then expanded across the general population, females, and in both urban and rural areas, while consistently increasing among males. In terms of geographical distribution, the East, Middle, and West regions show significant heterogeneity, with the East-West gap being the most pronounced (Gini coefficients of 0.0249, 0.0230, 0.0263). The contribution rate of regional gaps was highest (54.40% -64.69%), followed by regional disparities (24.78% -27.15%), and the contribution of hypervariable density difference was the smallest (10.53% -19.75%). Despite a slight improvement in overall national physical fitness, the absolute regional disparities have further widened. Provinces with lower levels of national physical fitness demonstrate a 'club convergence' trend, indicating regional clustering of similar fitness levels. Additionally, a 'catch-up effect' is evident in rural areas, particularly in provinces with historically lower levels of national physical fitness. These findings suggest the need for region-specific public health strategies to address the growing disparities in national physical fitness across China.

On the analysis of two-time correlation functions: equilibrium versus non-equilibrium systems.

X-ray photon correlation spectroscopy (XPCS) is a powerful tool for the investigation of dynamics covering a broad range of timescales and length scales. The two-time correlation function (TTC) is commonly used to track non-equilibrium dynamical evolution in XPCS measurements, with subsequent extraction of one-time correlations. While the theoretical foundation for the quantitative analysis of TTCs is primarily established for equilibrium systems, where key parameters such as the diffusion coefficient remain constant, non-equilibrium systems pose a unique challenge. In such systems, different projections ('cuts') of the TTC may lead to divergent results if the underlying fundamental parameters themselves are subject to temporal variations. This article explores widely used approaches for TTC calculations and common methods for extracting relevant information from correlation functions, particularly in the light of comparing dynamics in equilibrium and non-equilibrium systems.

Non-equilibrium and self-organization evolution in hot-spot ignition processes

Non-equilibrium and self-organization evolution in hot-spot ignition processes

Non-Equilibrium Scour Evolution around an Emerged Structure Exposed to a Transient Wave

The present study evaluates the performance of two numerical approaches in estimating non-equilibrium scour patterns around a non-slender square structure subjected to a transient wave, by comparing numerical findings with experimental data. This study also investigates the impact of the structure’s positioning on bed evolution, analyzing configurations where the structure is either attached to the sidewall or positioned at the centerline of the wave flume. The first numerical method treats sediment particles as a distinct continuum phase, directly solving the continuity and momentum equations for both sediment and fluid phases. The second method estimates sediment transport using the quadratic law of bottom shear stress, yielding robust predictions of bed evolution through meticulous calibration and validation. The findings reveal that both methods underestimate vortex-induced near-bed vertical velocities. Deposits formed along vortex trajectories are overestimated by the first method, while the second method satisfactorily predicts the bed evolution beneath these paths. Scour holes caused by wave impingement tend to backfill as the flow intensity diminishes. The second method cannot sufficiently capture this backfilling, whereas the first method adequately reflects the phenomenon. Overall, this study highlights significant variations in the predictive capabilities of both methods in regard to the evolution of non-equilibrium scour at low Keulegan–Carpenter numbers.

H and CO Co-Induced Roughening of Cu Surface in CO2 Electroreduction Conditions.

The dynamic restructuring of Cu has been observed under electrochemical conditions, and it has been hypothesized to underlie the unique reactivity of Cu toward CO2 electroreduction. Roughening is one of the key surface phenomena for Cu activation, whereby numerous atomic vacancies and adatoms form. However, the atomic structure of such surface motifs in the presence of relevant adsorbates has remained elusive. Here, we explore the chemical space of Cu surface restructuring under coverage of CO and H in realistic electroreduction conditions, by combining grand canonical DFT and global optimization techniques, from which we construct a potential-dependent grand canonical ensemble representation. The regime of intermediate and mixed CO and H coverage─where structures exhibit some elevated surface Cu─is thermodynamically unfavorable yet kinetically inevitable. Therefore, we develop a quasi-kinetic Monte Carlo simulation to track the system's evolution during a simulated cathodic scan. We reveal the evolution path of the system across coverage space and identify the accessible metastable structures formed along the way. Chemical bonding analysis is performed on the metastable structures with elevated Cu*CO species to understand their formation mechanism. By molecular dynamics simulations and free energy calculations, the surface chemistry of the Cu*CO species is explored, and we identify plausible mechanisms via which the Cu*CO species may diffuse or dimerize. This work provides rich atomistic insights into the phenomenon of surface roughening and the structure of involved species. It also features generalizable methods to explore the chemical space of restructuring surfaces with mixed adsorbates and their nonequilibrium evolution.

Raman time-delay in attosecond transient absorption of strong-field created krypton vacancy

Strong field ionization injects a transient vacancy in the atom which is entangled to the outgoing photoelectron. When the electron is finally detached, the ion is populated at different excited states with part of coherence information lost. The preserved coherence of matter after interacting with intense short pulses has important consequences on the subsequent nonequilibrium evolution and energy relaxation. Here we employ attosecond transient absorption spectroscopy to measure the time-delay of resonant transitions of krypton vacancy during their creation. We have observed that the absorptions by the two spin-orbit split states are modulated at different paces when varying the time-delay between the near-infrared pumping pulse and the attosecond probing pulse. It is shown that the coupling of the ions with the remaining field leads to a suppression of ionic coherence. Comparison between theory and experiments uncovers that coherent Raman coupling induces time-delay between the resonant absorptions, which provides insight into laser-ion interactions enriching attosecond chronoscopy.

Quasi-instantaneous materials processing technology via high-intensity electrical nano pulsing

Despite many efforts, the outcomes obtained with field-assisted processing of materials still rely on long-term coupling with other electroless processes. This conceals the efficacy and the intrinsic contributions of electric current. A new device utilizing electrical nano pulsing (ENP) has been designed and constructed to bring quasi-instantaneous modifications to the micro- and nano-structure in materials. Featuring ultra-high intensity (~ 1011 A/m2) and ultra-short duration (< 1 μs), the ENP technology activates non-equilibrium structural evolutions at nanometer spatial scale and nanosecond temporal scale. Several examples are provided to demonstrate its utility far outpacing any conventional materials processing technology. The ENP technology gives a practical tool for exploring the intrinsic mechanism of electric-field effects and a pathway towards the rapid industrial manufacturing of materials with unique properties.

Influence of laser-induced Au-plasma plume collision on the efficiency of x-ray radiations and the energy-transport process relevant to ICF

Experiments and simulations have been carried out to study the colliding process by two lasers irradiating a gold half-hohlraum. Via analyzing the evolutionary x-ray images, radiation fluxes and self-emission spectrum of tracers, influence on the x-ray conversion efficiency and the local plasma temperature Te,i from two gold-plasma plumes have been investigated deeply, which is similar as the configuration in Inertial Confinement Fusion (ICF). Experimental results confirm a region with high electron and ion temperatures Te,i are induced, satisfying the strong collision condition of λi<ΔL , where λ i and ΔL are respectively the ion mean-free path and the gradient length of Te . It leads to almost 30% increasing of M-band component compared to that from a single laser-irradiation case. Meanwhile ion temperature in this region increases more rapidly than electrons, reaching about Ti≈(16±4) keV ( Te≈(2±0.2) keV). Thus, our studies provide the experimental evidence of quantitative x-ray enhancement and a non-equilibrium evolution simultaneously due to the plasma collision for the first time. Besides, two-dimensional simulation results reveal that this process can not be precisely described by the traditional shock-heating model by dissipating the shock energy only to ions. But by distributing the viscous heating between both electrons and ions as theoretically discussed by Miller (2020 Comput. Fluids 210 104672), numerical results can match experiments better. This discovery will be of great importance to improve the precision of prediction for ICF.

Phase separation of a magnetic fluid: Asymptotic states and nonequilibrium kinetics.

We study self-assembly in a colloidal suspension of magnetic particles by performing comprehensive molecular dynamics simulations of the Stockmayer (SM) model, which comprises spherical particles decorated by a magnetic moment. The SM potential incorporates dipole-dipole interactions along with the usual Lennard-Jones interaction and exhibits a gas-liquid phase coexistence observed experimentally in magnetic fluids. When this system is quenched from the high-temperature homogeneous phase to the coexistence region, the nonequilibrium evolution to the condensed phase proceeds with the development of spatial as well as magnetic order. We observe density-dependent coarsening mechanisms-a diffusive growth law ℓ(t)∼t^{1/3} in the nucleation regime and hydrodynamics-driven inertial growth law ℓ(t)∼t^{2/3} in the spinodal regimes. [ℓ(t) is the average size of the condensate at time t after the quench.] While the spatial growth is governed by the expected conserved order parameter dynamics, the growth of magnetic order in the spinodal regime exhibits unexpected nonconserved dynamics. The asymptotic morphologies have density-dependent shapes which typically include the isotropic sphere and spherical bubble morphologies in the nucleation region, and the anisotropic cylinder, planar slab, cylindrical bubble morphologies in the spinodal region. The structures are robust and nonvolatile, and exhibit characteristic magnetic properties. For example, the oppositely magnetized hemispheres in the spherical morphology impart the characteristics of a Janus particle to it. The observed structures have versatile applications in catalysis, drug delivery systems, memory devices, and magnetic photonic crystals, to name a few.

Constraining Circumgalactic Turbulence with QSO Absorption Line Measurements

Our knowledge of the circumgalactic medium (CGM) is mostly based on quasar absorption line measurements. These have uncovered a multiphase medium that is likely highly turbulent, but constraints of this turbulence are limited to measurements of the nonthermal width of absorption line components (b turb) and the line-of-sight velocity dispersion between components (σ LOS). Here we analyze a suite of CGM simulations to determine how well these indirect measures are related to the underlying CGM. Our simulations track the nonequilibrium evolution of all commonly observed ions and consist of two main types: small-scale simulations of regions of homogenous CGM turbulence and global simulations of inhomogenous turbulence throughout a galactic halo. From each simulation, we generate mock spectra of Si ii, Si iv, C iv, and O vi, which allow us to directly compare b turb and σ LOS to the true line-of-sight turbulence (σ 1D). In the small-scale simulations, b turb is only weakly correlated with σ 1D, likely because it measures random motions within individual warm CGM clouds, which do not sample the overall random motions. Meanwhile, σ LOS and σ 1D are strongly correlated with σ 1D ≈ σ LOS + 10 km s−1 in the densest regions we simulated, although the strength of this correlation depended weakly on the gas phase being probed. Our large-scale simulations also indicate that b turb and σ 1D are largely uncorrelated and that σ 1D ≈ σ LOS + 10 km s−1 on average, although it varies along individual sight lines. Moreover, the σ LOS distributions from our global simulations are similar to recent observations, suggesting that this quantity may provide useful constraints on circumgalactic turbulence regardless of the axis probed.

Application of Boltzmann kinetic equations to model X-ray-created warm dense matter and plasma.

In this review, we describe the application of Boltzmann kinetic equations for modelling warm dense matter and plasma formed after irradiation of solid materials with intense femtosecond X-ray pulses. Classical Boltzmann kinetic equations are derived from the reduced N-particle Liouville equations. They include only single-particle densities of ions and free electrons present in the sample. The first version of the Boltzmann kinetic equation solver was completed in 2006. It could model non-equilibrium evolution of X-ray-irradiated finite-size atomic systems. In 2016, the code was adapted to study plasma created from X-ray-irradiated materials. Additional extension of the code was then also performed, enabling simulations in the hard X-ray irradiation regime. In order to avoid treatment of a very high number of active atomic configurations involved in the excitation and relaxation of X-ray-irradiated materials, an approach called 'predominant excitation and relaxation path' (PERP) was introduced. It limited the number of active atomic configurations by following the sample evolution only along most PERPs. The performance of the Boltzmann code is illustrated in the examples of X-ray-heated solid carbon and gold. Actual model limitations and further model developments are discussed. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Dynamics of molecular rotors in bulk superfluid helium.

Molecules immersed in liquid helium are excellent probes of superfluidity. Their electronic, vibrational, and rotational dynamics provide valuable clues about the superfluid at the nanoscale. Here we report on the experimental study of the laser-induced rotation of helium dimers inside the superfluid 4He bath at variable temperature. The coherent rotational dynamics of [Formula: see text] is initiated in a controlled way by ultrashort laser pulses and tracked by means of time-resolved laser-induced fluorescence. We detect the decay of rotational coherence on the nanosecond time scale and investigate the effects of temperature on the decoherence rate. The observed temperature dependence suggests a nonequilibrium evolution of the quantum bath, accompanied by the emission of the wave of second sound. The method offers ways of studying superfluidity with molecular nanoprobes under variable thermodynamic conditions.

Effects of rapid heating on non-equilibrium microstructure evolution and strengthening mechanisms of titanium alloy

In this paper, the effects of heating parameters, including temperature ranging from 900 °C to 1000 °C, heating rates ranging from 2 °C∙s−1 to 100 °C∙s−1, and 120 s soaking on the non-equilibrium microstructure evolution of Ti-6Al-4V alloy were studied. Microstructures after heating were characterized to reveal the mechanism of non-equilibrium phase transformation. Uniaxial tensile tests at room temperature were carried out to evaluate the effects of non-equilibrium microstructure on the mechanical properties. Results show that higher heating rate and lower temperature lead to lower β phase volume fraction and finer β grains. A transition region with element gradient forms in the αp grain near the αp/β phase boundary and transfers into β phase gradually during the heating. Rapid heating could confine the movement of the transition region, and therefore reduce the α→β transition and growth of the β phase. When the Ti-6Al-4V alloy was heated to 1000 °C at a rate of 50 °C/s and then quenched immediately, the tensile strength was improved by 19.5% and reached up to 1263.0 MPa with the elongation only decreasing from 13.6% to 9.6% compared with the initial material. The main strengthening mechanism is that the rapid heating in the single-phase region avoids the rapid growth of the β phase, which leads to fully fine martensite formation after water quenching.

Approach to Equilibrium of Statistical Systems: Classical Particles and Quantum Fields Off-Equilibrium

Non-equilibrium evolution at absolute temperature T and approach to equilibrium of statistical systems in long-time (t) approximations, using both hierarchies and functional integrals, are reviewed. A classical non-relativistic particle in one spatial dimension, subject to a potential and a heat bath (hb), is described by the non-equilibrium reversible Liouville distribution (W) and equation, with a suitable initial condition. The Boltzmann equilibrium distribution Weq generates orthogonal (Hermite) polynomials Hn in momenta. Suitable moments Wn of W (using the Hn’s) yield a non-equilibrium three-term hierarchy (different from the standard Bogoliubov–Born–Green–Kirkwood–Yvon one), solved through operator continued fractions. After a long-t approximation, the Wn’s yield irreversibly approach to equilibrium. The approach is extended (without hb) to: (i) a non-equilibrium system of N classical non-relativistic particles interacting through repulsive short range potentials and (ii) a classical ϕ4 field theory (without hb). The extension to one non-relativistic quantum particle (with hb) employs the non-equilibrium Wigner function (WQ): difficulties related to non-positivity of WQ are bypassed so as to formulate approximately approach to equilibrium. A non-equilibrium quantum anharmonic oscillator is analyzed differently, through functional integral methods. The latter allows an extension to relativistic quantum ϕ4 field theory (a meson gas off-equilibrium, without hb), facing ultraviolet divergences and renormalization. Genuine simplifications of quantum ϕ4 theory at high T and large distances and long t occur; then, through a new argument for the field-theoretic case, the theory can be approximated by a classical ϕ4 one, yielding an approach to equilibrium.

Universal equilibration dynamics of the Sachdev-Ye-Kitaev model

Equilibrium quantum many-body systems in the vicinity of phase transitions generically manifest universality. In contrast, limited knowledge has been gained on possible universal characteristics in the non-equilibrium evolution of systems in quantum critical phases. In this context, universality is generically attributed to the insensitivity of observables to the microscopic system parameters and initial conditions. Here, we present such a universal feature in the equilibration dynamics of the Sachdev-Ye-Kitaev (SYK) Hamiltonian – a paradigmatic system of disordered, all-to-all interacting fermions that has been designed as a phenomenological description of quantum critical regions. We drive the system far away from equilibrium by performing a global quench, and track how its ensemble average relaxes to a steady state. Employing state-of-the-art numerical simulations for the exact evolution, we reveal that the disorder-averaged evolution of few-body observables, including the quantum Fisher information and low-order moments of local operators, exhibit within numerical resolution a universal equilibration process. Under a straightforward rescaling, data that correspond to different initial states collapse onto a universal curve, which can be well approximated by a Gaussian throughout large parts of the evolution. To reveal the physics behind this process, we formulate a general theoretical framework based on the Novikov–Furutsu theorem. This framework extracts the disorder-averaged dynamics of a many-body system as an effective dissipative evolution, and can have applications beyond this work. The exact non-Markovian evolution of the SYK ensemble is very well captured by Bourret–Markov approximations, which contrary to common lore become justified thanks to the extreme chaoticity of the system, and universality is revealed in a spectral analysis of the corresponding Liouvillian.