Nonequilibrium Correlation Research Articles

Microscopic theory for nonequilibrium correlation functions in dense active fluids.

One of the key hallmarks of dense active matter in the liquid, supercooled, and solid phases is the so-called equal-time velocity correlations. Crucially, these correlations can emerge spontaneously, i.e., they require no explicit alignment interactions, and therefore represent a generic feature of dense active matter. This indicates that for a meaningful comparison or possible mapping between active and passive liquids one not only needs to understand their structural properties, but also the impact of these velocity correlations. This has already prompted several simulation and theoretical studies, though they are mostly focused on athermal systems and thus overlook the effect of translational diffusion. Here, we present a fully microscopic method to calculate nonequilibrium correlations in two-dimensional systems of thermal active Brownian particles (ABPs). We use the integration through transients formalism together with (active) mode-coupling theory and analytically calculate qualitatively consistent static structure factors and active velocity correlations. We complement our theoretical results with simulations of both thermal and athermal ABPs which exemplify the disruptive role that thermal noise has on velocity correlations.

Correlation-driven nonequilibrium exciton site transition in a WSe2/WS2 moiré supercell

Moiré superlattices of transition metal dichalcogenides offer a unique platform to explore correlated exciton physics with optical spectroscopy. Whereas the spatially modulated potentials evoke that the exciton resonances are distinct depending on a site in a moiré supercell, there have been no clear demonstration how the moiré excitons trapped in different sites dynamically interact with the doped carriers; so far the exciton-electron dynamic interactions were presumed to be site-dependent. Thus, the transient emergence of nonequilibrium correlations are open questions, but existing studies are limited to steady-state optical measurements. Here we report experimental fingerprints of site-dependent exciton correlations under continuous-wave as well as ultrashort optical excitations. In near-zero angle-aligned WSe2/WS2 heterobilayers, we observe intriguing polarization switching and strongly enhanced Pauli blocking near the Mott insulating state, dictating the dominant correlation-driven effects. When the twist angle is near 60°, no such correlations are observed, suggesting the strong dependence of atomic registry in moiré supercell configuration. Our studies open the door to largely unexplored nonequilibrium correlations of excitons in moiré superlattices.

Nonequilibrium correlation dynamics in the one-dimensional Fermi-Hubbard model: A testbed for the two-particle reduced density matrix theory

Nonequilibrium correlation dynamics in the one-dimensional Fermi-Hubbard model: A testbed for the two-particle reduced density matrix theory

Impact of Manufacturing Agglomeration on the Green Innovation Efficiency—Spatial Effect Based on China’s Provincial Panel Data

Improving the efficiency of green innovation has become an urgent issue in the transformation of manufacturing industries in most developing countries within the context of increasing resource scarcity and environmental constraints. As an important feature of manufacturing development, agglomeration also plays a substantial role the promotion of technological progress and green transformation. Taking China as an example, this paper investigates the spatial impact of manufacturing agglomeration (MAGG) on green innovation efficiency (GIE). We first measure the level of MAGG and GIE in 30 provinces (autonomous regions and municipalities) in China during the period from 2010 to 2019, and then we utilize the spatial Durbin model in order to empirically test the spatial effect and heterogeneity based on theoretical analysis. The findings demonstrate that (1) the overall GIE in China has maintained a steady increase, and the level of MAGG slowly decreased from 2010 to 2019 with characteristics of obvious regional non-equilibrium and spatial correlations; (2) MAGG has a significant effect on the improvement of GIE nationally; (3) under the constraints of regional heterogeneity, the impacts of MAGG on GIE show significant differences between eastern, central and western China; (4) in terms of industry heterogeneity, high-tech MAGG can significantly enhance local GIE, while the indirect effect of non-high-tech MAGG is significantly negative. Our findings not only contribute to the advancement of studies pertaining to industry agglomeration and innovation, but also present policy implications for China and the world at large in terms of the development of high-quality and green economy.

Phase-space stochastic quantum hydrodynamics for interacting Bose gases

Hydrodynamic theories offer successful approaches that are capable of simulating the otherwise difficult-to-compute dynamics of quantum many-body systems. In this work we derive, within the positive-P phase-space formalism, a new stochastic hydrodynamic method for the description of interacting Bose gases. It goes beyond existing hydrodynamic approaches, such as superfluid hydrodynamics or generalized hydrodynamics, in its capacity to simulate the full quantum dynamics of these systems: it possesses the ability to compute non-equilibrium quantum correlations, even for short-wavelength phenomena. Using this description, we derive a linearized stochastic hydrodynamic scheme which is able to simulate such non-equilibrium situations for longer times than the full positive-P approach, at the expense of approximating the treatment of quantum fluctuations, and show that this linearized scheme can be directly connected with existing Bogoliubov approaches. Furthermore, we go on to demonstrate the usefulness and advantages of this formalism by exploring the correlations that arise in a quantum shock wave scenario and comparing its predictions to other established quantum many-body approaches.

Machine Learning for analysis of speckle dynamics: quantification and outlier detection

X-ray photon correlation spectroscopy (XPCS) provides an understanding of complex dynamics in materials that are tied to their synthesis, properties, and behaviors. Analysis of XPCS data for dynamics that are far from equilibrium is labor intense and often can impede the discovery process, especially in experiments with high collection rates. Moreover, binning and averaging, involved in the analysis for alleviating poor signal-to-noise ratio, leads to a loss of temporal resolution and the accumulation of systematic error for the parameters quantifying the dynamics. Here, we integrate a denoising autoencoder model into workflows for the analysis of nonequilibrium two-time intensity-intensity correlation functions. Noise reduction allows for extracting the parameters that characterize the sample's dynamics with the temporal resolution limited only by frame rates. Not only does it improve the quantitative usage of the data, but it also creates the potential for automating the analytical workflow, which is a key to high-throughput or autonomous XPCS experiments. Various approaches for the uncertainty quantification and extension of the model for anomalies' detection are discussed.

Shock-Induced Mesoparticles and Turbulence Occurrence

The development of a new approach to describe turbulent motions in condensed matter on the basis of nonlocal modeling of highly non-equilibrium processes in open systems is performed in parallel with an experiment studying the mesostructure of dynamically deformed solids. The shock-induced mesostructure formation inside the propagating waveform registered in real time allows the transient stages of non-equilibrium processes to be qualitatively and quantitatively revealed. A new nonlocal approach, developed on the basis of the nonlocal and retarded transport equations obtained within the non-equilibrium statistical physics, is used to describe the occurrence of turbulence. Within the approach, the reason for the transition to turbulence is that the non-equilibrium spatiotemporal correlation function generates the dynamic structures in the form of finite-size clusters on the mesoscale, with almost identical values of macroscopic densities moving as almost solid particles that can interact and rotate. The fragmentation of spatiotemporal correlations upon impact forms the mesoparticles that move at different speeds and transfer mass, momentum and energy-like wave packets. The movements recorded simultaneously at two scale levels indicate the energy exchange between them. Its description required a redefinition of the concept of energy far from local thermodynamic equilibrium. The experimental results show that the irreversible part of the dynamic mesostructure remains frozen into material as a new defect.

Correlations in nonequilibrium diffusive systems.

We study the behavior of stationary nonequilibrium two-body correlation functions for diffusive systems with equilibrium reference states (DSe). We describe a DSe at the mesoscopic level by M locally conserved continuum fields that evolve through coupled Langevin equationswith white noises. The dynamic is designed such that the system may reach equilibrium states for a set of boundary conditions. In this form, we make the system driven to a nonequilibrium stationary state by changing the equilibrium boundary conditions. We decompose the correlations in a known local equilibrium part and another one that contains the nonequilibrium behavior and that we call correlation's excess C[over ¯](x,z). We formally derive the differential equationsfor C[over ¯]. To solve them order by order, we define a perturbative expansion around the equilibrium state. We show that the C[over ¯]'s first-order expansion, C[over ¯]^{(1)}, is always zero for the unique field case, M=1. Moreover, C[over ¯]^{(1)} is always long range or zero when M>1. We obtain the surprising result that their associated fluctuations, the space integrals of C[over ¯]^{(1)}, are always zero. Therefore, fluctuations are dominated by local equilibrium up to second order in the perturbative expansion around the equilibrium. We derive the behaviors of C[over ¯]^{(1)} in real space for dimensions d=1 and 2 explicitly. Finally, we derive the two first perturbative orders of the correlation's excess for a generic M=2 case and a hydrodynamic model.

A statistical quasi-particles thermofield theory with Gaussian environments: System-bath entanglement theorem for nonequilibrium correlation functions.

For open quantum systems, the Gaussian environmental dissipative effect can be represented by statistical quasi-particles, namely, dissipatons. We exploit this fact to establish the dissipaton thermofield theory. The resulting generalized Langevin dynamics of absorptive and emissive thermofield operators are effectively noise-resolved. The system-bath entanglement theorem is then readily followed between an important class of nonequilibrium steady-state correlation functions. All these relations are validated numerically. A simple corollary is the transport current expression, which exactly recovers the result obtained from the nonequilibrium Green's function formalism.

Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations

Nous considérons des processus d’exclusion partielle, et des processus d’inclusion sur un graphe général en contact avec des réservoirs. Nous autorisons la présence de inhomogenéités sur les arrêts ainsi que sur les sommets du graph. Nous généralisons les “dualités classiques” dans ce contexte et nous démontrons des nouvelles dualités orthogonales. À partir des dualités classiques, nous démontrons l’unicité de l’état stationnaire non-équilibre, ainsi que des inégalités de corrélation. À partir des dualités orthogonales nous démontrons des propriétés universelles des fonctions de corrélation à n points dans l’état stationnaire non-équilibre pour des systèmes avec deux paramètres de réservoirs inégaux, comme par exemple une chaîne avec des réservoirs à droite et à gauche.

Dynamics in condensed phase for systems involving phase functions obeying Gaussian statistics

The study of non-equilibrium processes in condensed phase has been fascinating and has attracted considerable attention of experimentalists as well as theoreticians during the last few decades. Since the theoretical treatment using Liouville equation involves multi-dimensional phase space functions, it is very difficult to visualize and also to obtain analytical expressions for the time-dependent distribution functions in Liouville space, which has led to formulation of various reduced space descriptions. The bottleneck in describing the non-equilibrium processes in the reduced space lies in the appearance of coupled velocity and position correlation functions in the equations, which are difficult to evaluate in general. In this work, we have developed a scheme to decouple the complicated multi-point coupled correlation function into two-point velocity and position correlation functions for situations characterized by a time-dependent phase function obeying Gaussian distribution, by making use of the Novikov's theorem. As an illustrative application, we have investigated the problem of optically controlled solvation dynamics and obtained exact expressions for the non-equilibrium solvation time correlation functions showing explicit dependence on the excitation frequency, as observed experimentally. We have shown that the linear response theory result is valid as long as the energy gap obeys the Gaussian distribution, rescuing the linear response theory based result from the domain of validity for small fluctuations in solvation coordinate.

How non-equilibrium correlations in active matter reveal the topological crossover in glasses

As shown by early studies on mean-field models of the glass transition, the geometrical features of the energy landscape provide fundamental information on the crossover from high-temperature simple relaxational dynamics to low-temperature activated relaxation. In particular, the critical slowing down of dynamics typical of glass formers has been related to a crossover from a saddle-dominated energy landscape (at high temperatures) to a minima-dominated landscape (at low temperatures). We show that active particles can serve as a useful tool to gain insight into this topological crossover. Once configurations equilibrated down in the glassy phase are provided, we show how features of the landscape are revealed by switching on some activity in particle dynamics. In particular we explain here the mechanism, taking as a reference point the pure p-spin model, by which the presence of self-propulsion is expected to induce critical stationary non-equilibrium correlations in correspondence to the minima-to-saddles crossover.

Long-Range Fluctuation-Induced Forces in Driven Electrolytes.

We study the stochastic dynamics of an electrolyte driven by a uniform external electric field and show that it exhibits generic scale invariance despite the presence of Debye screening. The resulting long-range correlations give rise to a Casimir-like fluctuation-induced force between neutral boundaries that confine the ions; this force is controlled by the external electric field, and it can be both attractive and repulsive with similar boundary conditions, unlike other long-range fluctuation-induced forces. This work highlights the importance of nonequilibrium correlations in electrolytes and shows how they can be used to tune interactions between uncharged biological or synthetic structures at large separations.

Effective temperature of a superfluid flowing in a random potential

The spatial fluctuations of a superfluid flowing in a weak random potential are investigated. We employ classical field theory to demonstrate that the disorder-averaged nonequilibrium second-order correlation of the order parameter at zero temperature is identical to the thermally averaged equilibrium counterpart of a uniform superfluid at an effective temperature. The physics behind this equivalence is that scattering of a moving condensate by disorder has the same effect on the correlation function as equilibrium thermal excitations. The correlation function exhibits an exponential decay in one dimension and a power-law decay in two dimensions. We show that the effective temperature can be measured in an interference experiment of ultracold atomic gases.

Non-equilibrium solvation dynamics: results beyond linear response theory

Optically controlled non-equilibrium solvation dynamics in condensed phase have been studied extensively both experimentally and theoretically. The main drawback of linear response theory (LRT) and other existing theories is that they are unable to elucidate the dependence of non-equilibrium solvation time correlation function, S(t), on the excitation wavelength, as observed in the experiment. In order to explain the experimental observation, we first develop a kinetic equation in 1D solvation coordinate (SC) space and then we propose a new perturbative method to derive an analytical expression for S(t) for an anharmonic potential in SC space. We observe from the result of S(t) that the calculated results of the same depend strongly on the innumerable optical states through excitation wavelength, when the potential is anharmonic in SC space, indicating the breakdown of LRT. We have shown that both excitation wavelength and rotational relaxation time carry the information of micro-heterogeneity. Another significant aspect of our work is that the analytical expression obtained for S(t) corresponding to the anharmonic potential decays multi-exponentially, whereas S(t) decays single exponentially for a harmonic potential. More significantly, the calculated results for S(t) are found to be in excellent agreement with the available experimental results for the heterogeneous system.

Green's function of the Smoluchowski equation with reaction sink: Application to geminate and bulk recombination reactions.

By applying a recently developed solution method for the Fredholm integral equation of the second kind, we obtain an expression for Green's function of the Smoluchowski equation with a reaction sink. The result is applied to obtain accurate analytical expressions for the time-dependent survival probability of a geminate reactant pair and the rate coefficient of the bulk recombination between reactants undergoing diffusive motions under strong Coulomb interactions. The effects of both repulsive and attractive interactions are considered, and the results are compared with the numerical results obtained by solving the equation for the survival probability and the nonequilibrium pair correlation function. It is shown that the solutions are accurate enough for most reasonable parameter values.

Diagrammatic time-local master equation for open quantum systems

We introduce simple diagrams and rules to calculate the exact time-local master equation for an arbitrary open quantum system interacting with a bath. In it, the time-convolutionless generator is expanded in the system-bath coupling to all orders, and the $n\mathrm{th}$-order contribution is expressed by the superoperators generated from the system operator in the system-bath coupling and the associated $n$-point nonequilibrium correlation functions of the environment operators. This theory generalizes previous attempts to obtain the time-convolutionless generator and provides a general framework to study the non-Markovian, nonequilibrium dynamics of open quantum systems.

Concept of reaction coordinate for dynamics of optically controlled non-equilibrium processes in condensed phase

Optically controlled non-equilibrium processes in condensed phase, such as solvation of ions and electron transfer reactions, have been widely studied both experimentally and theoretically. The dynamics of these processes is investigated through the experimentally observable quantities, like non-equilibrium solvation time correlation function $$ S\left( t \right) $$ and the time-dependent survival probability $$ P\left( t \right) $$ of the reactant, respectively. On the theoretical side, although the linear response theory and Marcus theory have been widely used to predict $$ S\left( t \right) $$ and $$ P\left( t \right) $$, respectively, their main drawback is that their prediction of $$ S\left( t \right) $$ and $$ P\left( t \right) $$ does not show dependence on the initial preparation of the system, while experimental observations suggest that both these quantities depend on the initial preparation through dependence on the excitation wavelength. In this work, we address this issue and introduce the concept of a new reaction coordinate, which can take into account the effect of initial optically prepared innumerable phase space coordinates through a single parameter, viz. the optical excitation wavelength. We first project the dynamics in multi-dimensional Liouville space onto a one-dimensional reaction coordinate (RC) space, obtaining thereby a new kinetic equation for the RC. We have calculated both $$ S\left( t \right) $$ and $$ P\left( t \right) $$ by numerically solving this new equation in one-dimensional RC space for harmonic as well as anharmonic potentials and studied the effect of the initial preparation of the system by considering the excitation wavelength dependence. It is found that for solvation process, the calculated $$ S\left( t \right) $$ depends strongly on the initial preparation of the system (i.e. the excitation wavelength) only for anharmonic effective potentials. For electron transfer reaction, however, $$ P\left( t \right) $$ depends on the excitation wavelength for both harmonic and anharmonic potentials, which cannot be predicted by the Marcus theory.

Effect of Nonequilibrium Correlations on the Effective Resistances between Sites in the Theory of Hopping Conductivity

It has been shown that the nonequilibrium correlations in hopping conductivity can be taken into account by generalizing the Miller–Abrahams network of resistors. The resistances of resistors between nodes in such a network are related to their environment. Moreover, some nonlocal elements exist, which create the voltage on one resistor proportional to the current through the other resistor. These elements are required to make controllable the approximation used to construct the network. The greatest change in the resistance takes place in the resistors, whose resistance is lower than the critical resistance of the percolation theory.

System of correlation kinetic equations and the generalized equivalent circuit for hopping transport

We derive the system of equations that allows to include nonequilibrium correlations of filling numbers into the theory of the hopping transport. The system includes the correlations of arbitrary order in a universal way and can be cut at any place relevant to a specific problem to achieve the balance between rigor and computation possibilities. In the linear-response approximation, it can be represented as an equivalent electric circuit that generalizes the Miller-Abrahams resistor network. With our approach, we show that nonequilibrium correlations are essential to calculate conductivity and distribution of currents in certain disordered systems. Different types of disorder affect the correlations in different applied fields. The effect of energy disorder is most important at weak electric fields while the position disorder by itself leads to nonzero correlations only in strong fields.