Critical wetting transitions under nonequilibrium conditions are studied numerically and analytically by means of an interface-displacement model defined by a Kardar-Parisi-Zhang equation, plus some extra terms representing a limiting, short-ranged attractive wall. Its critical behavior is characterized in detail by providing a set of exponents for both the average height and the surface order-parameter in one dimension. The emerging picture is qualitatively and quantitatively different from recently reported mean-field predictions for the same problem. Evidence is shown that the presence of the attractive wall induces an anomalous scaling of the interface local slopes.
We present an extension of equilibrium wetting to nonequilibrium situations particularly suited to systems with anisotropic interactions. Both critical and complete wetting transitions were found and characterized. We have identified a region in the space of parameters (temperature and chemical potential) where the wet and non-wet phases coexist. Emphasis is made on the analogies and differences between equilibrium and nonequilibrium wetting.
Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a two-dimensional Ising spin lattice at zero temperature with two boundaries subject to opposing surface fields. Local spin excitations are only allowed by absorbing an energy quantum (photon) below a cutoff energy E_c. Local spin relaxation takes place by emitting a photon which leaves the lattice. Using Monte Carlo simulation nonequilibrium critical wetting transiti…
Models with a nonequilibrium wetting transition display a transition also in finite systems. This is different from nonequilibrium phase transitions into an absorbing state, where the stationary state is the absorbing one for any value of the control parameter in a finite system. In this paper, we study what kind of transition takes place in finite systems of nonequilibrium wetting models. By solving exactly a microscopic model with three and four sites and performing numerical simulations we show that the phase transition taking place in a finite system is characterized by the average interfa…
A model for nonequilibrium wetting in 1+1 dimensions is introduced. It comprises adsorption and desorption processes with a dynamics which generically does not obey detailed balance. Depending on the rates of the dynamical processes the wetting transition is either of first or second order. It is found that the wet (unbound) and the non-wet (pinned) states coexist and are both thermodynamically stable in a domain of the dynamical parameters which define the model. This is in contrast with equilibrium transitions where coexistence of thermodynamically stable states takes place only on the trans…
When a nonequilibrium growing interface in the presence of a wall is considered a nonequilibrium wetting transition may take place. This transition can be studied trough Langevin equations or discrete growth models. In the first case, the Kardar-Parisi-Zhang equation, which defines a very robust universality class for nonequilibrium moving interfaces, with a soft-wall potential is considered. While in the second, microscopic models, in the corresponding universality class, with evaporation and deposition of particles in the presence of hard-wall are studied. Equilibrium wetting is related to a…
A self-consistent mean-field method is used to study critical wetting transitions under nonequilibrium conditions by analyzing Kardar-Parisi-Zhang (KPZ) interfaces in the presence of a bounding substrate. In the case of positive KPZ nonlinearity a single (Gaussian) regime is found. On the contrary, interfaces corresponding to negative nonlinearities lead to three different regimes of critical behavior for the surface order-parameter: (i) a trivial Gaussian regime, (ii) a weak-fluctuation regime with a trivially located critical point and nontrivial exponents, and (iii) a highly non-trivial str…
As a canonical model for wetting far from thermal equilibrium we study a Kardar-Parisi-Zhang interface growing on top of a hard-core substrate. Depending on the average growth velocity the model exhibits a non-equilibrium wetting transition which is characterized by an additional surface critical exponent theta. Simulating the single-step model in one spatial dimension we provide accurate numerical estimates for theta and investigate the distribution of contact points between the substrate and the interface as a function of time. Moreover, we study the influence of finite-size effects, in part…
We analyze within mean-field theory as well as numerically a KPZ equation that describes nonequilibrium wetting. Both complete and critical wettitng transitions were found and characterized in detail. For one-dimensional substrates the critical wetting temperature is depressed by fluctuations. In addition, we have investigated a region in the space of parameters (temperature and chemical potential) where the wet and nonwet phases coexist. Finite-size scaling analysis of the interfacial detaching times indicates that the finite coexistence region survives in the thermodynamic limit. Within this…
A simple two dimensional model of a phase growing on a substrate is introduced. The model is characterized by an adsorption rate q, and a desorption rate p. It exhibits a wetting transition which may be viewed as an unbinding transition of an interface from a wall. For p=1, the model may be mapped onto an exactly soluble equilibrium model exhibiting complete wetting with critical exponents gamma = 1/3 for the diverging interface width and x_0 = 1 for the zero-level occupation. For 0 < p != 1 a crossover to different exponents is observed which is related to a KPZ type nonlinearity.
We study the entropy production of a microscopic model for nonequilibrium wetting. We show that, in contrast to the equilibrium case, a bound interface in a nonequilibrium steady state produces entropy. Interestingly, in some regions of the phase diagram a bound interface produces more entropy than a free interface. Moreover, by solving exactly a four-site system, we find that the first derivative of the entropy production with respect to the control parameter displays a discontinuity at the critical point of the wetting transition.
Hydrodynamic theory of wetting by active particles
Department of Applied Mathematics and Theoretical Physics, University of Cambridge（剑桥大学应用数学与理论物理系）；Yusuf Hamied Department of Chemistry, University of Cambridge（剑桥大学尤素福·哈米德化学系）
Motivated by the observations of intracellular phase separations and the wetting of cell membranes by protein droplets, we study the nonequilibrium surface wetting by Monte Carlo simulations of a lattice gas model involving particle creation. We find that, even when complete wetting should occur in equilibrium, the fast creation of particles can hinder the surface wetting for a long time due to the bulk droplet formation. Performing molecular dynamics simulations, we show that this situation also holds in colloidal particle systems when the disorder density is sufficiently high. The results su…
The irreversible growth of magnetic films is studied in three-dimensional confined geometries of size $L\times L\times M$, where $M\gg L$ is the growing direction. Competing surface magnetic fields, applied to opposite corners of the growing system, lead to the observation of a localization-delocalization (weakly rounded) transition of the interface between domains of up and down spins on the planes transverse to the growing direction. This effective transition is the precursor of a true far-from-equilibrium corner wetting transition that takes place in the thermodynamic limit. The phenomenon …
The growth of confined magnetic films with ferromagnetic interactions between nearest-neighbor spins is studied in a stripped $(1+1)-$dimensional rectangular geometry. Magnetic films are grown irreversibly by adding spins at the boundaries of the growing interface. A competing situation with two opposite short range surface magnetic fields of the same magnitude is analyzed. Due to the antisymmetric condition considered, an interface between domains with spins having opposite orientations develops along the growing direction. Such interface undergoes a localization-delocalization transition tha…
A lattice model for active matter is studied numerically, showing that it displays wettings transitions between three distinctive phases when in contact with an impenetrable wall. The particles in the model move persistently, tumbling with a small rate $α$, and interact via exclusion volume only. When increasing the tumbling rates $α$, the system transits from total wetting to partial wetting and unwetting phases. In the first phase, a wetting film covers the wall, with increasing heights when $α$ is reduced. The second phase is characterized by wetting droplets on the wall with a periodic spa…
We use the grand canonical Monte Carlo method to study the nature of wetting transitions on a variety of heterogeneous surfaces. The model system we explore, Ne adsorption on Mg, is one for which a prewetting transition has been found in our previous simulations. We find that the first order transition present on the flat surface is absent from the rough surface. Nevertheless, the resulting isotherms are, in some cases, so close to being discontinuous that the distinction would be difficult to discern in most experiments.
The wetting of solid surfaces by fluids is a problem of great practical importance that has been extensively studied over the years. Most often, the experimental work has involved measurements of the contact angle made by a liquid on the solid surface of interest. Young's equation gives the relation between the contact angle and the interfacial tensions. An alternative to the contact angle computation is the more generally applicable formulation of this problem based on simulations (and measurements) of adsorption isotherms for a fluid on a weakly interacting solid surface. We present some GCM…
In this thesis I study the dynamics of some nonequilibrium systems, using both computer simulations and theoretical tools. In particular, the following topics are studied: (i) metastability in a nonequilibrium ferromagnetic system, (ii) the onset of scale-free avalanches during metastable state decay, (iii) phase segregation under anisotropic nonequilibrium conditions, (iv) the microscopic basis of heat conduction and Fourier's law in low dimensional systems and, finally, (v) a problem related with the physics of absorbing states. The study of these nonequilibrium dynamic phenomena provides an…
With the guidance offered by nonequilibrium statistical thermodynamics, simulation techniques are elevated from brute-force computer experiments to systematic tools for extracting complete, redundancy-free and consistent coarse grained information for dynamic systems. We sketch the role and potential of Monte Carlo, molecular dynamics and Brownian dynamics simulations in the thermodynamic approach to coarse graining. A melt of entangled linear polyethylene molecules serves us as an illustrative example.
We combine computer simulations and analytical theory to investigate the glassy dynamics in dense assemblies of athermal particles evolving under the sole influence of self-propulsion. The simulations reveal that when the persistence time of the self-propelled particles is increased, the local structure becomes more pronounced whereas the long-time dynamics first accelerates and then slows down. These seemingly contradictory evolutions are explained by constructing a nonequilibrium mode-coupling-like theory for interacting self-propelled particles. To predict the collective dynamics the theory…
We investigate the percolation properties of a two-state (occupied - empty) cellular automaton, where at each time step a cluster of occupied sites is removed and the same number of randomly chosen empty sites are occupied again. We find a finite region of critical behavior, formation of synchronized stripes, additional phase transitions, as well as violation of the usual finite-size scaling and hyperscaling relations, phenomena that are very different from conventional percolation systems. We explain the mechanisms behind all these phenomena using computer simulations and analytic arguments.
We study the effects of time-varying environmental noise on nonequilibrium phase transitions in spreading and growth processes. Using the examples of the logistic evolution equation as well as the contact process, we show that such temporal disorder gives rise to a distinct type of critical points at which the effective noise amplitude diverges on long time scales. This leads to enormous density fluctuations characterized by an infinitely broad probability distribution at criticality. We develop a real-time renormalization-group theory that provides a general framework for the effects of tempo…
Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and Kawasaki-type spin-exchange kinetics at infinite temperature T are investigated here in one dimension from the point of view of phase transition and critical behaviour. Branching annihilating random walks with an even number of offspring (on the part of the ferromagnetic domain boundaries), is a decisive process in forming the steady state of the system for a range of parameters, in the family of models considered. A wide variety of quantities characterize the critical behaviour of the…
Lecture notes for LES HOUCHES 2002 SUMMER SCHOOL - SESSION LXXVII on SLOW RELAXATIONS AND NONEQUILIBRIUM DYNAMICS IN CONDENSED MATTER; Les Houches: July 1-26, 2002
We comment on some recent, yet unpublished results concerning instabilities in complex systems and their applications. In particular, we briefly describe main observations during extensive computer simulations of two lattice nonequilibrium models. One exhibits robust and efficient processes of pattern recognition under synaptic coherent activity; the second example exhibits interesting critical behavior and simulates nucleation and spinodal decomposition processes in driven fluids.
We use analytic theory and computer simulation to study patterns formed during the growth of two-component assemblies in 2D and 3D. We show that these patterns undergo a nonequilibrium phase transition, at a particular growth rate, between mixed and demixed arrangements of component types. This finding suggests that principles of nonequilibrium statistical mechanics can be used to predict the outcome of multicomponent self-assembly, and suggests an experimental route to the self-assembly of multicomponent structures of a qualitatively defined nature.
In stationary nonequilibrium states coupling between hydrodynamic modes causes thermal fluctuations to become long ranged inducing nonequilibrium Casimir pressures. Here we consider nonequilibrium Casimir pressures induced in liquids by a velocity gradient. Specifically, we have obtained explicit expressions for the magnitude of the shear-induced pressure enhancements in a liquid layer between two horizontal plates that complete and correct results previously presented in the literature. In contrast to nonequilibrium Casimir pressures induced by a temperature or concentration gradient, we find…
The main subject of this thesis rests on the study ---at different levels of description--- of instabilities in systems which are driven, i.e., maintained far from equilibrium by an external forcing. We focus here on two main classes, namely, driven--diffusive fluids and driven granular gases. A particular driven-diffusive lattice model, prototype for nonequilibrium phase transitions, is investigated. A well-known disadvantage of lattice models is that, when they are compared directly with experiment, often do not account for important features of the corresponding nonequilibrium phase diagram…
The effects of locally broken spin symmetry are investigated in one dimensional nonequilibrium kinetic Ising systems via computer simulations and cluster mean field calculations. Besides a line of directed percolation transitions, a line of transitions belonging to N-component, two-offspring branching annihilating random-walk class (N-BARW2) is revealed in the phase diagram at zero branching rate. In this way a spin model for N-BARW2 transitions is proposed for the first time.
We study the effects of quenched extended impurities on nonequilibrium phase transitions in the directed percolation universality class. We show that these impurities have a dramatic effect: they completely destroy the sharp phase transition by smearing. This is caused by rare strongly coupled spatial regions which can undergo the phase transition independently from the bulk system. We use extremal statistics to determine the stationary state as well as the dynamics in the tail of the smeared transition, and we illustrate the results by computer simulations.
Boundary-induced phase transitions are one of the surprising phenomena appearing in nonequilibrium systems. These transitions have been found in driven systems, especially the asymmetric simple exclusion process. However, so far no direct observations of this phenomenon in real systems exists. Here we present evidence for the appearance of such a nonequilibrium phase transition in traffic flow occurring on highways in the vicinity of on- and off-ramps. Measurements on a German motorway close to Cologne show a first-order nonequilibrium phase transition between a free-flow phase and a congested…
We propose a mean field theory for interfaces growing according to the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. The mean field equations are formulated in terms of densities at different heights, taking surface tension and the influence of the nonlinear term in the KPZ equation into account. Although spatial correlations are neglected, the mean field equations still reflect the spatial dimensionality of the system. In the special case of Edwards-Wilkinson growth,our mean field theory correctly reproduces all features. In the presence of a nonlinear term one observes a crossover to…
Most computer simulations of molecular dynamics take place under equilibrium conditions--in a closed, isolated system, or perhaps one held at constant temperature or pressure. Sometimes, extra tensions, shears, or temperature gradients are introduced to those simulations to probe one type of nonequilibrium response to external forces. Catalysts and molecular motors, however, function based on the nonequilibrium dynamics induced by a chemical reaction's thermodynamic driving force. In this scenario, simulations require chemostats capable of preserving the chemical concentrations of the nonequil…
Experimental simulation of non-equilibrium quantum piston on a programmable photonic quantum computer
KTH Royal Institute of Technology（皇家理工学院）；Single Quantum B.V.（Single Quantum有限公司）；RISE Research Institutes of Sweden（瑞典RISE研究院）；Huazhong University of Science and Technology（华中科技大学）
We use extensive computer simulations to probe local thermodynamic equilibrium (LTE) in a quintessential model fluid, the two-dimensional hard-disks system. We show that macroscopic LTE is a property much stronger than previously anticipated, even in the presence of important finite size effects, revealing a remarkable bulk-boundary decoupling phenomenon in fluids out of equilibrium. This allows us to measure the fluid's equation of state in simulations far from equilibrium, with an excellent accuracy comparable to the best equilibrium simulations. Subtle corrections to LTE are found in the fl…
Dense particle packings acquire rigidity through a nonequilibrium jamming transition commonly observed in materials from emulsions to sandpiles. We describe athermal packings and their observed geometric phase transitions using fully equilibrium statistical mechanics and develop a microscopic many-body mean-field theory of the jamming transition for soft repulsive spherical particles. We derive analytically some of the scaling laws and exponents characterizing the transition and obtain predictions for microscopic correlation functions of jammed states that are amenable to experimental verifica…
The small wavenumber $k$ behavior of the structure factor $S(k)$ of overcompressed amorphous hard-sphere configurations was previously studied for a wide range of densities up to the maximally random jammed state, which can be viewed as a prototypical glassy state [A. Hopkins, F. H. Stillinger and S. Torquato, Phys. Rev. E, 86, 021505 (2012)]. It was found that a precursor to the glassy jammed state was evident long before the jamming density was reached as measured by a growing nonequilibrium length scale extracted from the volume integral of the direct correlation function $c(r)$, which beco…
Emergent symmetry is one of the characteristic phenomena in deconfined quantum critical point (DQCP). As its nonequilibrium generalization, the dual dynamic scaling was recently discovered in the nonequilibrium imaginary-time relaxation dynamics in the DQCP of the $J$-$Q_3$ model. In this work, we study the nonequilibrium imaginary-time relaxation dynamics in the $J$-$Q_2$ model, which also hosts a DQCP belonging to the same equilibrium universality class. We not only verify the universality of the dual dynamic scaling at the critical point, but also investigate the breakdown and the vestige o…
Recent works unraveled an intriguing finite-time dynamical phase transition in the thermal relaxation of the mean field Curie-Weiss model. The phase transition reflects a sudden switch in the dynamics. Its existence in systems with a finite range of interaction, however, remained unclear. Here we demonstrate the dynamical phase transition for nearest-neighbor Ising systems on the square and Bethe lattices through extensive computer simulations and by analytical results. Combining large-deviation techniques and Bethe-Guggenheim theory we prove the existence of the dynamical phase transition for…
This is our current research perspective on models providing insight into statistical mechanics. It is necessarily personal, emphasizing our own interest in simulation as it developed from the National Laboratories' work to the worldwide explosion of computation of today. We contrast the past and present in atomistic simulations, emphasizing those simple models which best achieve reproducibility and promote understanding. Few-body models with pair forces have led to today's "realistic" simulations with billions of atoms and molecules. Rapid advances in computer technology have led to change. T…
We report on the computer study of a lattice system that relaxes from a metastable state. Under appropriate nonequilibrium randomness, relaxation occurs by avalanches, i.e., the model evolution is discontinuous and displays many scales in a way that closely resembles the relaxation in a large number of complex systems in nature. Such apparent scale invariance simply results in the model from summing over many exponential relaxations, each with a scale which is determined by the curvature of the domain wall at which the avalanche originates. The claim that scale invariance in a nonequilibrium s…
A simple deterministic and time reversal invariant type of thermostat is proposed to be used for computer simulations of classical systems. It acts on collisions with the walls of the container exclusively. It maps the incoming and outgoing velocity of an impinging particle onto each other uniquely, in a way that satisfies a detailed balance condition with respect to the (local) wall temperature. It is fast to implement on a computer, leads to rapid equilibration or approach to a stationary nonequilibrium state and it effects the physical properties of the system in a narrow boundary layer onl…
Quantum computers are a leading platform for the simulation of many-body physics. This task has been recently facilitated by the possibility to program directly the time-dependent pulses sent to the computer. Here, we use this feature to simulate quantum lattice models with long-range hopping. Our approach is based on an exact mapping between periodically driven quantum systems and one-dimensional lattices in the synthetic Floquet direction. By engineering a periodic drive with a power-law spectrum, we simulate a lattice with long-range hopping, whose decay exponent is freely tunable. We propo…
In the preceding paper (cond-mat/0405252), we have conjectured that the main transport properties of a dilute gas of inelastic hard spheres (IHS) can be satisfactorily captured by an equivalent gas of elastic hard spheres (EHS), provided that the latter are under the action of an effective drag force and their collision rate is reduced by a factor $(1+α)/2$ (where $α$ is the constant coefficient of normal restitution). In this paper we test the above expectation in a paradigmatic nonequilibrium state, namely the simple or uniform shear flow, by performing Monte Carlo computer simulations of th…
Digital quantum computers are potentially an ideal platform for simulating open quantum many-body systems beyond the digital classical computers. Many studies have focused on obtaining the ground state by simulating time dynamics or variational approaches of closed quantum systems. However, dynamics of open quantum systems has not been given much attention with a reason being their non-unitary dynamics not natural to simulate on a set of unitary gate operations in quantum computing. Here we study prototypical models in open quantum systems with Trotterisations for the modified stochastic Schr{…
Interfaces involving coexisting phases in condensed matter are essential in various examples of soft matter phenomena such as wetting, nucleation, morphology, phase separation kinetics, membranes, phase coexistence in nanomaterials, etc. Most analytical theories available use concepts derived from mean field theory which does not describe adequately these systems. Satisfactory numerical simulations for interfaces at atomistic to mesoscopic scales remains a challenge. In the present work, the interfacial tension between mixtures of organic solvents and water is obtained from mesoscopic computer…
Different computational techniques in combination with molecular dynamics computer simulation are used to to determine the wall-liquid and the wall-crystal interfacial free energies of a modified Lennard-Jones (LJ) system in contact with a solid wall. Two different kinds of solid walls are considered: a flat structureless wall and a structured wall consisting of an ideal crystal with the particles rigidly attached to fcc lattice sites. Interfacial free energies are determined by a thermodynamic integration scheme, the anisotropy of the pressure tensor, the non-equilibrium work method based on …
