Nonequilibrium Phase Transition Research Articles

Criticality and entanglement in nonunitary quantum circuits and tensor networks of noninteracting fermions

Entanglement dynamics in nonunitary quantum systems have been found to exhibit novel nonequilibrium quantum phase transitions and have attracted tremendous attention with connections to various aspects of quantum information theory. This work establishes, for systems of noninteracting fermions, an exact three-way correspondence between (i) nonunitary (as well as unitary) quantum circuits dynamics in $d$ spatial dimensions; (ii) ($d$+1)-dimensional Gaussian tensor networks, and (iii) fermion systems in ($d$+1) spatial dimensions subject to unitary evolution with static Hamiltonians. Through this correspondence, $d$-dimensional random quantum circuits are connected with the classic subject area of Anderson localization in ($d$+1) spatial dimensions and consequently follow the ``tenfold way'' Altland-Zirnbauer classification. Selected examples of quantum circuits exhibiting entanglement phases and criticalities are used to illustrate these general principles.

Study of nonequilibrium phase transitions mechanisms in exclusive network and node model of heterogeneous assignment based on real experimental data of KIF3AC and KIF3CC motors

Study of nonequilibrium phase transitions mechanisms in exclusive network and node model of heterogeneous assignment based on real experimental data of KIF3AC and KIF3CC motors

Noise-induced sustainability of cooperation in Prisoner's Dilemma game

Based on the concept of stochastic Prisoner’s Dilemma (SPD) game in experimental economics proposed by Bereby-Meyer and Roth (Am Econ Rev 96 (2006) 1029–1042) (see also H. Kunreuther et al., Judgm. Decis. Mak. 4 (5) (2009) 363–384), the dynamical properties of the SPD game is investigated in this paper. For the non-repeated SPD game, we can see that the increase of noise intensity will not only lead to loss of the stochastic stability of the boundary state corresponding to defection but also the non-equilibrium phase transition of the quasi-stationary distribution of the system, and that the fixation probability of cooperation will increase with the increase of noise intensity. However, for the stochastic TFT-AllD game, the increase of noise intensity will lead to the loss of the stochastic stability of the two boundaries corresponding to cooperation and defection respectively, but will not lead to the non-equilibrium phase transition of the quasi-stationary distribution of the system. Moreover, as a special case of the stochastic TFT-AllD game (i.e., (m−1)(b−c)=2c), we show that the fixation probability of TFT will increase (decrease) with the increase of noise intensity if the initial frequency of TFT is less (or larger) than 1/2.

Nonequilibrium Lattice Dynamics in Photoexcited 2D Perovskites.

Interplay between structural and photophysical properties of metal halide perovskites is critical to their utility in optoelectronics, but there is limited understanding of lattice response upon photoexcitation. Here, 2D perovskites butylammonium lead iodide, (BA)2 PbI4 , and phenethylammonium lead iodide, (PEA)2 PbI4 , are investigated using ultrafast transient X-ray diffraction as a function of optical excitation fluence to discern structural dynamics. Both powder X-ray diffraction and time-resolved photoluminescence linewidths narrow over 1 ns following optical excitation for the fluence range studied, concurrent with slight redshifting of the optical bandgaps. These observations are attributed to transient relaxation and ordering of distorted lead iodide octahedra stimulated mainly by electron-hole pair creation. The c axis expands up to 0.37% over hundreds of picoseconds; reflections sampling the a and b axes undergo one tenth of this expansion with the same timescale. Post-photoexcitation appearance of the (110) reflection in (BA)2 PbI4 would suggest a transient phase transition,however, through new single-crystal XRD, reflections are found that violate glide plane conditions in the reported Pbca structure. The static structure space group is reassigned as P21 21 21 . With this, a nonequilibrium phase transition is ruled out. These findings offer increased understanding of remarkable lattice response in 2D perovskites upon excitation.

Contact process with simultaneous spatial and temporal disorder

We study the absorbing-state phase transition in the one-dimensional contact process under the combined influence of spatial and temporal random disorders. We focus on situations in which the spatial and temporal disorders decouple. Couched in the language of epidemic spreading, this means that some spatial regions are, at all times, more favorable than others for infections, and some time periods are more favorable than others independent of spatial location. We employ a generalized Harris criterion to discuss the stability of the directed percolation universality class against such disorder. We then perform large-scale Monte Carlo simulations to analyze the critical behavior in detail. We also discuss how the Griffiths singularities that accompany the nonequilibrium phase transition are affected by the simultaneous presence of both disorders.

Engineering Floquet dynamical quantum phase transitions

Floquet dynamical quantum phase transitions (FDQPTs) are signified by recurrent nonanalytic behaviors of observables in time. In this work, we introduce a quench-free and generic approach to engineer and control FDQPTs for both pure and mixed Floquet states. By applying time-periodic modulations with two commensurate driving frequencies to a general class of spin chain model, we find multiple FDQPTs within each driving period. The nonanalytic cusps of return probability form sublattice structures in time domain. Notably, the number and time-locations of these cusps can be flexibly controlled by tuning the Hamiltonian parameter and the higher frequency of the drive. We further employ the dynamical topological order parameter (DTOP), which shows a quantized jump whenever a DQPT happens, to identify the topological feature of FDQPTs. Our findings reveal the advantage of engineering nonequilibrium phase transitions with multi-frequency driving fields.

Nonequilibrium phase transitions in competitive markets caused by network effects

Network effects are the added value derived solely from the popularity of a product in an economic market. Using agent-based models inspired by statistical physics, we propose a minimal theory of a competitive market for (nearly) indistinguishable goods with demand-side network effects, sold by statistically identical sellers. With weak network effects, the model reproduces conventional microeconomics: there is a statistical steady state of (nearly) perfect competition. Increasing network effects, we find a phase transition to a robust nonequilibrium phase driven by the spontaneous formation and collapse of fads in the market. When sellers update prices sufficiently quickly, an emergent monopolist can capture the market and undercut competition, leading to a symmetry- and ergodicity-breaking transition. The nonequilibrium phase simultaneously exhibits three empirically established phenomena not contained in the standard theory of competitive markets: spontaneous price fluctuations, persistent seller profits, and broad distributions of firm market shares.

Effects of lattice dilution on the nonequilibrium phase transition in the stochastic susceptible-infectious-recovered model.

We investigate how site dilution, as would be introduced by immunization, affects the properties of the active-to-absorbing nonequilibrium phase transition in the paradigmatic susceptible-infectious-recovered (SIR) model on regular cubic lattices. According to the Harris criterion, the critical behavior of the SIR model, which is governed by the universal scaling exponents of the dynamic isotropic percolation (DyIP) universality class, should remain unaltered after introducing impurities. However, when the SIR reactions are simulated for immobile agents on two- and three-dimensional lattices subject to quenched disorder, we observe a wide crossover region characterized by varying effective exponents. Only after a sufficient increase of the lattice sizes does it become clear that the SIR system must transition from that crossover regime before the effective critical exponents asymptotically assume the expected DyIP values. We attribute the appearance of this exceedingly long crossover to a time lag in a complete recovery of small disconnected clusters of susceptible sites, which are apt to be generated when the system is prepared with Poisson-distributed quenched disorder. Finally, we demonstrate that this transient region becomes drastically diminished when we significantly increase the value of the recovery rate or enable diffusive agent mobility through short-range hopping.

Diverging current fluctuations in critical Kerr resonators

The parametrically pumped Kerr model describes a driven-dissipative nonlinear cavity, whose nonequilibrium phase diagram features both continuous and discontinuous quantum phase transitions. We consider the consequences of these critical phenomena for the fluctuations of the photocurrent obtained via continuous weak measurements on the cavity. Considering both direct photodetection and homodyne detection schemes, we find that the current fluctuations diverge exponentially at the discontinuous phase transition. However, we find strikingly different current fluctuations for these two detection schemes near the continuous transition, a behaviour which is explained by the complementary information revealed by measurements in different bases. To obtain these results, we develop formulas to efficiently compute the diffusion coefficient -- which characterises the long-time current fluctuations -- directly from the quantum master equation, thus connecting the formalisms of full counting statistics and stochastic quantum trajectories. Our findings highlight the rich features of current fluctuations near nonequilibrium phase transitions in quantum-optical systems.

Dynamical phase transitions in annihilating random walks with pair deposition

Exact results are presented for conditioned dynamics in a system of interacting random walks in one dimension that annihilate immediately when two particles meet on the same site and where pairs of particles are deposited randomly on neighbouring sites. For an atypical hopping activity one finds dynamical nonequilibrium phase transitions analogous to the zero-temperature equilibrium phase transitions that appear in the spin-1/2 quantum XY spin chain in a transverse magnetic field. Along the critical line the approach of the particle density to its stationary value is algebraic with an unexpected mean field exponent. The time-dependent local stationary density correlations are universal with dynamical exponent z = 1. Inside the disordered phase spatially oscillating correlations appear below the typical activity.

Transport and nonequilibrium phase transitions in polygonal urn models.

We study the deterministic dynamics of N point particles moving at a constant speed in a 2D table made of two polygonal urns connected by an active rectangular channel, which applies a feedback control on the particles, inverting the horizontal component of their velocities when their number in the channel exceeds a fixed threshold. Such a bounce-back mechanism is non-dissipative: it preserves volumes in phase space. An additional passive channel closes the billiard table forming a circuit in which a stationary current may flow. Under specific constraints on the geometry and on the initial conditions, the large N limit allows nonequilibrium phase transitions between homogeneous and inhomogeneous phases. The role of ergodicity in making a probabilistic theory applicable is discussed for both rational and irrational urns. The theoretical predictions are compared with the numerical simulation results. Connections with the dynamics of feedback-controlled biological systems are highlighted.

Role of inflexible minorities in the evolution of alcohol consumption

In this work we study a simple contagion model for drinking behavior evolution, but including the presence of inflexible or zealot agents, i.e. individuals that never change their behavior (never drink or always drink a lot). We analyze the impact of such special agents in the evolution of drinking behavior in the population. Our analytical and numerical results indicate that the presence of only one class of inflexible agents destroys one of the two possible absorbing phases that are observed in the model without such inflexibles. In the presence of the both kinds of inflexible agents simultaneously, there are no absorbing states anymore. Since absorbing states are collective macroscopic states with the presence of only one kind of individuals in the population, we argue that the inclusion of inflexible agents in the population makes the model more realistic. Furthermore, the presence of inflexible agents are similar to the introduction of quenched disorder in the model, and here we observe the suppression of a nonequilibrium phase transition to absorbing states, which had not been reported before.

A quantum model of lasing without inversion

Starting from a quantum description of multiple Λ-type three-level atoms driven with a coherent microwave field and incoherent optical pumping, we derive a microscopic model of lasing from which we move towards a consistent macroscopic picture. Our analysis applies across the range of system sizes from nanolasers to the thermodynamic limit of conventional lasing. We explore the necessary conditions to achieve lasing without inversion in certain regimes by calculating the non-equilibrium steady state solutions of the model at, and between, its microscopic and macroscopic limits. For the macroscopic picture, we use mean-field theory to present a thorough analysis of the lasing phase transition. In the microscopic case, we exploit the underlying permutation symmetry of the density matrix to calculate exact solutions for N three-level systems. This allows us to show that the steady state solutions approach the thermodynamic limit as N increases, restoring the sharp non-equilibrium phase transition in this limit. We demonstrate how the lasing phase transition and degree of population inversion can be adjusted by simply varying the phase of the coherent driving field. The high level of quantum control presented by this microscopic model and the framework outlined here have applications to further understanding and developing nanophotonic technology.

From predicting to learning dissipation from pair correlations of active liquids.

Active systems, which are driven out of equilibrium by local non-conservative forces, can adopt unique behaviors and configurations. An important challenge in the design of novel materials, which utilize such properties, is to precisely connect the static structure of active systems to the dissipation of energy induced by the local driving. Here, we use tools from liquid-state theories and machine learning to take on this challenge. We first analytically demonstrate for an isotropic active matter system that dissipation and pair correlations are closely related when driving forces behave like an active temperature. We then extend a nonequilibrium mean-field framework for predicting these pair correlations, which unlike most existing approaches is applicable even for strongly interacting particles and far from equilibrium, to predicting dissipation in these systems. Based on this theory, we reveal a robust analytic relation between dissipation and structure, which holds even as the system approaches a nonequilibrium phase transition. Finally, we construct a neural network that maps static configurations of particles to their dissipation rate without any prior knowledge of the underlying dynamics. Our results open novel perspectives on the interplay between dissipation and organization out of equilibrium.

Net-proton number cumulant ratios as a function of beam energy from an expanding nonequilibrium chiral fluid

The beam energy scan program at RHIC provides data on net-proton number fluctuations with the goal to detect the QCD critical end point and first-order phase transition. Interpreting these experimental signals requires a vital understanding of the interplay of critical phenomena and the nonequilibrium dynamics of the rapidly expanding fireball. We study these aspects with a fluid dynamic expansion coupled to the explicit propagation of the chiral order parameter sigma via a Langevin equation. Assuming a sigma-proton coupling through an effective proton mass, we relate cumulants of the order parameter and the net-proton number at freeze-out and obtain observable cumulant ratios as a function of beam energy. We emphasize the role of the nonequilibrium first-order phase transition where a mixed phase with gradual freeze-out can significantly alter the cumulants. We find that the presence of a critical end point is clearly visible in the cumulant ratios for a relatively wide range of center-of-mass energies.

Kibble-Zurek mechanism for nonequilibrium phase transitions in driven systems with quenched disorder

We show that the Kibble-Zurek mechanism applies to nonequilibrium phase transitions found in driven assemblies of superconducting vortices and colloids moving over quenched disorder where a transition occurs from a plastic disordered flowing state to a moving anisotropic crystal. We measure the density of topological defects as a function of quench rate through the nonequilibrium phase transition, and find that on the ordered side of the transition, the topological defect density ρd scales as a power law, {rho }_{{{{{{{{rm{d}}}}}}}}}propto 1/{t}_{{{{{{{{rm{q}}}}}}}}}^{beta }, where tq is the quench time duration, consistent with the Kibble-Zurek mechanism. We show that scaling with the same exponent holds for varied strengths of quenched disorder and that the exponents fall in the directed percolation universality class. Our results suggest that the Kibble-Zurek mechanism can be applied to the broader class of systems that exhibit absorbing phase transitions.

Nonequilibrium phase transitions of a nematic liquid crystal under ac field-driven electroconvection.

We report on phase transitions between isotropic and nematic liquid crystal phases in nonequilibrium systems (NESs). ac field-driven electroconvection (EC) provides an NES, which can be well controlled by the voltage V and frequency f; it arises electrohydrodynamically at a threshold voltage V_{c}. In continuous cooling and heating processes with various rates R, the critical temperature T_{c} was determined at a critical time t_{c} for phase transitions. Moreover, the morphological and dynamical features in the phase transitions were examined using an electro-optical image processing method. In comparison with an equilibrium system (V=0), two typical turbulent ECs (i.e., NESs), which are called dynamic scattering mode 1 (DSM1 for V>V_{c}) and DSM2 (for V≫V_{c}), were examined to understand the nonequilibrium phase transitions. In particular, our results show that in high voltage-induced turbulence (i.e., DSM2), T_{c} can be determined effectively without considering R; this provides a possibility for a material technology application in nonequilibrium-based circumstances.

Transfer learning of phase transitions in percolation and directed percolation.

The latest advances of statistical physics have shown remarkable performance of machine learning in identifying phase transitions. In this paper, we apply domain adversarial neural network (DANN) based on transfer learning to studying nonequilibrium and equilibrium phase transition models, which are percolation model and directed percolation (DP) model, respectively. With the DANN, only a small fraction of input configurations (two-dimensional images) needs to be labeled, which is automatically chosen, to capture the critical point. To learn the DP model, the method is refined by an iterative procedure in determining the critical point, which is a prerequisite for the data collapse in calculating the critical exponent ν_{⊥}. We then apply the DANN to a two-dimensional site percolation with configurations filtered to include only the largest cluster which may contain the information related to the order parameter. The DANN learning of both models yields reliable results which are comparable to the ones from Monte Carlo simulations. Our study also shows that the DANN can achieve quite high accuracy at much lower cost, compared to the supervised learning.

Rare events and disorder control the brittle yielding of well-annealed amorphous solids

We use atomistic computer simulations to provide a microscopic description of the brittle failure of amorphous materials, and we assess the role of rare events and quenched disorder. We argue that brittle yielding originates at rare soft regions, similarly to Griffiths effects in disordered systems. We numerically demonstrate how localized plastic events in such soft regions trigger macroscopic failure via the propagation of a shear band. This physical picture, which no longer holds in poorly annealed ductile materials, allows us to discuss the role of finite size effects in brittle yielding and reinforces the similarities between yielding and other disorder-controlled nonequilibrium phase transitions.

Spontaneous condensation of carbon dioxide in flue gas at supersonic state

A cleaning method of removing CO2 from flue gas by supersonic flow is investigated. A condensation flow model is developed based on the classical droplet nucleation and growth theory. The non-equilibrium phase transition in supersonic flow is predicted by adding transport equations. The effects of converging-diverging nozzle, inlet subcooling and gas composition on CO2 spontaneous condensation in flue gas are studied. The results show that the nozzle with Witoszynski curve is the first to nucleate, at x = 0.121 m. Without considering the backpressure, the shrinkage ratio and diverging angle only affect the flow behavior behind the throat. With the increase of shrinkage ratio or diverging angle, the liquid mass fraction increases from 0.062 to 0.085 and 0.056 to 0.089 respectively, but there are hazards such as increased pressure loss and reduced nozzle flow rate. The diverging length has no significant effect on the flow behavior but the increase of length can prolong the droplet growth time. The higher inlet subcooling not only makes the supersonic flow reach the critical state in advance, from x = 0.121 m to x = 0.111 m, but also significantly improves the droplet growth rate, from 0.649 m/s to 0.854 m/s. The increase of CO2 concentration greatly enhances the mass and heat transfer process.