Nonequilibrium Phase Transition Research Articles

Adiabatic-impulse approximation in the non-Hermitian Landau-Zener model

In the non-Hermitian Landau-Zener models, we investigate the dynamical transition both in parity-time symmetric and symmetry-broken regimes. Taking into account the complex nature of the energy of the non-Hermitian systems, the absolute value of the gap was used to determine the relaxation rate of the system. To show the dynamics of the phase transitions, the relative population is used to estimate the topological defect density in nonequilibrium phase transitions, rather than the excitations in the corresponding Hermitian systems. The result shows that the adiabatic-impulse approximation, which is fundamental to the Kibble-Zurek mechanism, may be adapted to the parity-time symmetric non-Hermitian Landau-Zener models to examine the dynamics near the critical point. The most basic non-Hermitian two-level models with an exact solution exhibiting the Kibble-Zurek mechanism are presented. It would be interesting to extend this scenario to quantum many-body models, such as the quantum phase transition in the Ising model.

Electric-field driven nonequilibrium phase transitions in AdS/CFT

We study phase transitions and critical phenomena in nonequilibrium steady states controlled by an electric field. We employ the D3/D7 model in the presence of a charge density and electric field at finite temperatures. The system undergoes the first-order and the second-order phase transitions under the variation of the electric field in the presence of dissipation. We numerically find that the critical exponents which we define for the nonequilibrium phase transition in this model take the mean-field values.

Analysis of the dehydration performance in a two-phase variable-section gas wave oscillation tube

The two-phase gas wave oscillation tube (TPGWOT) is subjected to several problems in the application of moisture-containing gas dehydration (e.g., less accurate prediction of the results of phase transition in the tube, and strong interference effect of reverse compression waves in the tube). The predicted phase transition results approach the experimental values by coupling the CPA real gas model and the non-equilibrium phase transition model. The performance of the proposed variable-section TPGWOT is investigated using numerical and experimental methods, and the following results are achieved. The variable-section structure is capable of optimizing the wave system in the tube, as manifested by the ability to strengthen the reflected expansion wave and weaken the reverse compression waves. As a result, the maximum condensation rate of condensate droplets is increased by 2 % to 5 %, and the proportion of evaporation capacity of condensate droplets is reduced by 3 % to 7 %. The variable-section structure is capable of enhancing the performance of the GWOTs, as manifested by the ability to improve the gas temperature drop (ΔT) of nearly 20 % and increase the dehydration rate by 2.6 % to 5 %. This study is no longer limited to optimizing the wave system in the tube by changing the ports at both ends of TPGWOTs, and it provides a favorable reference for other wave rotor application research.

Generic two-phase coexistence in a type-2 Schloegl model for autocatalysis on a square lattice: Analysis via heterogeneous master equations.

Schloegl's second model (also known as the quadratic contact process) on a square lattice involves spontaneous annihilation of particles at lattice sites at rate p, and their autocatalytic creation at unoccupied sites with n≥2 occupied neighbors at rate k_{n}. Kinetic Monte Carlo (KMC) simulation reveals that these models exhibit a nonequilibrium discontinuous phase transition with generic two-phase coexistence: the p value for equistability of coexisting populated and vacuum states, p_{eq}(S), depends on the orientation or slope, S, of a planar interface separating those phases. The vacuum state displaces the populated state for p>p_{eq}(S), and the opposite applies for p<p_{eq}(S) for 0<S<∞. The special "combinatorial" rate choice k_{n}=n(n-1)/12 facilitates an appealing simplification of the exact master equations for the evolution of spatially heterogeneous states in the model, which aids analytic investigation of these equations via hierarchical truncation approximations. Truncation produces coupled sets of lattice differential equations which can describe orientation-dependent interface propagation and equistability. The pair approximation predicts that p_{eq}(max)=p_{eq}(S=1)=0.09645 and p_{eq}(min)=p_{eq}(S→∞)=0.08827, values deviating less than 15% from KMC predictions. In the pair approximation, a perfect vertical interface is stationary for all p<p_{eq}(S=∞)=0.08907, a value exceeding p_{eq}(S→∞). One can regard an interface for large S→∞ as a vertical interface decorated with isolated kinks. For p<p_{eq}(S=∞), the kink can move in either direction along this otherwise stationary interface depending upon p, but for p=p_{eq}(min) the kink is also stationary.

Controllable Floquet edge modes in a multifrequency driving system

A driven quantum system was recently studied in the context of nonequilibrium phase transitions and their responses. In particular, for a periodically driven system, its dynamics are described in terms of the multidimensional Floquet lattice with a lattice size depending on the number of driving frequencies and their rational or irrational ratio. So far, for a multifrequency driving system, the energy pumping between the sources of frequencies has been widely discussed as a signature of topologically nontrivial Floquet bands. However, the unique edge modes emerging in the Floquet lattice have not been explored yet. Here, we discuss how the edge modes in the Floquet lattice are controlled and result in the localization at particular frequencies, when multiple frequencies are present and their magnitudes are commensurate values. First, we construct the minimal model to exemplify our argument, focusing on a two-level system with two driving frequencies. For the strong frequency limit, one can describe the system as a quasi-one-dimensional Floquet lattice where the effective hopping between the neighboring sites depends on the relative magnitudes of the potential for two frequency modes. With multiple driving modes, nontrivial Floquet lattice boundaries always exist from controlling the frequencies, and this gives rise to states that are mostly localized at such Floquet lattice boundaries, i.e., particular frequencies. We suggest the time-dependent Creutz ladder model as a realization of our theoretical Hamiltonian and show the emergence of controllable Floquet edge modes.

Tuning nonequilibrium phase transitions with inertia.

In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation-dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. This density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions.

Heterogeneous Nucleation in Finite-Size Adaptive Dynamical Networks

Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive dynamical networks feature a connectivity structure that changes over time, coevolving with the nodes' dynamical state. In this Letter, we show the emergence of two distinct first-order nonequilibrium phase transitions in a finite-size adaptive network of heterogeneous phase oscillators. Depending on the nature of defects in the internal frequency distribution, we observe either an abrupt single-step transition to full synchronization or a more gradual multistep transition. This observation has a striking resemblance to heterogeneous nucleation. We develop a mean-field approach to study the interplay between adaptivity and nodal heterogeneity and describe the dynamics of multicluster states and their role in determining the character of the phase transition. Our work provides a theoretical framework for studying the interplay between adaptivity and nodal heterogeneity.

Dynamical demographic phases explain how population growth and mutation control the evolutionary impact of bottlenecks

Population bottlenecks involve steep declines in population size as well as changes to composition; they are an important aspect of contemporary evolution, and have been implicated across a wide range of taxa. However, the precise mechanisms by which such bottlenecks translate into altered evolutionary outcomes remain poorly understood. Here, we demonstrate how the fixation probabilities associated with such outcomes can depend nontrivially on the rates of post-bottleneck growth and mutation as a population recovers. Notably, increased population growth can invert naive expectations, driving fixation to attractors that are different to those from within whose basin the bottleneck constrained the population, initially, despite more rapidly suppressing the intrinsic fluctuations that are ostensibly required to switch between basins of attraction. Such behavior moreover only occurs beneath a critical threshold of mutation, which is itself a function of the rate of population growth. We explain our results in terms of statistically distinct regimes of demographic behavior, drawing parallels with the notion of nonequilibrium phase transitions. These regimes are delimited by sharp transitions in time, as a population grows, and ultimately result from a time-dependent antagonism between mutation and the stochastically induced effects of frequency-dependent birth. Recast in this context, the rates of population growth and mutation are seen to control long-term fixation probabilities by altering the duration and character of post-bottleneck dynamical demographic regimes.

Dynamical quantum phase transitions in a spinor Bose-Einstein condensate and criticality enhanced quantum sensing

Quantum phase transitions universally exist in the ground and excited states of quantum many-body systems, and they have a close relationship with the nonequilibrium dynamical phase transitions, which however are challenging to identify. In the system of spin-1 Bose-Einstein condensates, though dynamical phase transitions with correspondence to equilibrium phase transitions in the ground state and uppermost excited state have been probed, those taking place in intermediate excited states remain untouched in experiments thus far. Here we unravel that both the ground- and excited-state quantum phase transitions in spinor condensates can be diagnosed with dynamical phase transitions. A connection between equilibrium phase transitions and nonequilibrium behaviors of the system is disclosed in terms of the quantum Fisher information. We also demonstrate that near the critical points parameter estimation beyond the standard quantum limit can be implemented. This work not only advances the exploration of excited-state quantum phase transitions via a scheme that can immediately be applied to a broad class of few-mode quantum systems, but also provides a new perspective on the relationship between quantum criticality and quantum enhanced sensing.

Ultrafast Energy Transfer Process in Confined Gold Nanospheres Revealed by Femtosecond X-ray Imaging and Diffraction.

Femtosecond laser pulses drive nonequilibrium phase transitions via reaction paths hidden in thermal equilibrium. This stimulates interest to understand photoinduced ultrafast melting processes, which remains incomplete due to challenges in resolving accompanied kinetics at the relevant space-time resolution. Here, by newly establishing a multiplexing femtosecond X-ray probe, we have successfully revealed ultrafast energy transfer processes in confined Au nanospheres. Real-time images of electron density distributions with the corresponding lattice structures elucidate that the energy transfer begins with subpicosecond melting at the specimen boundary earlier than the lattice thermalization, and proceeds by forming voids. Two temperature molecular dynamics simulations uncovered the presence of both heterogeneous melting with the melting front propagation from surface and grain boundaries and homogeneous melting with random melting seeds and nanoscale voids. Supported by experimental and theoretical results, we provide a comprehensive atomic-scale picture that accounts for the ultrafast laser-induced melting and evaporation kinetics.

Radicalization phenomena: Phase transitions, extinction processes and control of violent activities

In this work, we study a simple mathematical model to analyze the emergence and control of radicalization phenomena. The population consists of core and sensitive subpopulations, and their ways of life may be at least partially incompatible. In such a case, if a conflict exists, core agents act as inflexible individuals about the issue. On the other hand, the sensitive agents choose between two options: live peacefully with core population, or oppose it. This kind of modeling was recently considered by Galam and Javarone (2016) with constant pairwise couplings. Here, we consider the more general case with time-dependent transition rates, with the aim of study the impact of such time dependence on the critical behavior of the model. The analytical and numerical results show that the nonequilibrium active-absorbing phase transition can be suppressed in some cases, with the destruction of the absorbing phase where the radical agents disappear of the population in the stationary states.

Effect of Li element on shocking behavior of Fe-Li alloys

Understanding the effect of alloying elements on shock behaviors is significant for constitutive model of alloy materials at under dynamic high pressure. However, an in-depth understanding about the microscopic mechanism of alloying elements effect on plasticity and phase transition is still limited. In this work, applying non-equilibrium molecular dynamic (NEMD) simulations, shock-induced plasticity and phase transition of Fe-Li alloys was investigated in terms of the compositions of Li, crystallographic direction and shock velocity. The results show that yield stress (or phase change pressure) of Fe-Li alloy was reduced doping Li element, and the large internal stresses caused by concentration of Li element effectively activated the nucleation and multiplication of dislocation loops. But with the increase of Li composition, phase transition is inhibited for shock along [111] direction because of stress release caused by multiplication of dislocation. There is a strong dependence between these microscopic processes and the law of plastic wave propagation. Moreover, with the increase of Li composition, the diversity of phase transition variants was inhibited for shock along [110] direction due to the destruction of initial stress and potential energy uniformity.

Random process with a turbulent power spectrum

Random processes with large fluctuations are simulated by a system of nonlinear stochastic equations describing coupled nonequilibrium phase transitions. It is shown that under the action of white noise a critical state can arise, which is characterized by a turbulent spectrum and a scale-invariant probability density function. Under the action of a periodic force on a random process with a turbulent spectrum, a resonant response of scale-invariant functions arises. The lumped system is generalized to the spatially distributed case. To study the sustainability and stationarity of a random process, the principle of maximum entropy is used.

Efficient quantum information probes of nonequilibrium quantum criticality

Quantum information-based approaches, in particular the fidelity, have been flexible probes for phase boundaries of quantum matter. A major hurdle to a more widespread application of fidelity and other quantum information measures to strongly correlated quantum materials is the inaccessibility of the fidelity susceptibility to most state-of-the-art numerical methods. This is particularly apparent away from equilibrium where, at present, no general critical theory is available and many standard techniques fail. Motivated by the usefulness of quantum information-based measures we show that a widely accessible quantity, the single-particle affinity, is able to serve as a versatile instrument to identify phase transitions beyond Landau’s paradigm. We demonstrate that it not only is able to signal previously identified nonequilibrium phase transitions but also has the potential to detect hitherto unknown phases in models of quantum matter far from equilibrium.

Ultrafast Martensitic Phase Transition Driven by Intense Terahertz Pulses

We report on an ultrafast nonequilibrium phase transition with a strikingly long-lived martensitic anomaly driven by above-threshold single-cycle terahertz pulses with a peak field of more than 1 MV/cm. A nonthermal, terahertz-induced depletion of low-frequency conductivity in Nb 3 Sn indicates increased gap splitting of high-energy Γ 12 bands by removal of their degeneracies, which induces the martensitic phase above their equilibrium transition temperature. In contrast, optical pumping leads to a Γ 12 gap thermal melting. Such light-induced nonequilibrium martensitic phase exhibits a substantially enhanced critical temperature up to ∼100 K, i.e., more than twice the equilibrium temperature, and can be stabilized beyond technologically relevant, nanosecond time scales. Together with first-principle simulations, we identify a compelling terahertz tuning mechanism of structural order via Γ 12 phonons to achieve the ultrafast phase transition to a metastable electronic state out of equilibrium at high temperatures far exceeding those for equilibrium states.

Full quantum theory of nonequilibrium phonon condensation and phase transition

Fr\"olich condensation is a room-temperature nonequilibrium phenomenon which is expected to occur in many physical and biological systems. Though predicted theoretically a half century ago, the nature of such condensation remains elusive. In this Letter, we derive a full quantum theory of Fr\"ohlich condensation from the Wu-Austin Hamiltonian and present for the first time an analytical proof that a second-order phase transition induced by nonequilibrium and nonlinearity emerges in the large-$D$ limit with and without decorrelation approximation. This critical behavior cannot be witnessed if external sources are treated classically. We show that the phase transition is accompanied by large fluctuations in the statistical distribution of condensate phonons and that the Mandel-Q factor which characterizes fluctuations becomes negative in the limit of excessive external energy input. In contrast with the cold atom equilibrium BEC, the Fr\"ohlich condensate is a result of the nonequilibrium driving where the pump plays a role of setting the number of particles, and the medium plays a role of setting the temperature. Hence, BEC can either arise by reducing the medium temperature at fixed pump (equilibrium case), or by increasing the pump at fixed medium temperature (nonequilibrium case).

Microbial biofilms are shaped by the constant dialogue between biological and physical forces in the extracellular matrix.

Microbial biofilms are shaped by the constant dialogue between biological and physical forces in the extracellular matrix.

Quantum statistical theory for an exciton-polariton condensate: Fluctuations and coherence

A full quantum theory beyond the mean-field regime is developed for an exciton-polariton condensate, for a complete understanding of quantum fluctuations. We find an analytical solution for the polariton density matrix, showing the nonlinearity causing fast relaxation correlated with the pump so as to yield the quantum condensation above threshold. Increasing the pump intensity, a nonequilibrium phase transition towards the condensation of the lower polaritons emerges, with a statistics transiting from a thermal, through a super-Poissonian, and towards a nonclassical distribution; the latter two possess off-diagonal long-range order but the last one is beyond. The results signify the role of dark states for polariton fluctuations, and lead to a nonclassical counting statistics of emitted photons, which elaborates the role of the key parameters, e.g., pump, detuning, and temperature.

Nonclassical correlated optical multistability at low photon level for cavity electromagnetically induced transparency

We study the nonequilibrium dynamic behaviors in a driven-dissipative single-atom cavity electromagnetically induced transparency. The optical bistability and multistability beyond a Kerr nonlinearity are observed utilizing the optical Stark shift induced strong nonlinearity. We show that the nonequilibrium dynamical phase transition between bistability and multistability is highly tunable by the system parameters in a large parameter region. The first-order dissipative optical bistability (multistability) always corresponds to the photon-bunching quantum statistics, which indicates that the quantum fluctuations and correlations play important roles in nonequilibrium dynamics. Interestingly, bistability and multistability with photon-bunching quantum statistics occurring at extremely low steady-state cavity photon number are observed, even under a very strong cavity driven field. Furthermore, we demonstrate that the unique cavity steady-state solution of the full quantum calculation is excellently consistent with the lowest solution based on the semiclassical mean-field approach in bistability and multistability regimes when the cavity photon number is much less than unity, albeit these nonclassical quantum states should possess strong quantum fluctuations in this parameter regime. Our results pave the way to exploring nonclassical correlated optical multistability in quantum regime, which may bring exciting opportunities for potential applications from quantum information processing to quantum metrology.

Entropy production and its large deviations in an active lattice gas

Active systems are characterized by a continuous production of entropy at steady state. We study the statistics of entropy production within a lattice-based model of interacting active particles that is capable of motility-induced phase separation. Exploiting a recent formulation of the exact fluctuating hydrodynamics for this model, we provide analytical results for its entropy production statistics in both typical and atypical (biased) regimes. This complements previous studies of the large deviation statistics of entropy production in off-lattice active particle models that could only be addressed numerically. Our analysis uncovers an unexpectedly intricate phase diagram, with five different phases arising (under bias) within the parameter regime where the unbiased system is in its homogeneous state. Notably, we find the concurrence of first order and second order nonequilibrium phase transition curves at a bias-induced tricritical point, a feature not yet reported in previous studies of active systems.