Nonequilibrium First-order Phase Transition Research Articles

Density fluctuations as signature of a non-equilibrium first-order phase transition

We show that in the presence of spinodal instabilities which develop at a first-order phase transition, the fluctuations of conserved charges can be as strong as those at the critical end point (CEP). In particular, the net baryon number susceptibility diverges as the system crosses the isothermal spinodal lines. This indicates that charge density fluctuations can be used not only to probe the CEP but also the non-equilibrium first-order chiral phase transition in heavy-ion collisions.

Self-organization of multiple polariton-polariton scattering in semiconductor microcavities

Sharp transformations of polariton-polariton scattering patterns in a semiconductor microcavity with an increase in pump intensity are observed. These transformations are manifestations of nonequilibrium first-order phase transitions in a strongly driven multimode Bose system. The effect arises from the interplay between the bistability of the pumped polariton mode and the parametric instability in the nonlinear polariton system.

Density fluctuations and chiral phase transition

Based on an effective QCD Lagrangian, we discuss the properties of charge-density fluctuations in the vicinity of chiral phase transition. We explore thermodynamics in the presence of spinodal phase separation. We show that the appearance of spinodal decomposition in a non-equilibrium first-order phase transition results in divergence of the charge-density fluctuations related to the electric charge and baryon number conservation. Consequently, divergent fluctuations at the chiral phase transition are not only attributed to the critical end point but also to the first-order phase transition if the spinodal phase separation takes place. Based on the mean field dynamics, the critical exponents for these singular behavior of charge susceptibilities are also discussed.

Density Fluctuations in the Presence of Spinodal Instabilities

Density fluctuations resulting from spinodal decomposition in a nonequilibrium first-order chiral phase transition are explored. We show that such instabilities generate divergent fluctuations of conserved charges along the isothermal spinodal lines appearing in the coexistence region. Thus, divergent density fluctuations could be a signal not only for the critical end point but also for the first-order phase transition expected in strongly interacting matter. We also compute the mean-field critical exponent at the spinodal lines. Our analysis is performed in the mean-field approximation to the Nambu-Jona-Lasinio model formulated at finite temperature and density. However, our main conclusions are expected to be generic and model independent.

Theory of Photoinduced Phase Transitions: From Semiclassical to Quantum Aspects

We review recent progress of theoretical studies for the photoinduced phase tran- sitions (PIPTs) to clarify what the PIPTs are. There are two types of the PIPTs: (a) global change via optically excited states and (b) new material phase creation in optically excited states. First, concerning (a), photoinduced structural phase transitions via excited electronic states are discussed using a minimal one-dimensional model composed of localized electrons and lattices. We show that the global structural change by photoexcitation only at a single site is possible under the adiabatic or diabatic approximation. This dynamics of the domain bound- aries (domain walls) is called the “photoinduced domino process,” which is the photoinduced nucleation in nonequilibrium first-order phase transition. Second, concerning (b), we discuss quantum orders of electron-hole (e-h) systems, which are optically excited states of insulators consisting of many electrons and holes in two bands. In particular, the “exciton Mott transi- tion,” i.e., the “from-insulator-to-metal” transition of the e-h systems as the particle density increases is introduced. We stress that this transition depends strongly on dimensionality of the system.

First-order transitions in a two-dimensional nonequilibrium replicator model

A single-component, two-dimensional lattice model of self-replicating entities (replicators) which exhibits a nonequilibrium first-order phase transition into a unique absorbing state is introduced and studied through extensive numerical simulations. The basic dynamic processes are auto-catalytic replication, in which groups of at least K + 1 adjacent replicators are required to create a new replicator in a neighboring empty cell, and spontaneous decay. In contrast to the one-dimensional versions known as pair-creation ( K = 1 ) and trimer-creation ( K = 2 ) models which present only continuous transitions into the vacuum, we find a discontinuous transition for K = 2 , provided the replication probability is less than some threshold value, beyond which the transition becomes continuous. For the K = 0 and K = 1 models the transitions are continuous and belong to the class of universality of directed percolation, regardless of the value of the replication probability. Using the conserved contact process we show that in the discontinuous case the density of replicators exhibits a non-monotonic dependence on the decay probability. This steady-state analysis is complemented by the spreading analysis which allows the calculation of the dynamic critical exponents associated to the asymptotic behavior of the survival probability of a small colony of replicators in an infinite lattice.

Decay of metastable phases in a model for the catalytic oxidation of CO

We study by kinetic Monte Carlo simulations the dynamic behavior of a Ziff-Gulari-Barshad model with CO desorption for the reaction CO + O-->CO(2) on a catalytic surface. Finite-size scaling analysis of the fluctuations and the fourth-order order-parameter cumulant show that below a critical CO desorption rate, the model exhibits a nonequilibrium first-order phase transition between low and high CO coverage phases. We calculate several points on the coexistence curve. We also measure the metastable lifetimes associated with the transition from the low CO coverage phase to the high CO coverage phase, and vice versa. Our results indicate that the transition process follows a mechanism very similar to the decay of metastable phases associated with equilibrium first-order phase transitions and can be described by the classic Kolmogorov-Johnson-Mehl-Avrami theory of phase transformation by nucleation and growth. In the present case, the desorption parameter plays the role of temperature, and the distance to the coexistence curve plays the role of an external field or supersaturation. We identify two distinct regimes, depending on whether the system is far from or close to the coexistence curve, in which the statistical properties and the system-size dependence of the lifetimes are different, corresponding to multidroplet or single-droplet decay, respectively. The crossover between the two regimes approaches the coexistence curve logarithmically with system size, analogous to the behavior of the crossover between multidroplet and single-droplet metastable decay near an equilibrium first-order phase transition.

Nonequilibrium first-order phase transition in semiconductor system driven by colored noise

We examine the mechanisms of action of colored multiplicative noise in a positionally disordered semiconductor with Moss–Burstein shift. It is shown that the action of multiplicative noise causes nonequilibrium first-order phase transition of the disorder–order-type in electron subsystem of semiconductor. There are relatively little changes in a condensed matter at such phase transitions, but the electron subsystem undergoes a strong reorganization. The steady photocarriers concentration distribution is studied within a unified colored-noise approximation.

Phase transition of a photogenerated electron gas in semiconductors

We study a nonequilibrium phase-transition-like behavior of a photogenerated electron gas in semiconductors. The kinetics of the electron gas is given by a set of nonlinear rate equations. For low temperatures we show that they have three steady-state solutions when the photoexcitation energy is in a certain interval that depends on the electron-electron interaction. Two of them are stable and the other is unstable. By defining a generalized free potential we obtain the Maxwell construction that determines the order parameter, namely, the difference of the electron population in the bottom of the conduction band of the two steady-stable states. Hence, this phase transition is a nonequilibrium first-order phase transition.

Domino mechanisms in photoinduced phase transitions

Photoinduced structural phase transitions via excited electronic states are discussed theoretically using a one-dimensional model composed of localized electrons and lattices under the adiabatic or diabatic approximation. We show that the global structural change by photoexcitation only at a site is possible, and we clarify conditions for the occurrence of such phenomena. Spatiotemporal dynamics of nonequilibrium first-order phase transitions is also investigated in detail in terms of photoinduced nucleations and domino processes of the domain boundaries (domain walls), which are in striking contrast to the mean-field dynamics. In the adiabatic regime, after the spontaneous emission of a photon, an initial local structural change (i) remains locally, (ii) induces cooperatively a global structural change, or (iii) disappears and returns to the initial phase. Dynamical features of the case (ii) are characterized by the deterministic (semichaotic) domino process; domain walls between the two phases move determinis-tically at a constant velocity (with changing speed) without further spontaneous emissions in the case of strong (weak) dissipation. In the diabatic regime, similar three types of structural change exist. The domain-wall dynamics is described as the stochastic domino process, which is accompanied by the successive radiative transitions. A new theoretical treatment is also proposed to study crossover between the adiabatic and diabatic regimes.

Theory of Domino Processes in Photoinduced Cooperative Phenomena

Photoinduced phase transitions via excited electronic states are discussed theoretically using a minimal model composed of localized electrons and one-dimensional lattices under the adiabatic and diabatic approximations. We show that the global structural transition by photoexcitation only at a site is possible, and we clarify conditions for the occurrence of such cooperative phenomena. Spatiotemporal dynamics of nonequilibrium first-order phase transitions is also investigated in terms of the domino process in photoinduced nucleations.

Kinetics of the photoinduced phase transition at the surface of a semiconductor with renormalizedbandgap

A unified approach to describing all the stages of a nonequilibriumfirst-order phase transition is proposed based on the analogy with thedecomposition of a supersaturated solid solution without using the generalizedthermodynamic potential. Expressions for the asymptotic particle sizedistribution function for the new phase at the late transition stages, as wellas for the critical particle radius are obtained.

The formation kinetics of a strongly absorbing state in a bistable excitonic noncavity system

A unified approach allowing the description of all formation stages of a strongly absorbing state in a bistable excitonic noncavity system as a nonequilibrium first-order phase transition is proposed. In the fast-switching-wave approximation, the switching-wave front velocity is determined, and the thickness of the phase discontinuity interface is estimated. The size distributions of subcritical and supercritical nuclei and an asymptotic expression for the nucleus radius are obtained.

Relaxation spectrum of the asymmetric exclusion process with open boundaries

We calculate numerically the exact relaxation spectrum of the totally asymmetric simple exclusion process (TASEP) with open boundary conditions on lattices up to 16 sites. In the low- and high-density phases and along the nonequilibrium first-order phase transition between these phases, but sufficiently far away from the second-order phase transition into the maximal-current phase, the low-lying spectrum (corresponding to the longest relaxation times) agrees well with the spectrum of a biased random walker confined to a finite lattice of the same size. The hopping rates of this random walk are given by the hopping rates of a shock (a domain wall separating stationary low- and high-density regions), which are calculated in the framework of a recently developed non-equilibrium version of Zel'dovich's theory of the kinetics of first-order transitions. We conclude that the description of the domain wall motion in the TASEP in terms of this theory of boundary-induced phase transitions is meaningful for very small systems of the order of ten lattice sites.

Nonequilibrium first-order phase transition induced by additive noise.

We show that a nonequilibrium first-order phase transition can be induced by additive noise. As a model system to study this phenomenon, we consider a nonlinear lattice of overdamped oscillators with both additive and multiplicative noise terms. Predictions from mean field theory are successfully confirmed by numerical simulations. A physical explanation for the mechanism of the transition is given.

Stochastic escape processes from a non-symmetric potential normal form III: extended explosive systems

The stochastic dynamics to reach the hot attractor of an explosive extended system is analytically studied by using a previously reported scheme: The stochastic path perturbation approach (Cáceres M O, Budde C E and Sibona G J 1995 J. Phys. A: Math. Gen. 28 3877). A perturbation theory in the small noise parameter is introduced to analyse the random escape of the stochastic field from criticality. The anomalous fluctuations of the order parameter (the temperature profile) are calculated analytically using an instanton-like approximation. Emphasis is placed on a thermal non-homogeneous explosion in order to exemplify a system undergoing hysteresis in a first-order non-equilibrium phase transition. Concerning the stochastic propagation of the flame front we have carried out Monte Carlo simulations showing good agreement with our theoretical predictions.

Theory of nonequilibrium first-order phase transitions for stochastic dynamics

A dynamic definition of a first-order phase transition is given. It is based on a master equation description of the time evolution of a system. When the operator generating that time evolution has an isolated near degeneracy there is a first-order phase transition. Conversely, when phenomena describable as first-order phase transitions occur in a system, the corresponding operator has near degeneracy. Estimates relating degree of degeneracy and degree of phase separation are given. This approach harks back to early ideas on phase transitions and degeneracy, but now enjoys greater generality because it involves an operator present in a wide variety of systems. Our definition is applicable to what have intuitively been considered phase transitions in nonequilibrium systems and to problematic near equilibrium cases, such as metastability.

First-order nonequilibrium phase transition in a spatially extended system

We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling, we find for infinitely many constituents the coexistence of several ergodic components and a bifurcation behavior like in first-order phase transitions. These results are compared with simulations for finite systems both for global coupling and for nearest-neighbor coupling on two- and three-dimensional cubic lattices. The mean-field-type results for global coupling provide a better understanding of the more complex behavior in the latter case.

Stochastic escape processes from a nonsymmetric potential normal form

The lifetime from the normal form X=aX2+b+ square root ( epsilon xi )(t) is analytically studied in terms of the escape time of leaving the unstable point X=0. A perturbation theory, in the small noise parameter square root epsilon , is introduced to analyse the escape of the stochastic paths. We show that the first passage time density satisfies a scale transformation. The anomalous fluctuation of the phase-space variable X(t) (when there is saturation in the potential of the normal form) is analytically calculated using an instanton-like approximation. An emphasis is placed on thermal explosions in order to exemplify a system undergoing hysteresis in a first-order non-equilibrium phase transition. We carried out Monte Carlo simulations showing excellent agreement with our theoretical predictions.

About the shift between the advanced and delayed thermal explosion times

The shift between the advanced and delayed explosion times is analytically studied in terms of the escape time to leave the point of marginal stability. A perturbation theory, in the small noise parameter, is introduced to analyze the escape of the stochastic path. Special emphasis on thermal explosion is given in order to exemplify a system undergoing hysteresis in a first-order non-equilibrium phase transition.