External non-white noise and nonequilibrium phase transitions

Langevin equations with external non-white noise are considered. A Fokker Planck equation valid in general in first order of the correlation time of the noise is derived. In some cases its validity can be extended to any value of. The effect of a finite in the nonequilibrium phase transitions induced by the noise is analyzed, by means of such Fokker Planck equation, in general, for the Verhulst equation under two different kind of fluctuations, and for a genetic model. It is shown that new transitions can appear and that the threshold value of the parameter can be changed.     

Additive noise-induced Turing transitions in spatial systems with application to neural fields and the Swift-Hohenberg equation

This work studies the spatio-temporal dynamics of a generic integral-differential equation subject to additive random fluctuations. It introduces a combination of the stochastic center manifold approach for stochastic differential equations and the adiabatic elimination for Fokker-Planck equations, and studies analytically the systems’ stability near Turing bifurcations. In addition two types of fluctuation are studied, namely fluctuations uncorrelated in space and time, and global fluctuations, which are constant in space but uncorrelated in time. We show that the global fluctuations shift the Turing bifurcation threshold. This shift is proportional to the fluctuation variance. Applications to a neural field equation and the Swift-Hohenberg equation reveal the shift of the bifurcation to larger control parameters, which represents a stabilization of the system. All analytical results are confirmed by numerical simulations of the occurring mode equations and the full stochastic integral-differential equation. To gain some insight into experimental manifestations, the sum of uncorrelated and global additive fluctuations is studied numerically and the analytical results on global fluctuations are confirmed qualitatively.     

Nonequilibrium noise-induced phase transitions in simple systems

The theory and the results of an investigation of nonequilibrium noise-induced phase transitions in the simple example of a physical pendulum with a randomly oscillating pivot are presented. It is shown that such transitions lead to the appearance of a more ordered state of the system. The possibility of a difference between noise-induced oscillations and chaotic oscillations of dynamic origin is discussed. Zh. éksp. Teor. Fiz. 111, 358–378 (January 1997)     

Optical properties in nonequilibrium phase transitions

An open question about the dynamical behavior of materials is how phase transition occurs in highly nonequilibrium systems. One important class of study is the excitation of a solid by an ultrafast, intense laser. The preferential heating of electrons by the laser field gives rise to initial states dominated by hot electrons in a cold lattice. Using a femtosecond laser pump-probe approach, we have followed the temporal evolution of the optical properties of such a system. The results show interesting correlation to nonthermal melting and lattice disordering processes. They also reveal a liquid-plasma transition when the lattice energy density reaches a critical value.     

Critical phenomena in nonequilibrium phase transitions

We discuss a number of models associated with phase transitions in purely kinetic models where detailed balance does not hold as in thermal equilibrium systems. These models include some of the features of heterogeneous catalysis on a surface, and are used to examine the effect of local correlations on the reaction process. We argue that many models which do not include desorption will show the same kind of critical behavior if they have a continuous transition to a poisoned state. We also present results for a model with a continuous transition to a non-poisoned state. The effect of adding desorption, diffusion, and anisotropy to these idealized models is also discussed.     

Anomalous latent heat in nonequilibrium phase transitions

We study first-order phase transitions in a two-temperature system, where due to the time-scale separation all the basic thermodynamical quantities (free energy, entropy, etc.) are well defined. The sign of the latent heat is found to be counterintuitive: it is positive when going from the phase where the temperatures and the entropy are higher to the one where these quantities are lower. The effect exists only out of equilibrium and requires conflicting interactions. It is displayed on a lattice gas model of ferromagnetically interacting spin-1/2 particles.     

Detection of nonequilibrium phase transitions in water

The time dependence of the temperature of distillated water upon its cooling and heating in the temperature range from 3 to 5°C has been investigated. Nonequilibrium phase transitions indicating the presence of ordered over-molecular structures have been detected.     

Transient behavior of nonequilibrium phase transitions

The transient behavior of a simple Malthus-Verhulst like nonlinear chemical system is analyzed. This model exhibits a nonequilibrium phase transition analogous to the laser instability. We first perform a qualitative analysis of the model in the space of the rate parameters. We show, both with a nonperturbative calculation and a direct computer simulation, that the fluctuations in the transient regime are enhanced above the steady state value. This anomalous behavior occurs in a given range for the rate parameters.     

Bulk-driven nonequilibrium phase transitions in a mesoscopic ring

We study a periodic one-dimensional exclusion process composed of a driven and a diffusive part. In a mesoscopic limit where both dynamics compete we identify bulk-driven phase transitions. We employ mean-field theory complemented by Monte Carlo simulations to characterize the emerging nonequilibrium steady states. Monte Carlo simulations reveal interesting correlation effects that we explain phenomenologically.     

A characteristic critical quantity in nonequilibrium phase transitions

The bit-number variance, a generalization of specific heat, which was already introduced in earlier papers [7-10] is discussed, with respect to the critical behaviour in equilibrium-and nonequilibrium phase transitions. In the considered mean field examples it shows a uniform behaviour dependent on to which of two classes the system belongs. With it a new characteristic critical quantity is found appropriate for the comparison of different nonequilibrium phase transitions. New arguments are given with respect to the connection between critical correlations and the bit-number cumulants.     

Channel noise-induced temporal coherence transitions and synchronization transitions in adaptive neuronal networks with time delay

Using spike-timing-dependent plasticity (STDP), we study the effect of channel noise on temporal coherence and synchronization of adaptive scale-free Hodgkin-Huxley neuronal networks with time delay. It is found that the spiking regularity and spatial synchronization of the neurons intermittently increase and decrease as channel noise intensity is varied, exhibiting transitions of temporal coherence and synchronization. Moreover, this phenomenon depends on time delay, STDP, and network average degree. As time delay increases, the phenomenon is weakened, however, there are optimal STDP and network average degree by which the phenomenon becomes strongest. These results show that channel noise can intermittently enhance the temporal coherence and synchronization of the delayed adaptive neuronal networks. These findings provide a new insight into channel noise for the information processing and transmission in neural systems.     

Factorised steady states and condensation transitions in nonequilibrium systems

Systems driven out of equilibrium can often exhibit behaviour not seen in systems in thermal equilibrium —for example phase transitions in one-dimensional systems. In this talk I will review a simple model of a nonequilibrium system known as the ‘zero-range process’ and its recent developments. The nonequilibrium stationary state of this model factorises and this property allows a detailed analysis of several ‘condensation’ transitions wherein a finite fraction of the constituent particles condenses onto a single lattice site. I will then consider a more general class of mass transport models, encompassing continuous mass variables and discrete time updating, and present a necessary and sufficient condition for the steady state to factorise. The property of factorisation again allows an analysis of the condensation transitions which may occur.     

On the revealing of nonequilibrium phase transitions in water

It has been found that the jump and stabilization of the temperature observed in [L.N. Baturov et al., JETP Lett. 93, 91 (2011)] upon the heating/cooling of water near 4°C at a rate of ∼10⁻³ K/s are observed in water of any purification degree. However, we have not found the process of the formation/melting of supermolecular structures assumed by Baturov et al., which is sought in the shift of the center of the OH band of Raman scattering, e.g., at ∼150 cm⁻¹, as at the melting of hexagonal 1h ice [S.M. Pershin and A.F. Bunkin, Opt. Spectrosc. 85, 190 (1998); Patent RF No. 98, 103249 (1998)]. It has been shown that the revealed temperature features are absent in the presence of the mixing of water and artificial limitation of convection, as well as in a thin layer; this indicates that the regularity of the phenomenon is doubtful and that convection plays an important role. The visualization of convection flows by potassium permanganate made it possible to detect the reversion of their circulation over the trajectory of surface-wall-bottom-volume symmetry axis at the transition through a point of 4°C. The observed features have been interpreted as a manifestation of Archimedes’ principle.     

Electron-electron scattering and nonequilibrium noise in sharvin contacts

We consider wide ballistic microcontacts with electron-electron scattering in the leads and calculate electric noise and nonlinear conductance in them. Due to a restricted geometry the collisions of electrons result in a shot noise even though they conserve the total momentum of electrons. We obtain the noise and the conductivity for arbitrary relations between voltage V and temperature T. The positive inelastic correction to the Sharvin conductance is proportional to T at low voltages eV ≪ T, and to |V| at high voltages. At low voltages the noise is defined by the Nyquist relation and at high voltages the noise is related with the inelastic correction to the current by the Schottky formula S _in = 2eI _in.     

Some comments on nonequilibrium phase transitions in chemical systems

Two new approaches for investigating critical fluctuations near an instability point of unstable chemical models are proposed. The master equation approach is used. For a homogeneous system without the effect of diffusion, three single-component chemical systems exhibiting critical behavior are considered. The cumulant functions are expanded in a small parameter-the inverse size of the system-and singular perturbation solutions of the master equation are developed. Exponents describing the divergence of the second-order variance are found to be classical. For a system including diffusion effects, spatial correlations for a quasi-one-dimensional case are investigated by considering scale transformation behavior within the multivariate master equation formalism.This work was supported in part by NSF grants MPS-7411925 and CHE 76-05583.     

Surface critical behavior in systems with nonequilibrium phase transitions

We study the surface critical behavior of branching-annihilating random walks with an even number of offspring (BARW) and directed percolation (DP) using a variety of theoretical techniques. Above the upper critical dimensions d(c), with d(c)=4 (DP) and d(c)=2 (BARW), we use mean field-theory to analyze the surface phase diagrams using the standard classification into ordinary, special, surface, and extraordinary transitions. For the case of BARW, at or below the upper critical dimension d相似文献