Nonequilibrium phase transitions induced by multiplicative noise: Effects of self-correlation (original) (raw)

Disordering Effects of Color in Nonequilibrium Phase Transitions Induced by Multiplicative Noise

Physical Review Letters, 1997

The model introduced by Van den Broeck, Parrondo and Toral [Phys. Rev. Lett. 73, 3395 (1994)]-leading to a second-order-like noise-induced nonequilibrium phase transition which shows reentrance as a function of the (multiplicative) noise intensity σ-is investigated beyond the white-noise assumption. Through a Markovian approximation and within a mean-field treatment it is found that-in striking contrast with the usual behavior for equilibrium phase transitions-for noise self-correlation time τ > 0, the stable phase for (diffusive) spatial coupling D → ∞ is always the disordered one. Another surprising result is that a large noise "memory" also tends to destroy order. These results are supported by numerical simulations.

Phase transitions induced by noise cross-correlations

Physical Review E, 2005

A general approach to consider spatially extended stochastic systems with correlations between additive and multiplicative noises subject to nonlinear damping is developed. Within modified cumulant expansion method, we derive an effective Fokker-Planck equation whose stationary solutions describe a character of ordered state. We find that fluctuation cross-correlations lead to a symmetry breaking of the distribution function even in the case of the zero-dimensional system. In general case, continuous, discontinuous and reentrant noise induced phase transitions take place. It is appeared the cross-correlations play a role of bias field which can induce a chain of phase transitions being different in nature. Within mean field approach, we give an intuitive explanation of the system behavior through an effective potential of thermodynamic type. This potential is written in the form of an expansion with coefficients defined by temperature, intensity of spatial coupling, autoand cross-correlation times and intensities of both additive and multiplicative noises.

Nonequilibrium phase transitions induced by multiplicative noise

1997

Noise is usually thought of as a phenomenon which perturbs the observation and creates disorder. This idea is based mainly on our day to day experience and, in the context of physical theories, on the study of equilibrium systems. The effect of noise can, however, be quite different in nonlinear nonequilibrium systems.

Noise-induced phase transitions: Effects of the noises' statistics and spectrum

2007

The study of the effect of the noises' statistics and spectrum on second-order, purely noiseinduced phase transition (NIPT) is of wide interest: It is simplified if the noises are dynamically generated by means of stochastic differential equations driven by white noises, a well known case being that of Ornstein-Uhlenbeck noises with a self-correlation time x whose effect on the NIPT phase diagram has been studied some time ago. Another case is when the stationary pdf is a (colored) q-Gaussian which, being a. fat-tail distribution for q > 1 and a compact-support one for q < 1, allows for a controlled study of the effects of the departure from Gaussian statistics. As done with stochastic resonance and other phenomena, we exploit this tool to study-within a simple meanfield approximation-the combined effect on NIPT of the noises' statistics and spectrum. Even for relatively small T, it is shown that whereas for fat-tail noise distributions counteract the effect of self-correlation, compact-support ones enhance it.

Influence of multiplicative noise on properties of first order dynamical phase transition

Zeitschrift f�r Physik B Condensed Matter, 1986

Critical phenomena in distributed dynamical two-dimensional nonlinear system near the point of the Turing instability are discussed. The system is considered in the presence of thermal fluctuations and multiplicative noise (MN) representing fluctuations of the bifurcation parameter. Since such a noise of the control parameter can have macroscopic (not thermal) nature, the intensity is considered as sufficiently large in comparison with the amplitude of thermal fluctuations, and it is shown that in the system the first order phase transition occurs with the characteristics which are independent on the thermal noise. Hence the discontinuous transtion could be observable in experimental situations where this would not be possible in the absence of MN (like the Rayleigh-Benard problem). When the correlation length of MN is small, the transition results in the formation of a complex state possessing only short-range order, and when MN is spatially uniform, a quasi-one-dimensional structure will be formed.

Linear Instability Mechanisms of Noise-Induced Phase Transitions

2000

We review the role of linear instabilities on phase transition processes induced by external spatiotemporal noise. In particular, we present a detailed linear stability analysis of a standard Ginzburg-Landau model with multiplicative noise. The results show the well-known constructive role of fluctuations in this case. The analysis is performed for both non-conserved and conserved dynamics, corresponding to order-disorder and phase separation transitions, respectively.

Intrinsic noise-induced phase transitions: Beyond the noise interpretation

2003

We discuss intrinsic noise effects in stochastic multiplicative-noise partial differential equations, which are qualitatively independent of the noise interpretation (Itô vs. Stratonovich), in particular in the context of noise-induced ordering phase transitions. We study a model which, contrary to all cases known so far, exhibits such ordering transitions when the noise is interpreted not only according to Stratonovich, but also to Itô. The main feature of this model is the absence of a linear instability at the transition point. The dynamical properties of the resulting noise-induced growth processes are studied and compared in the two interpretations and with a reference Ginzburg-Landau type model. A detailed discussion of new numerical algorithms used in both interpretations is also presented.

Phase Diagrams of Noise Induced Transitions: Exact Results for a Class of External Coloured Noise

Progress of Theoretical Physics, 1980

By using the formula for the steady state probability distribution o£ fluctuation in a nonlinear :;ystems uncl'er the influence of two-level i'viarkovian noise, the existence of phase transitions of such a system with the variation of intensity and correlation time of the noise is shown. Explicit results for the Verhulst model and a model for population genetics are given and compared with the previous results for the white noise case.

1/f Noise in Spatially Extended Systems with Order-Disorder Phase Transitions, submitted to Phys

1999

Noise power spectra in spatially extended dynamical systems are investigated, using as a model the Complex Ginzburg-Landau equation with a stochastic term. Analytical and numerical investigations show that the temporal noise spectra are of 1 f α form, where α = − 2 2 D with D the spatial dimension of the system. This suggests that nonequilibrium order-disorder phase transitions may play a role for the universally observed 1 f noise.