Quantum-classical transition in the Caldeira-Leggett model

The quantum-classical transition in the Caldeira-Leggett model is investigated in the framework of the functional renormalization group method. It is shown that a divergent quadratic term arises in the action due to the heat bath in the model. By removing the divergence with a frequency cutoff we considered the critical behavior of the model. The critical exponents belonging to the susceptibility and the correlation length are determined and their independence of the frequency cutoff and the renormalization scheme is shown.Comment: 8 pages, 4 figure

Moment Equations for a Spatially Extended System of Two Competing Species

The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulations of the time discrete version of LV equations, that is coupled map lattice (CML) model, we conclude that the anticorrelated oscillations of the species densities are strictly related to non-overlapping spatial patterns.Comment: 10 pages, 3 figure

Moment equations in a Lotka-Volterra extended system with time correlated noise

A spatially extended Lotka-Volterra system of two competing species in the presence of two correlated noise sources is analyzed: (i) an external multiplicative time correlated noise, which mimics the interaction between the system and the environment; (ii) a dichotomous stochastic process, whose jump rate is a periodic function, which represents the interaction parameter between the species. The moment equations for the species densities are derived in Gaussian approximation, using a mean field approach. Within this formalism we study the effect of the external time correlated noise on the ecosystem dynamics. We find that the time behavior of the $1^{st}$ order moments are independent on the multiplicative noise source. However the behavior of the $2^{nd}$ order moments is strongly affected both by the intensity and the correlation time of the multiplicative noise. Finally we compare our results with those obtained studying the system dynamics by a coupled map lattice model.Comment: 12 pages, 7 figures, to appear in Acta Phys. Pol.

Critical exponents in quantum Einstein gravity

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Noise Induced Complexity: From Subthreshold Oscillations to Spiking in Coupled Excitable Systems

We study stochastic dynamics of an ensemble of N globally coupled excitable elements. Each element is modeled by a FitzHugh-Nagumo oscillator and is disturbed by independent Gaussian noise. In simulations of the Langevin dynamics we characterize the collective behavior of the ensemble in terms of its mean field and show that with the increase of noise the mean field displays a transition from a steady equilibrium to global oscillations and then, for sufficiently large noise, back to another equilibrium. Diverse regimes of collective dynamics ranging from periodic subthreshold oscillations to large-amplitude oscillations and chaos are observed in the course of this transition. In order to understand details and mechanisms of noise-induced dynamics we consider a thermodynamic limit $N\to\infty$ of the ensemble, and derive the cumulant expansion describing temporal evolution of the mean field fluctuations. In the Gaussian approximation this allows us to perform the bifurcation analysis; its results are in good agreement with dynamical scenarios observed in the stochastic simulations of large ensembles

Interplay of fixed points in scalar models

We performed the renormalization group analysis of scalar models exhibiting spontaneous symmetry breaking. It is shown that an infrared fixed point appears in the broken symmetric phase of the models, which induces a dynamical scale, that can be identified with the correlation length. This enables one to identify the type of the phase transition which shows similarity to the one appearing in the crossover scale. The critical exponent $\nu$ of the correlation length also proved to be equal in the crossover and the infrared scaling regimes.Comment: 11 pages, 4 figure

Onset of symmetry breaking by the functional RG method

A numerical algorithm is used to solve the bare and the effective potential for the scalar $\phi^4$ model in the local potential approximation. An approximate dynamical Maxwell-cut is found which reveals itself in the degeneracy of the action for modes at some scale. This result indicates that the potential develop singular field dependence as far as one can see it by an lgorithm of limited numerical accuracyComment: 19 pages, 10 figures, accepted version. To appear in International Journal of Modern Physics