Related papers: Critical stationary fluctuations in reaction--diff…
This is a pedagogical account on reaction-diffusion systems and their relationship with integrable quantum spin chains. Reaction-diffusion systems are paradigmatic examples of non-equilibrium systems. Their long-time behaviour is strongly…
The lattice model of Coulomb Glass in two dimensions with box-type random field distribution is studied at zero temperature for system size upto $96^{2}$. To obtain the minimum energy state we annealed the system using Monte Carlo…
We study the fluctuations of the area $A(t)= \int_0^t x(\tau)\, d\tau$ under a self-similar Gaussian process (SGP) $x(\tau)$ with Hurst exponent $H>0$ (e.g., standard or fractional Brownian motion, or the random acceleration process) that…
Systems close to a phase transition turn weak perturbations into large responses. At equilibrium, this amplification is closely linked to criticality: fluctuations grow, dynamics slow, and a common soft mode controls the response. Whether…
An investigation of the spatial fluctuations and their manifestations in the vicinity of the quantum critical point within the framework of the renormalized $\phi^{4}$ theory is proposed. Relevant features are reported through the…
We discuss a Curie-Weiss model with two groups in the critical regime. This is the region where the central limit theorem does not hold any more but the mean magnetization still goes to zero as the number of spins grows. We show that the…
Relationships are obtained expressing the breaking of spin-reversal symmetry by an external magnetic field in Gibbsian canonical equilibrium states of spin systems under specific assumptions. These relationships include an exact fluctuation…
The magnetic properties of the weak itinerant ferromagnet ZrZn_2 are analyzed using Landau theory based on a comparison of density functional calculations and experimental data as a function of field and pressure. We find that the magnetic…
We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. Analytic results for the stationary state are presented in mean-field approximation, exhibiting a…
We consider the properties of the diffusion controlled reaction A+B->0 in the steady state, where fixed currents of A and B particles are maintained at opposite edges of the system. Using renormalisation group methods, we explicitly…
The microscopic structure and movement of reaction fronts in reaction diffusion systems far from equilibrium are investigated. We show that some three-site interaction models exhibit exact diffusive shock measures, i.e. domains of different…
We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…
We find that in generic field theories the combined effect of fluctuations and interactions leads to a probability distribution function which describes fractional Brownian Motion (fBM) and ``complex behavior''. To show this we use the…
We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently-introduced macroscopic fluctuation theory to nonlinear driven…
We investigate the nonequilibrium behavior of the d-dimensional Ising model with purely dissipative dynamics during its critical relaxation from a magnetized initial configuration. The universal scaling forms of the two-time response and…
The study by Glauber of the time-dependent statistics of the Ising chain is extended to the case where each spin is influenced unequally by its nearest neighbours. The asymmetry of the dynamics implies the failure of the detailed balance…
We consider stationary fluctuations for the multi-species zero range process with long jumps in one dimension, where the underlying transition probability kernel is $p(x) = c_+ |x|^{-1-\alpha}$ if $x > 0$ and $= c_-|x|^{-1-\alpha}$ if $x <…
The computation of observables in high energy QCD involves an average over stochastic semiclassical small-x gluon fields. The weight of various configurations is determined by the effective action. We introduce a method to study…
We study the effect of site dilution and quantum fluctuations in an antiferromagnetic spin system on a square lattice within the linear spin-wave approximation. By performing numerical diagonalization in real space and finite-size scaling,…
A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean squared displacement, yet with a non-Gaussian distribution of increments. Based on the…