Fluctuation dissipation ratio in the one dimensional kinetic Ising model

The exact relation between the response function $R(t,t^{\prime})$ and the two time correlation function $C(t,t^{\prime})$ is derived analytically in the one dimensional kinetic Ising model subjected to a temperature quench. The fluctuation dissipation ratio $X(t,t^{\prime})$ is found to depend on time through $C(t,t^{\prime})$ in the time region where scaling $C(t,t^{\prime}) = f(t/t^{\prime})$ holds. The crossover from the nontrivial form $X(C(t,t^{\prime}))$ to $X(t,t^{\prime}) \equiv 1$ takes place as the waiting time $t_w$ is increased from below to above the equilibration time $t_{eq}$.Comment: 2 figure

Inverse design technique for cascades

A numerical technique to generate cascades is presented. The basic prescribed parameters are: inlet angle, exit pressure, and distribution of blade thickness and lift along a blade. Other sets of parameters are also discussed. The technique is based on the lambda scheme. The problem of stability of the computation as a function of the prescribed set of parameters and the treatment of boundary conditions is discussed. A one dimensional analysis to indicate a possible way for assuring stability for any two dimensional calculation is provided

Preasymptotic multiscaling in the phase-ordering dynamics of the kinetic Ising model

The evolution of the structure factor is studied during the phase-ordering dynamics of the kinetic Ising model with conserved order parameter. A preasymptotic multiscaling regime is found as in the solution of the Cahn-Hilliard-Cook equation, revealing that the late stage of phase-ordering is always approached through a crossover from multiscaling to standard scaling, independently from the nature of the microscopic dynamics.Comment: 11 pages, 3 figures, to be published in Europhys. Let

Heat fluctuations of Brownian oscillators in nonstationary processes: fluctuation theorem and condensation transition

We study analytically the probability distribution of the heat released by an ensemble of harmonic oscillators to the thermal bath, in the nonequilibrium relaxation process following a temperature quench. We focus on the asymmetry properties of the heat distribution in the nonstationary dynamics, in order to study the forms taken by the Fluctuation Theorem as the number of degrees of freedom is varied. After analysing in great detail the cases of one and two oscillators, we consider the limit of a large number of oscillators, where the behavior of fluctuations is enriched by a condensation transition with a nontrivial phase diagram, characterized by reentrant behavior. Numerical simulations confirm our analytical findings. We also discuss and highlight how concepts borrowed from the study of fluctuations in equilibrium under symmetry breaking conditions [Gaspard, J. Stat. Mech. P08021 (2012)] turn out to be quite useful in understanding the deviations from the standard Fluctuation Theorem.Comment: 16 pages, 7 figure

Energy and Heat Fluctuations in a Temperature Quench

Fluctuations of energy and heat are investigated during the relaxation following the instantaneous temperature quench of an extended system. Results are obtained analytically for the Gaussian model and for the large $N$ model quenched below the critical temperature $T_C$. The main finding is that fluctuations exceeding a critical threshold do condense. Though driven by a mechanism similar to that of Bose-Einstein condensation, this phenomenon is an out-of-equilibrium feature produced by the breaking of energy equipartition occurring in the transient regime. The dynamical nature of the transition is illustrated by phase diagrams extending in the time direction.Comment: To be published in the Proceedings of the Research Program "Small system non equilibrium fluctuations, dynamics and stochastics, and anomalous behavior", Kavli Institute for Theoretical Physics China, July 2013. 40 pages, 9 figure

Off equilibrium response function in the one dimensional random field Ising model

A thorough numerical investigation of the slow dynamics in the d=1 random field Ising model in the limit of an infinite ferromagnetic coupling is presented. Crossovers from the preasymptotic pure regime to the asymptotic Sinai regime are investigated for the average domain size, the autocorrelation function and staggered magnetization. By switching on an additional small random field at the time tw the linear off equilibrium response function is obtained, which displays as well the crossover from the nontrivial behavior of the d=1 pure Ising model to the asymptotic behavior where it vanishes identically.Comment: 12 pages, 10 figure

Growth Law and Superuniversality in the Coarsening of Disordered Ferromagnets

We present comprehensive numerical results for domain growth in the two-dimensional {\it Random Bond Ising Model} (RBIM) with nonconserved Glauber kinetics. We characterize the evolution via the {\it domain growth law}, and two-time quantities like the {\it autocorrelation function} and {\it autoresponse function}. Our results clearly establish that the growth law shows a crossover from a pre-asymptotic regime with "power-law growth with a disorder-dependent exponent" to an asymptotic regime with "logarithmic growth". We compare this behavior with previous results on one-dimensional disordered systems and we propose a unifying picture in a renormalization group framework. We also study the corresponding crossover in the scaling functions for the two-time quantities. Super-universality is found not to hold. Clear evidence supporting the dimensionality dependence of the scaling exponent of the autoresponse function is obtained.Comment: Thoroughly revised manuscript. The Introduction, Section 2 and Section 4 have been largely rewritten. References added. Final version accepted for publication on Journal of Statistical Mechanics: Theory and Experimen

Nonlinear susceptibilities and the measurement of a cooperative length

We derive the exact beyond-linear fluctuation dissipation relation, connecting the response of a generic observable to the appropriate correlation functions, for Markov systems. The relation, which takes a similar form for systems governed by a master equation or by a Langevin equation, can be derived to every order, in large generality with respect to the considered model, in equilibrium and out of equilibrium as well. On the basis of the fluctuation dissipation relation we propose a particular response function, namely the second order susceptibility of the two-particle correlation function, as an effective quantity to detect and quantify cooperative effects in glasses and disordered systems. We test this idea by numerical simulations of the Edwards-Anderson model in one and two dimensions.Comment: 5 pages, 2 figure

Non trivial behavior of the linear response function in phase ordering kinetics

Drawing from exact, approximate and numerical results an overview of the properties of the out of equilibrium response function in phase ordering kinetics is presented. Focusing on the zero field cooled magnetization, emphasis is on those features of this quantity which display non trivial behavior when relaxation proceeds by coarsening. Prominent among these is the dimensionality dependence of the scaling exponent $a_{\chi}$ which leads to failure of the connection between static and dynamic properties at the lower dimensionality $d_L$, where $a_{\chi}=0$. We also analyse the mean spherical model as an explicit example of a stochastic unstable system, for which the connection between statics and dynamics fails at all dimensionalities.Comment: 10 pages, 2 figures. Contribution to the International Conference "Perspectives on Quantum Field Theory, Statistical Mechanics and Stochastics" in honour of the 60th birthday of Francesco Guerr