Relaxation processes and entropic traps in the Backgammon model

We examine the density-density correlation function in a model recently proposed to study the effect of entropy barriers in glassy dynamics. We find that the relaxation proceeds in two steps with a fast beta process followed by alpha relaxation. The results are physically interpreted in the context of an adiabatic approximation which allows to separate the two processes, and to define an effective temperature in the off-equilibrium dynamics of the model. We investigate the behavior of the response function associated to the density, and find violations of the fluctuation dissipation theorem.Comment: 4 Pages including 3 Figures, Revte

Slow relaxation in the large N model for phase ordering

The basic features of the slow relaxation phenomenology arising in phase ordering processes are obtained analytically in the large $N$ model through the exact separation of the order parameter into the sum of thermal and condensation components. The aging contribution in the response function $\chi_{ag}(t,t_w)$ is found to obey a pattern of behavior, under variation of dimensionality, qualitatively similar to the one observed in Ising systems. There exists a critical dimensionality $(d=4)$ above which $\chi_{ag}(t,t_w)$ is proportional to the defect density $\rho_D(t)$, while for $d<4$ it vanishes more slowly than $\rho_D(t)$ and at $d=2$ does not vanish. As in the Ising case, this behavior can be understood in terms of the dependence on dimensionality of the interplay between the defect density and the effective response associated to a single defect.Comment: 27 pages, 4 figures, accepted for publication on Phys.Rev.

Condensation transition in a model with attractive particles and non-local hops

We study a one dimensional nonequilibrium lattice model with competing features of particle attraction and non-local hops. The system is similar to a zero range process (ZRP) with attractive particles but the particles can make both local and non-local hops. The length of the non-local hop is dependent on the occupancy of the chosen site and its probability is given by the parameter $p$. Our numerical results show that the system undergoes a phase transition from a condensate phase to a homogeneous density phase as $p$ is increased beyond a critical value $p_c$. A mean-field approximation does not predict a phase transition and describes only the condensate phase. We provide heuristic arguments for understanding the numerical results.Comment: 11 Pages, 6 Figures. Published in Journal of Statistical Mechanics: Theory and Experimen

Universal dependence of the fluctuation-dissipation ratio on the transition rates in trap models

We investigate violations of the fluctuation-dissipation theorem in two classes of trap models by studying the influence of the perturbing field on the transition rates. We show that for perturbed rates depending upon the value of the observable at the arrival trap, a limiting value of the fluctuation-dissipation ratio does exist. However, the mechanism behind the emergence of this value is different in both classes of models. In particular, for an entropically governed dynamics (where the perturbing field shifts the relative population of traps according to the value of the observable) perturbed rates are argued to take a form that guarantees the existence of a limiting value for the effective temperature, utterly related to the exponential character of the distribution of trap energies. Fluctuation-dissipation (FD) plots reproduce some of the patterns found in a broad class of glassy systems, reinforcing the idea that structural glasses self-generate a dynamical measure that is captured by phenomenological trap models.Comment: 15 pages, 4 figures (Latex) Misprints corrected and additional comments included in Section 4. Contribution to a special issue of J. Phys. A "Statistical Physics of Disordered Systems

Relaxation and overlap probability function in the spherical and mean spherical model

The problem of the equivalence of the spherical and mean spherical models, which has been thoroughly studied and understood in equilibrium, is considered anew from the dynamical point of view during the time evolution following a quench from above to below the critical temperature. It is found that there exists a crossover time $t^* \sim V^{2/d}$ such that for $t < t^*$ the two models are equivalent, while for $t > t^*$ macroscopic discrepancies arise. The relation between the off equilibrium response function and the structure of the equilibrium state, which usually holds for phase ordering systems, is found to hold for the spherical model but not for the mean spherical one. The latter model offers an explicit example of a system which is not stochastically stable.Comment: 11 pages, 1 figure, references corrected, to appear in Phys.Rev.

Aging in One-Dimensional Coagulation-Diffusion Processes and the Fredrickson-Andersen Model

We analyse the aging dynamics of the one-dimensional Fredrickson-Andersen (FA) model in the nonequilibrium regime following a low temperature quench. Relaxation then effectively proceeds via diffusion limited pair coagulation (DLPC) of mobility excitations. By employing a familiar stochastic similarity transformation, we map exact results from the free fermion case of diffusion limited pair annihilation to DLPC. Crucially, we are able to adapt the mapping technique to averages involving multiple time quantities. This relies on knowledge of the explicit form of the evolution operators involved. Exact results are obtained for two-time correlation and response functions in the free fermion DLPC process. The corresponding long-time scaling forms apply to a wider class of DLPC processes, including the FA model. We are thus able to exactly characterise the violations of the fluctuation-dissipation theorem (FDT) in the aging regime of the FA model. We find nontrivial scaling forms for the fluctuation-dissipation ratio (FDR) X = X(tw/t), but with a negative asymptotic value X = -3*pi/(6*pi - 16) = -3.307. While this prevents a thermodynamic interpretation in terms of an effective temperature, it is a direct consequence of probing FDT with observables that couple to activated dynamics. The existence of negative FDRs should therefore be a widespread feature in non mean-field systems.Comment: 39 pages, 4 figure

Is the Stillinger and Weber decomposition relevant for coarsening models?

We study three kinetic models with constraint, namely the Symmetrically Constrained Ising Chain, the Asymmetrically Constrained Ising Chain, and the Backgammon Model. All these models show glassy behavior and coarsening. We apply to them the Stillinger and Weber decomposition, and find that they share the same configurational entropy, despite of their different nonequilibrium dynamics. We conclude therefore that the Stillinger and Weber decomposition is not relevant for this type of models.Comment: 14 pages, 12 figure

Order in glassy systems

A directly measurable correlation length may be defined for systems having a two-step relaxation, based on the geometric properties of density profile that remains after averaging out the fast motion. We argue that the length diverges if and when the slow timescale diverges, whatever the microscopic mechanism at the origin of the slowing down. Measuring the length amounts to determining explicitly the complexity from the observed particle configurations. One may compute in the same way the Renyi complexities K_q, their relative behavior for different q characterizes the mechanism underlying the transition. In particular, the 'Random First Order' scenario predicts that in the glass phase K_q=0 for q>x, and K_q>0 for q<x, with x the Parisi parameter. The hypothesis of a nonequilibrium effective temperature may also be directly tested directly from configurations.Comment: Typos corrected, clarifications adde

Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map

We rationalize the somewhat surprising efficacy of the Hadamard transform in simplifying the eigenstates of the quantum baker's map, a paradigmatic model of quantum chaos. This allows us to construct closely related, but new, transforms that do significantly better, thus nearly solving for many states of the quantum baker's map. These new transforms, which combine the standard Fourier and Hadamard transforms in an interesting manner, are constructed from eigenvectors of the shift permutation operator that are also simultaneous eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal) symmetry.Comment: Version to appear in J. Phys. A. Added discussions; modified title; corrected minor error

Phase transitions and correlations in the bosonic pair contact process with diffusion: Exact results

The variance of the local density of the pair contact process with diffusion (PCPD) is investigated in a bosonic description. At the critical point of the absorbing phase transition (where the average particle number remains constant) it is shown that for lattice dimension d>2 the variance exhibits a phase transition: For high enough diffusion constants, it asymptotically approaches a finite value, while for low diffusion constants the variance diverges exponentially in time. This behavior appears also in the density correlation function, implying that the correlation time is negative. Yet one has dynamical scaling with a dynamical exponent calculated to be z=2.Comment: 20 pages, 5 figure