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P Sollich

Publications and source records attributed to P Sollich.

7 recordsLinked to original sources
PubMed2005

Universality of fluctuation-dissipation ratios: the ferromagnetic model.

We calculate analytically the fluctuation-dissipation ratio (FDR) for Ising ferromagnets quenched to criticality, both for the long-range model and its short-range analog in the limit of large dimension. Our exact solution shows that, for both models, if the system is unmagnetized while if the initial magnetization is nonzero. This indicates that two different classes of critical coarsening dynamics need to be distinguished depending on the initial conditions, each with its own nontrivial FDR. We also analyze the dependence of the FDR on whether local and global observables are used. These results clarify how a proper local FDR (and the corresponding effective temperature) should be defined in long-range models in order to avoid spurious inconsistencies and maintain the expected correspondence between local and global results; global observables turn out to be far more robust tools for detecting nonequilibrium FDRs.

Journal Article↗
PubMed2004

Heterogeneous dynamics of coarsening systems.

We show by means of experiments, theory, and simulations that the slow dynamics of coarsening systems displays dynamic heterogeneity similar to that observed in glass-forming systems. We measure dynamic heterogeneity via novel multipoint functions which quantify the emergence of dynamic, as opposed to static, correlations of fluctuations. Experiments are performed on a coarsening foam using time-resolved correlation, a recently introduced light scattering method. Theoretically we study the Ising model, and present exact results in one dimension, and numerical results in two dimensions. For all systems the same dynamic scaling of fluctuations with domain size is observed.

Journal Article↗
PubMed2003

Glassy dynamics in the asymmetrically constrained kinetic Ising chain.

We study the dynamics of the East model, comprising a chain of uncoupled spins in a downward-pointing field. Glassy effects arise at low temperatures T from the kinetic constraint that spins can only flip if their left neighbor is up. We give details of our previous solution of the nonequilibrium coarsening dynamics after a quench to low T [Phys. Rev. Lett. 83, 3238 (1999)], including the anomalous coarsening of down-spin domains with typical size d approximately t(T ln 2), and the pronounced "fragile glass" divergence of equilibration times as t(*)=exp(1/T(2) ln 2). We also link the model to the paste-all coarsening model, defining a family of interpolating models that all have the same scaling distribution of domain sizes. We then proceed to the problem of equilibrium dynamics at low T. Based on a scaling hypothesis for the relation between time scales and length scales, we propose a model for the dynamics of "superdomains" which are bounded by up-spins that are frozen on long time scales. From this we deduce that the equilibrium spin correlation and persistence functions should exhibit identical scaling behavior for low T, decaying as g(t). The scaling variable is t=(t/t(*))(T ln 2), giving strongly stretched behavior for low T. The scaling function g(.) decays faster than exponential, however, and in the limit T-->0 at fixed t reaches zero at a finite value of t.

Journal Article↗
PubMed2003

Equivalence of driven and aging fluctuation-dissipation relations in the trap model.

We study the nonequilibrium version of the fluctuation-dissipation (FD) relation in the glass phase of a trap model that is driven into a nonequilibrium steady state by external "shear." This extends our recent study of aging FD relations in the same model, where we found limiting, observable independent FD relations for "neutral" observables that are uncorrelated with the system's average energy. In this work, for such neutral observables, we find the FD relation for a stationary weakly driven system to be the same, to within small corrections, as for an infinitely aged system. We analyze the robustness of this correspondence with respect to non-neutrality of the observable, and with respect to changes in the driving mechanism.

Journal Article↗
PubMed1998

Online learning from finite training sets and robustness to input bias.

We analyze online gradient descent learning from finite training sets at noninfinitesimal learning rates eta. Exact results are obtained for the time-dependent generalization error of a simple model system: a linear network with a large number of weights N, trained on p = alphaN examples. This allows us to study in detail the effects of finite training set size alpha on, for example, the optimal choice of learning rate eta. We also compare online and offline learning, for respective optimal settings of eta at given final learning time. Online learning turns out to be much more robust to input bias and actually outperforms offline learning when such bias is present; for unbiased inputs, online and offline learning perform almost equally well.

Learning↗