# Workshop Programme

## for period 9 - 13 January 2006

### Relaxational Dynamics of Macroscopic Systems

9 - 13 January 2006

Timetable

 Monday 9 January 08:30-08:50 Registration 08:50-09:00 Franz, S; Godreche, C (ICTP, CEA-Saclay) Welcome Sem 1 09:00-09:50 Biroli, G (CEA-Saclay) Field theory and exact stochastic equations for interacting particle systems Sem 1 09:50-10:40 Sollich, P (Kings College, London) Activated aging dynamics and negative fluctuation-dissipation ratios Sem 1 In glassy materials aging proceeds at large times via thermal activation. We show that this can lead to negative dynamic response functions and novel and well-defined violations of the fluctuation-dissipation theorem, in particular, negative fluctuation-dissipation ratios. Our analysis is based on detailed theoretical and numerical results for the activated aging regime of simple kinetically constrained models. Our results are relevant to a variety of physical situations such as aging in glass-formers, thermally activated domain growth and granular compaction. 10:40-11:10 Coffee 11:10-12:00 Ruffo, S (Universita di Firenze) Slow dynamics in systems with long-range interactions Sem 1 12:30-13:30 Lunch at Wolfson Court 14:00-14:50 Stinchcombe, R (Oxford) Asymptotically exact scaling for nonequilibrium static and dynamic critical behaviour Sem 1 We present a scaling approach which we have recently developed for nonequilibrium static and dynamic critical behaviour. It is based on majority rule blocking implemented using complete operator algebra descriptions. These latter descriptions are generally available for particle exclusion models, but have only been pushed to an exact solution for special cases such as the steady-state of the Asymmetric Exclusion Process (biassed hopping of hard core particles). For that particular process we first show how the static scaling can be obtained using the reduced algebra which describes the steady state. We then outline how the full static and dynamic scaling follows from the complete operator algebra. The method gives for any (odd) dilatation factor $b$ the exact critical condition and exponent relations. For $b \rightarrow \infty$, it gives exact values for each exponent, including the dynamic exponent. Generalisations, eg to the partially asymmetric case, and applications, eg to relaxational dynamics of profiles and correlation functions, will be indicated. 14:50-15:20 Tea 15:20-16:10 Henkel, M (Universite Henri Poincare Nancy 1) Dynamical symmetries in phase-ordering kinetics Sem 1 Dynamical scaling in phase-ordering kinetics is well-accepted. We consider the possibility of a larger dynamical symmetry (called local scale-invariance) for this non-equilibrium relaxation phenomenon. Indeed, in many systems with and without detailed balance the Langevin equation can be decomposed into a deterministic' and a stochastic' part in such a way that if the deterministic' part is Galilei-invariant, then the calculation of the full noisy response and correlation functions reduces exactly to the calculation of certain n-point functions calculable within the deterministic' part of the theory. Galilei- and Schroedinger-invariant equations will be constructed. This leads to explicit predictions for the two-time response and correlation functions, in good agreement with simulational results and with the results of several exactly solvable models. 16:10-17:00 Toninelli, F (ENS Lyon) Pinning of random directed polymers: smoothening of the transition and some path properties Sem 1 I will consider a class of models of directed polymers in interaction with a line of random defects. This includes (d+1)-dimensional pinning problems, the (1+1)--dimensional interface wetting model, random copolymers at selective interfaces and other examples. These models are known to present a (de)localization transition at some critical line in the phase diagram. In absence of disorder, the transition can be either of first or of higher order. I will show that, as soon as disorder is present, the transition is always at least of second order. I will then concentrate on the delocalized phase and discuss some typical properties of the paths. (in collaboration with G. Giacomin (Paris 7)) 17:00-18:00 Wine Reception 18:45-19:30 Dinner at Wolfson Court (Residents Only)
 Tuesday 10 January 09:00-09:50 Bouchaud, J-P (CEA-Saclay) Dynamical heterogeneities and growing length scales in glassy systems: physical origin, models and experiments Sem 1 After decades of research, a clear picture of the glass transition phenomenon, common to scores of different materials (molecular glasses, polymers, colloids) is still lacking. Recent theoretical works suggest the existence of dynamic criticality and growing dynamic lengthscales associated to the dynamic slowing down. Various experiments support this view but in a rather indirect manner. We will discuss the physical mechanisms leading to such a growing length scale and define multi-point dynamic susceptibilities quantifying the cooperative dynamics of glass-forming materials that are accessible to experiments, and present some recent experiments supporting these ideas. 09:50-10:40 Garrahan, J-P (Nottingham) Dynamical facilitation view of glass formers Sem 1 This talk deals with the dynamic facilitation approach to the glass transition problem. This perspective is based on the idea that the interesting structure in glass-forming systems is found in the space of trajectories of the dynamics, rather than that of configurations. In contrast to mean-field approaches, dynamic facilitation naturally accounts for the dynamic heterogeneity of glass-forming materials and related fluctuation phenomena such as transport decoupling. I will describe how in the d+1 dimensions of trajectory space one finds order-disorder phenomena that can be organized according to scaling and universality classes. Various predictions from this viewpoint, some yet to be verified experimentally, will be discussed. 10:40-11:10 Coffee 11:10-12:00 Berthier, L (Universite Montpellier II) Length scale for the onset of Fickian diffusion in supercooled liquids Sem 1 12:30-13:30 Lunch at Wolfson Court 14:00-14:50 Coolen, T (King's College, London) Dynamics on finitely connected random graphs Sem 1 14:50-15:20 Tea 15:20-16:10 Poster session I 16:10-17:00 Guerra, F (Universita di Roma La Sapienza) Thermal stochastic dynamics in complex systems Sem 1 18:45-19:30 Dinner at Wolfson Court (Residents Only)
 Wednesday 11 January 09:00-09:50 Marinari, E (Universita di Roma) Low T scaling behavior of 2D disordered and frustrated models Sem 1 The ground state and low T behavior of two-dimensional spin systems with discrete binary couplings are subtle. I present an analysis based on exact computations of finite volume partition functions. I first discuss the fully frustrated model without disorder, and then introduce disorder by changing random links (spin glass) or by unfrustrating random plaquettes (plaquette disorder). In both cases the introduction of disorder changes the properties of the T=0 critical point. 09:50-10:40 Bovier, A (Technische Universitat Berlin) Spectral approaches to ageing Sem 1 We investigate spectral characteristics of Markov chains that exhibit ageing. We consider two rather systems with rather different properties, Bouchaud's trap model and Sinai's random walk, and show how in both cases it is possible to obtain enough information on eigennvalues and eigenfunctions to deduce in an easy way all relevant dynamical properties. 10:40-11:10 Coffee 11:10-12:00 Zippelius, A (Goettingen) Dynamics of gelling liquids Sem 1 The dynamics of randomly crosslinked liquids is addressed via a Rouse- and Zimm-type model with crosslink statistics taken either from bond percolation or Erdoes-Renyi random graphs. While the Rouse type model isolates the effects of the random connectivity on the dynamics of molecular clusters, the Zimm-type model also accounts for hydrodynamic interactions on a preaveraged level. The incoherent intermediate scattering function is computed in thermal equilibrium. It is shown that the cluster size distribution gives rise to an anomalous time decay (stretched exponential) in all of the sol phase. The critical behaviour near the sol-gel transition is analysed and related to the scaling of cluster diffusion constants at the critical point. Second, non-equilibrium dynamics is studied by looking at stress relaxation in simple shear flow. Anomalous stress relaxation and critical rheological properties are derived. Some of the exact results contradict long-standing scaling arguments. 12:30-13:30 Lunch at Wolfson Court 19:30-18:00 Conference Dinner - Pembroke College (Old Library)
 Thursday 12 January 09:00-09:50 Livi, R (Universitá di Firenze) Anomalous heat transport in low dimensional systems Sem 1 Statistical fluctuations are strongly dependent on the space dimension and may yield ill-defined transport coefficients in stationary out--of--equilibrium conditions. Numerical simulations reveal that the heat conductivity diverges in the thermodynamic limit as a power--law of the system size in several 1d models of coupled anharmonic oscillators and hard--sphere gases. Momentum conservation appears as a necessary ingredient for determining such anomalous behavior. Recent theoretical estimates based on the mode-coupling approach provide a possible interpretation of these results. 09:50-10:40 Montanari, A (LPT-ENS) On the relation between length and time scales in glassy systems Sem 1 10:40-11:10 Coffee 11:00-11:10 Ben Arous, G (New York) The Arcsine law and scaling limits for trap models Sem 1 12:30-13:30 Lunch at Wolfson Court 14:00-14:50 Lefevre, A (Oxford) Field theory for Brownian fluids, fluctuation-dissipation theorem and self-consistent resummations Sem 1 14:50-15:20 Tea 15:20-16:10 Poster session II 16:10-17:00 Evans, M (Edinburgh) Disorder and non-conservation in a driven diffusive system Sem 1 The asymmetric exclusion process is a prototypical driven diffusive system. I will discuss a disordered version of the model in which randomly chosen sites do not conserve particle number. The model is motivated by features of many interacting molecular motors such as RNA polymerases. I will discuss the appearance of Griffiths singularities in a nonequilibrium steady state despite the absence of any transition in the pure model. The disorder is also shown to induce a stretched exponential decay of system density with stretching exponent \phi= 2/5. 18:45-19:30 Dinner at Wolfson Court (Residents Only)
 Friday 13 January 09:00-09:50 Godreche, C (CEA-Saclay) Zero-range processes: prototypical stochastic models with slow dynamics and nonequilibrium phase transitions Sem 1 09:50-10:40 Dean, D (Universite Paul Sabatier) Statistics of a slave estimator Sem 1 We analyze the statistics of an estimator, denoted by $\xi_t$ and referred to as the slave, for the equilibrium susceptibility of a one dimensional Langevin process $x_t$ in a potential $\phi(x)$~. The susceptibility can be measured by evolving the slave equation in conjunction with the original Langevin process. This procedure yields a direct estimate of the susceptibility and avoids the need, when performing numerical simulations, to include applied external fields explicitly. The success of the method however depends on the statistical properties of the slave estimator. The joint probability density function for $x_t$ and $\xi_t$ is analyzed. In the case where the potential of the system has a concave component the probability density function of the slave acquires a power law tail characterized by a temperature dependent exponent. Thus we show that while the average value of the slave, in the equilibrium state, is always finite and given by the fluctuation dissipation relation, higher moments and indeed the variance may show divergences. The behavior of the power law exponent is analyzed in a general context and it is calculated explicitly in some specific examples. Our results are confirmed by numerical simulations and we discuss possible measurement discrepancies in the fluctuation dissipation relation which could arise due to this behavior. 10:40-11:10 Coffee 11:10-12:00 Moore, M (Manchester) Towards the theory of the structural glass transition Sem 1 It will be shown that the behaviour described as the "structural glass transition" can be related to that of the Ising spin glass in a magnetic field. 12:30-13:30 Lunch at Wolfson Court 14:00-14:50 Franz, S (ICTP) Metastable states, relaxation times and free-energy barriers in finite dimensional glassy systems Sem 1 14:50-15:20 Tea 15:20-16:10 Toninelli, C (Ecole Normale Superieure) Jamming percolation and glass transition in lattice models Sem 1 16:10-17:00 Ritort, F (Universitat de Barcelona) Recovering folding free energies of RNA molecules in an experimental test of Crooks fluctuation theorem Sem 1 18:45-19:30 Dinner at Wolfson Court (Residents Only)