Table of contents

A summer school on `Ageing and the glass transition' was held at the University of Luxembourg on 18–24 September 2005. It brought together about 60 scientists actively studying the related fields of physical ageing and of the thermodynamics of glass-forming systems when undergoing a glass transition. The programme of the school can be found on the homepage ( http://www.theorie1.physik.uni-erlangen.de/sommerschule.html). The school contained both invited lectures and contributed talks and posters. This volume presents the works contributed to the summer school, while the invited lectures will be published elsewhere (M Henkel, M Pleimling and R Sanctuary (eds), Ageing and the glass transition, Springer Lecture Notes in Physics, Springer (Heidelberg 2006)). We have tried to encourage the exchange between theorists and experimentalists to which the topics treated in these proceedings bear witness. They range from experimental studies on the mechanical response of glasses, biopolymers, and granular materials to the effects of ageing on the long-time modification of the properties of glass-forming polymers, from simulational and analytical studies of theoretical models describing the non-equilibrium statistical mechanics of systems displaying the dynamical scaling typical of ageing phenomena and which are thought to capture essential aspects of glass-forming materials close to a glass transition to more mathematically oriented investigations on the symmetries of these systems.

The `Grande Région' Sar-Lor-Lux is leading European efforts to overcome national and linguistic barriers, with the view of creating a common academic education. Physics has a standing internationalist tradition and the existing trinational integrated course in Physics SLLS (see the homepage http://www.uni-saarland.de/fak7/krueger/integ/sll/d/cursus.htm) is busily developing ways and means towards this goal, in particular through the delivery of multinational and multilingual university degrees in physics, recognized by the partner countries as national degrees. This summer school was a very welcome opportunity for our students to get in contact with leading international activities.

It is a pleasure to thank many individuals for their help, notably J Baller, E Apel, M Heinen-Krumreich and R Wagener. We gratefully acknowledge generous financial support form the Université Franco-Allemande/Deutsch-Französische Hochschule, the University of Luxembourg and the Institute of Physics making the holding of this school possible.

We give an introduction to phase transitions in the steady states of systems that evolve stochastically with equilibrium and nonequilibrium dynamics, the latter defined as those that do not possess a time-reversal symmetry. We try as much as possible to discuss both cases within the same conceptual framework, focussing on dynamically attractive 'peaks' in state space. A quantitative characterisation of these peaks leads to expressions for the partition function and free energy that extend from equilibrium steady states to their nonequilibrium counterparts. We show that for certain classes of nonequilibrium systems that have been exactly solved, these expressions provide precise predictions of their macroscopic phase behaviour.

The dynamics at a critical point provides a simple instance of slow collective evolution, characterised by aging phenomena and by a violation of the fluctuation-dissipation relation even for long times. By virtue of the universality in critical phenomena it is possible to provide quantitative predictions for some aspects of these behaviours by field-theoretical methods. We review some of the theoretical results that have been obtained in recent years for the relevant (universal) quantities, such as the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics.

We discuss some aspects of the non-equilibrium relaxational dynamics which occur after a quench at a disordered critical point. In particular, we focus on the violation of the fluctuation dissipation theorem for local as well as non-local observables and on persistence properties.

A particular type of nonequilibrium critical dynamics is discussed in this paper, in which the initial state is generated in the square lattice Ising model with random fields of zero mean and variance h. Thus we interpolate between the ordered (h = 0) and disordered (h → ∞) initial states. In particular we consider the square lattice Ising model in which for weak enough random fields the clusters of parallel spins are percolating in the initial state. We aim to study the effect of correlations in the initial state on the nonequilibrium dynamics, so we measure the nonequilibrium relaxation of the magnetization and the autocorrelation function. The relaxation of the magnetization, characterized by the initial slip exponent, θ, is not altered by the percolating nature of the initial state. However, the starting part of the magnetization curve is affected by a cluster dissolution effect leading to a reentrance in time.

Many recent experiments probed the off equilibrium dynamics of spin glasses and other glassy systems through temperature cycling protocols, and observed memory and rejuvenation phenomena. Here we show through numerical simulations, using powerful algorithms, that such features can already be observed to some extent in simple models such as two dimensional ferromagnets. We critically discuss these results and review some aspects of the literature in the light of our findings.

The Kovacs protocol, based on the temperature shift experiment originally conceived by A.J. Kovacs and applied on glassy polymers [1], is implemented in an exactly solvable model with facilitated dynamics. This model is based on interacting fast and slow modes represented respectively by spherical spins and harmonic oscillator variables. Due to this fundamental property and to slow dynamics, the model reproduces the characteristic nonmonotonic evolution known as the ''Kovacs effect'', observed in polymers, spin glasses, in granular materials and models of molecular liquids, when similar experimental protocols are implemented.

Some essential dynamical features of the Biroli-Mezard model are discussed. We observe a dynamical slowing down which for higher densities depends both on the observation time and the age of the system. We relate this aging behavior to the real space dynamics of the system, where due to some essential initial restructuring the system gains mobility. This allows us to get a better understanding of what is causing the two-time dependence of the correlation function. Finally, we quantify how heterogenous the slow dynamics of the BM model is by investigating the dynamical susceptibility and discuss its dependence on the age of the system.

The influence of quenching and physical aging on the relaxation behavior of poly(nalkyl methacrylates) with long alkyl groups in the side chain is studied by dielectric spectroscopy. Typical for these side chain polymers is a nanophase separation of incompatible main and side chain parts and the existence of alkyl nanodomains with a typical dimension of 0.5-1.5nm. In larger alkyl nanodomains a polyethylene-like glass transition α_PE occurs at temperatures below the conventional a relaxation. For quenched samples additional peaks on the high frequency wing of this aPE process have been detected in a similar frequency-temperature range where the Arrhenius-like β_PE process is observed for slowly cooled side chain polymers with short alkyl groups and small alkyl nanodomains. This is interpreted as an amplification of the localized dynamics in the alkyl nanodomains and related to the production of additional free volume in quenched samples which disappears during physical aging slightly below T_g(α). Similarities to the aging behavior of conventional glasses and the importance of non-equilibrium effects for the properties of nano-structured materials in the glassy state are discussed.

The concept of effective temperatures in nonequilibrium systems is studied within an exactly solvable model of non-Markovian diffusion. The system is coupled to two heat baths which are kept at different temperatures: one ('fast') bath associated with an uncorrelated Gaussian noise and a second ('slow') bath with an exponential memory kernel. Various definitions of effective temperatures proposed in the literature are evaluated and compared. The range of validity of these definitions is discussed. It is shown in particular, that the effective temperature defined from the fluctuation-dissipation relation mirrors the temperature of the slow bath in parameter regions corresponding to a separation of time scales. On the contrary, quasi-static and thermodynamic definitions of an effective temperature are found to display the temperature of the fast bath in most parameter regions.

I consider ageing behaviour in two exactly solvable reaction-diffusion systems. Ageing exponents and scaling functions are determined. I discuss in particular a case in which the equality of two critical exponents, known from systems with detailed balance, does not hold any more. Secondly it is shown that the form of the scaling functions can be understood by symmetry considerations.

In this paper we present the results obtained concerning the relaxation behaviour of a non equilibrium Ising quantum chain. In particular, we have focues our attention into the transverse magnetization. The out-of-equilibriumness is generated by setting up an initial thermal inhomogeneity. We present two different initial conditions: a completely factorized state, where all the spins are thermalized independently and second a system-bath case, where half of the chain called the system is thermalized at a temperature T_s and the remaining half is at a temperature T_b. In both cases, the magnetization profiles are calculated either analytically or numerically and show a scaling behaviour. It is also found that in the two-temperature case the magnetization relaxes in quantized steps in the strong transverse field region.

We show how to apply the absorbing Markov chain Monte Carlo algorithm of Novotny to simulate kinetically constrained models of glasses. In detail we consider the East model in one dimension. We investigate how to maximize the efficiency of the algorithms, and show that simulation times can be improved on standard continuous time Monte Carlo by several orders of magnitude. We discuss how the method can be applied to other kinetically constrained models with specific focus on the 2-spin facilitated FA model.

Thermal properties of native and denatured biopolymers with quite different chemical and steric structure (globular and fibrillar proteins, DNA, starches) were studied by means of differential scanning calorimetry in a wide range of temperatures and concentrations of water. It was shown that both native and denatured humid biopolymers are glassy systems. The glass transition temperature of these systems strongly depends on percentage of water, with water being simultaneously an intrinsic element of systems' ordered structure and a plasticizer of its amorphous state. On the base of the absolute values of heat capacities for biopolymer-water systems as a whole, heat capacities for biopolymers themselves were calculated as functions on water concentration at fixed temperatures. The S-shaped change of heat capacity observed on diagrams of state both for native and denatured biopolymers is the manifestation of biopolymers' passing through the vitrification region, as it occurs for denatured samples at heating.

The elastic properties of the isotropic state of condensed matter are given by the elastic constants ell and c44. In the liquid state the static shear stiffness c44 vanishes whereas at sufficient high probe frequencies a dynamic shear stiffness may appear. In that latter case the question about the existence of a Cauchy relation appears. It will be shown that a pure Cauchy relation can appear only under special conditions which are rarely fulfilled. For all investigated materials, including ceramics, liquids and glasses, a linear relation between ell and c44 called generalized Cauchy relation is observed, which, surprisingly, follows a linear transformation

In an application-oriented study, the effective transition temperature T_g of organic wood-clearcoatings between a hard, glassy state and a viscoelastic and rubbery state is measured. The value of T_g is important in the eventual development of cracks and a thermomechanical analysis is used to study the photostabilisation performance of some UV absorbers. A weathering exposure test suggests that certain organic UV absorbers have quite a low T_g and may inhibit the crack formation, in contrast with inorganic UV absorbers.

Interesting flow properties are observed when a concentrated suspension of colloidal particles flows into a geometrical constriction. We present here a description of two different experimental techniques used to study the pressure driven flow of dense suspensions of micron- sized hard spheres into glass capillaries. The first one involves the analysis of the driving pressure during the flow, the other one is based on fast confocal microscopy. Technical details are given, together with a selection of preliminary results.

We present an original experimental study of the slow compaction dynamics for two dimensional isotropic granular systems. Compaction dynamics is measured at three different scales : the macroscopic scale through the normalized packing fraction , the mesoscopic scale through the normalized fraction of domains ideally ordered in the system, and the microscopic scale through the grain mobility µ. The domains ideally ordered are found to obey a growth process dominated by the displacement of domain boundaries. We present also preliminary results of three-dimensional simulations with a model of contact dynamics. These results allow to discuss the difference between the two-dimensional and the three-dimensional cases.

Conditional Lie symmetries of semi-linear 1D Schrödinger and diffusion equations are studied in case the mass (or the diffusion constant) is considered as an additional variable and/or where the couplings of the non-linear part have a non-vanishing scaling dimension. In this way, dynamical symmetries of semi-linear Schrödinger equations become related to certain subalgebras of a three-dimensional conformal Lie algebra (conf₃)_C. The representations of these subalgebras are classified and the complete list of conditionally invariant semi-linear Schrödinger equations is obtained. Applications to the phase-ordering kinetics of simple magnets and to simple particle-reaction models are briefly discussed.

In this work we address the problem of analyzing the symmetries of Fokker-Planck equations with logarithmic coefficients. Starting from a nonlinear reaction-diffusion equation with known symmetry algebra, we solve the inverse problem, namely, we find all equations in a given class that are invariant under this symmetry algebra. The class we consider is that of nonlinear Fokker-Planck equations for which the source term is a monomial in the distribution.

We explore the mathematical structure of the infinite-dimensional Schrödinger- Virasoro algebra, and discuss possible applications to the integrability of anisotropic or outof- equilibrium statistical systems with a dynamical exponent z ≠ 1 by defining several correspondences with conformal field theory.