Aging in a simple glassformer

Using molecular dynamics computer simulations we investigate the out-of-equilibrium dynamics of a Lennard-Jones system after a quench from a high temperature to one below the glass transition temperature. By studying the radial distribution function we give evidence that during the aging the system is very close to the critical surface of mode-coupling theory. Furthermore we show that two-time correlation functions show a strong dependence on the waiting time since the quench and that their shape is very different from the one in equilibrium. By investigating the temperature and time dependence of the frequency distribution of the normal modes we show that the energy of the inherent structures can be used to define an effective (time dependent) temperature of the aging system.Comment: Talk presented at ``Unifying Concepts in Glass Physics'', ICTP, Trieste 15 - 18 September 1999; 12 pages of Late

Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases I: Equilibrium Systems

We compute the Lyapunov spectrum and the Kolmogorov-Sinai entropy for a moving particle placed in a dilute, random array of hard disk or hard sphere scatterers - i.e. the dilute Lorentz gas model. This is carried out in two ways: First we use simple kinetic theory arguments to compute the Lyapunov spectrum for both two and three dimensional systems. In order to provide a method that can easily be generalized to non-uniform systems we then use a method based upon extensions of the Lorentz-Boltzmann (LB) equation to include variables that characterize the chaotic behavior of the system. The extended LB equations depend upon the number of dimensions and on whether one is computing positive or negative Lyapunov exponents. In the latter case the extended LB equation is closely related to an "anti-Lorentz-Boltzmann equation" where the collision operator has the opposite sign from the ordinary LB equation. Finally we compare our results with computer simulations of Dellago and Posch and find very good agreement.Comment: 48 pages, 3 ps fig

Kinetics in one-dimensional lattice gas and Ising models from time-dependent density functional theory

Time-dependent density functional theory, proposed recently in the context of atomic diffusion and non-equilibrium processes in solids, is tested against Monte Carlo simulation. In order to assess the basic approximation of that theory, the representation of non-equilibrium states by a local equilibrium distribution function, we focus on one-dimensional lattice models, where all equilibrium properties can be worked exactly from the known free energy as a functional of the density. This functional determines the thermodynamic driving forces away from equilibrium. In our studies of the interfacial kinetics of atomic hopping and spin relaxation, we find excellent agreement with simulations, suggesting that the method is useful also for treating more complex problems.Comment: 8 pages, 5 figures, submitted to Phys. Rev.

Molecular mode-coupling theory for supercooled liquids: Application to water

We present mode-coupling equations for the description of the slow dynamics observed in supercooled molecular liquids close to the glass transition. The mode-coupling theory (MCT) originally formulated to study the slow relaxation in simple atomic liquids, and then extended to the analysis of liquids composed by linear molecules, is here generalized to systems of arbitrarily shaped, rigid molecules. We compare the predictions of the theory for the $q$-vector dependence of the molecular nonergodicity parameters, calculated by solving numerically the molecular MCT equations in two different approximation schemes, with ``exact'' results calculated from a molecular dynamics simulation of supercooled water. The agreement between theory and simulation data supports the view that MCT succeeds in describing the dynamics of supercooled molecular liquids, even for network forming ones.Comment: 22 pages 4 figures Late

Light scattering spectra of supercooled molecular liquids

The light scattering spectra of molecular liquids are derived within a generalized hydrodynamics. The wave vector and scattering angle dependences are given in the most general case and the change of the spectral features from liquid to solidlike is discussed without phenomenological model assumptions for (general) dielectric systems without long-ranged order. Exact microscopic expressions are derived for the frequency-dependent transport kernels, generalized thermodynamic derivatives and the background spectra.Comment: 12 page

Molecular mode-coupling theory applied to a liquid of diatomic molecules

We study the molecular mode coupling theory for a liquid of diatomic molecules. The equations for the critical tensorial nonergodicity parameters ${\bf F}_{ll'}^m(q)$ and the critical amplitudes of the $\beta$ - relaxation ${\bf H}_{ll'}^m(q)$ are solved up to a cut off $l_{co}$ = 2 without any further approximations. Here $l,m$ are indices of spherical harmonics. Contrary to previous studies, where additional approximations were applied, we find in agreement with simulations, that all molecular degrees of freedom vitrify at a single temperature $T_c$. The theoretical results for the non ergodicity parameters and the critical amplitudes are compared with those from simulations. The qualitative agreement is good for all molecular degrees of freedom. To study the influence of the cut off on the non ergodicity parameter, we also calculate the non ergodicity parameters for an upper cut off $l_{co}=4$. In addition we also propose a new method for the calculation of the critical nonergodicity parameterComment: 27 pages, 17 figure

Frequency dependent specific heat of viscous silica

We apply the Mori-Zwanzig projection operator formalism to obtain an expression for the frequency dependent specific heat c(z) of a liquid. By using an exact transformation formula due to Lebowitz et al., we derive a relation between c(z) and K(t), the autocorrelation function of temperature fluctuations in the microcanonical ensemble. This connection thus allows to determine c(z) from computer simulations in equilibrium, i.e. without an external perturbation. By considering the generalization of K(t) to finite wave-vectors, we derive an expression to determine the thermal conductivity \lambda from such simulations. We present the results of extensive computer simulations in which we use the derived relations to determine c(z) over eight decades in frequency, as well as \lambda. The system investigated is a simple but realistic model for amorphous silica. We find that at high frequencies the real part of c(z) has the value of an ideal gas. c'(\omega) increases quickly at those frequencies which correspond to the vibrational excitations of the system. At low temperatures c'(\omega) shows a second step. The frequency at which this step is observed is comparable to the one at which the \alpha-relaxation peak is observed in the intermediate scattering function. Also the temperature dependence of the location of this second step is the same as the one of the $\alpha-$peak, thus showing that these quantities are intimately connected to each other. From c'(\omega) we estimate the temperature dependence of the vibrational and configurational part of the specific heat. We find that the static value of c(z) as well as \lambda are in good agreement with experimental data.Comment: 27 pages of Latex, 8 figure

Dynamical field theory for glass-forming liquids, self-consistent resummations and time-reversal symmetry

We analyse the symmetries and the self-consistent perturbative approaches of dynamical field theories for glassforming liquids. In particular, we focus on the time-reversal symmetry (TRS), which is crucial to obtain fluctuation-dissipation relations (FDRs). Previous field theoretical treatment violated this symmetry, whereas others pointed out that constructing symmetry preserving perturbation theories is a crucial and open issue. In this work we solve this problem and then apply our results to the mode-coupling theory of the glass transition (MCT). We show that in the context of dynamical field theories for glass-forming liquids TRS is expressed as a nonlinear field transformation that leaves the action invariant. Because of this nonlinearity, standard perturbation theories generically do not preserve TRS and in particular FDRs. We show how one can cure this problem and set up symmetry-preserving perturbation theories by introducing some auxiliary fields. As an outcome we obtain Schwinger-Dyson dynamical equations that automatically preserve FDRs and that serve as a basis for carrying out symmetry-preserving approximations. We apply our results to MCT, revisiting previous field theory derivations of MCT equations and showing that they generically violate FDR. We obtain symmetry-preserving mode-coupling equations and discuss their advantages and drawbacks. Furthermore, we show, contrary to previous works, that the structure of the dynamic equations is such that the ideal glass transition is not cut off at any finite order of perturbation theory, even in the presence of coupling between current and density. The opposite results found in previous field theoretical works, such as the ones based on nonlinear fluctuating hydrodynamics, were only due to an incorrect treatment of TRS.Comment: 54 pages, 21 figure

Thermodynamic formalism for systems with Markov dynamics

The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time. We also generalize the formalism --a dynamical Gibbs ensemble construction-- to a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the much-studied fluctuation theorem. We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unravelled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window.Comment: 64 pages, LaTeX; version accepted for publication in Journal of Statistical Physic

Phase equilibria and glass transition in colloidal systems with short-ranged attractive interactions. Application to protein crystallization

We have studied a model of a complex fluid consisting of particles interacting through a hard core and a short range attractive potential of both Yukawa and square-well form. Using a hybrid method, including a self-consistent and quite accurate approximation for the liquid integral equation in the case of the Yukawa fluid, perturbation theory to evaluate the crystal free energies, and mode-coupling theory of the glass transition, we determine both the equilibrium phase diagram of the system and the lines of equilibrium between the supercooled fluid and the glass phases. For these potentials, we study the phase diagrams for different values of the potential range, the ratio of the range of the interaction to the diameter of the repulsive core being the main control parameter. Our arguments are relevant to a variety of systems, from dense colloidal systems with depletion forces, through particle gels, nano-particle aggregation, and globular protein crystallization.Comment: 20 pages, 10 figure