474 research outputs found
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 -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
and the critical amplitudes of the - relaxation
are solved up to a cut off = 2 without any
further approximations.
Here 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 . 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 . 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
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
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