67 research outputs found
Energy Landscape and Overlap Distribution of Binary Lennard-Jones Glasses
We study the distribution of overlaps of glassy minima, taking proper care of
residual symmetries of the system. Ensembles of locally stable, low lying
glassy states are efficiently generated by rapid cooling from the liquid phase
which has been equilibrated at a temperature . Varying , we
observe a transition from a regime where a broad range of states are sampled to
a regime where the system is almost always trapped in a metastable glassy
state. We do not observe any structure in the distribution of overlaps of
glassy minima, but find only very weak correlations, comparable in size to
those of two liquid configurations.Comment: 7 pages, 5 figures, uses europhys-style. Minor notational changes,
typos correcte
Thermal Equilibrium with the Wiener Potential: Testing the Replica Variational Approximation
We consider the statistical mechanics of a classical particle in a
one-dimensional box subjected to a random potential which constitutes a Wiener
process on the coordinate axis. The distribution of the free energy and all
correlation functions of the Gibbs states may be calculated exactly as a
function of the box length and temperature. This allows for a detailed test of
results obtained by the replica variational approximation scheme. We show that
this scheme provides a reasonable estimate of the averaged free energy.
Furthermore our results shed more light on the validity of the concept of
approximate ultrametricity which is a central assumption of the replica
variational method.Comment: 6 pages, 1 file LaTeX2e generating 2 eps-files for 2 figures
automaticall
Saddles on the potential energy landscape of a Lennard-Jones liquid
By means of molecular dynamics simulations, we study the stationary points of
the potential energy in a Lennard-Jones liquid, giving a purely geometric
characterization of the energy landscape of the system. We find a linear
relation between the degree of instability of the stationary points and their
potential energy, and we locate the energy where the instability vanishes. This
threshold energy marks the border between saddle-dominated and minima-dominated
regions of the energy landscape. The temperature where the potential energy of
the Stillinger-Weber minima becomes equal to the threshold energy turns out to
be very close to the mode-coupling transition temperature.Comment: Invited talk presented by A.C. at the Conference: Disordered and
Complex Systems, King's College London, July 200
Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials
We study a non-relativistic charged particle on the Euclidean plane R^2
subject to a perpendicular constant magnetic field and an R^2-homogeneous
random potential in the approximation that the corresponding random Landau
Hamiltonian on the Hilbert space L^2(R^2) is restricted to the eigenspace of a
single but arbitrary Landau level. For a wide class of Gaussian random
potentials we rigorously prove that the associated restricted integrated
density of states is absolutely continuous with respect to the Lebesgue
measure. We construct explicit upper bounds on the resulting derivative, the
restricted density of states. As a consequence, any given energy is seen to be
almost surely not an eigenvalue of the restricted random Landau Hamiltonian.Comment: 16 pages, to appear in "Journal of Mathematical Physics
A model for gelation with explicit solvent effects: Structure and dynamics
We study a two-component model for gelation consisting of -functional
monomers (the gel) and inert particles (the solvent). After equilibration as a
simple liquid, the gel particles are gradually crosslinked to each other until
the desired number of crosslinks has been attained. At a critical crosslink
density the largest gel cluster percolates and an amorphous solid forms. This
percolation process is different from ordinary lattice or continuum percolation
of a single species in the sense that the critical exponents are new. As the
crosslink density approaches its critical value , the shear viscosity
diverges: with a nonuniversal
concentration-dependent exponent.Comment: 6 pages, 9 figure
Goldstone-type fluctuations and their implications for the amorphous solid state
In sufficiently high spatial dimensions, the formation of the amorphous (i.e.
random) solid state of matter, e.g., upon sufficent crosslinking of a
macromolecular fluid, involves particle localization and, concommitantly, the
spontaneous breakdown of the (global, continuous) symmetry of translations.
Correspondingly, the state supports Goldstone-type low energy, long wave-length
fluctuations, the structure and implications of which are identified and
explored from the perspective of an appropriate replica field theory. In terms
of this replica perspective, the lost symmetry is that of relative translations
of the replicas; common translations remain as intact symmetries, reflecting
the statistical homogeneity of the amorphous solid state. What emerges is a
picture of the Goldstone-type fluctuations of the amorphous solid state as
shear deformations of an elastic medium, along with a derivation of the shear
modulus and the elastic free energy of the state. The consequences of these
fluctuations -- which dominate deep inside the amorphous solid state -- for the
order parameter of the amorphous solid state are ascertained and interpreted in
terms of their impact on the statistical distribution of localization lengths,
a central diagnostic of the the state. The correlations of these order
parameter fluctuations are also determined, and are shown to contain
information concerning further diagnostics of the amorphous solid state, such
as spatial correlations in the statistics of the localization characteristics.
Special attention is paid to the properties of the amorphous solid state in two
spatial dimensions, for which it is shown that Goldstone-type fluctuations
destroy particle localization, the order parameter is driven to zero, and
power-law order-parameter correlations hold.Comment: 20 pages, 3 figure
Critical behaviour of the Rouse model for gelling polymers
It is shown that the traditionally accepted "Rouse values" for the critical
exponents at the gelation transition do not arise from the Rouse model for
gelling polymers. The true critical behaviour of the Rouse model for gelling
polymers is obtained from spectral properties of the connectivity matrix of the
fractal clusters that are formed by the molecules. The required spectral
properties are related to the return probability of a "blind ant"-random walk
on the critical percolating cluster. The resulting scaling relations express
the critical exponents of the shear-stress-relaxation function, and hence those
of the shear viscosity and of the first normal stress coefficient, in terms of
the spectral dimension of the critical percolating cluster and the
exponents and of the cluster-size distribution.Comment: 9 pages, slightly extended version, to appear in J. Phys.
Shear viscosity of a crosslinked polymer melt
We investigate the static shear viscosity on the sol side of the
vulcanization transition within a minimal mesoscopic model for the
Rouse-dynamics of a randomly crosslinked melt of phantom polymers. We derive an
exact relation between the viscosity and the resistances measured in a
corresponding random resistor network. This enables us to calculate the
viscosity exactly for an ensemble of crosslinks without correlations. The
viscosity diverges logarithmically as the critical point is approached. For a
more realistic ensemble of crosslinks amenable to the scaling description of
percolation, we prove the scaling relation between the critical
exponent of the viscosity, the thermal exponent associated with the
gel fraction and the crossover exponent of a random resistor network.Comment: 8 pages, uses Europhysics Letters style; Revisions: results extende
The distance between Inherent Structures and the influence of saddles on approaching the mode coupling transition in a simple glass former
We analyze through molecular dynamics simulations of a Lennard-Jones binary
mixture the statistics of the distances between inherent structures (IS)
sampled at temperatures above the mode coupling transition temperature T_MCT.
We take equilibrated configurations and randomly perturb the coordinates of a
given number of particles. After that we take the nearest IS of both the
original configuration and the perturbed one and evaluate the distance between
them. This distance presents an inflection point near T~1 with a strong
decrease below this temperature and goes to a small but nonzero value on
approaching T_MCT. In the low temperature region we study the statistics of
events which give zero distance, i.e. dominated by minima, and find evidence
that the number of saddles decreases exponentially near T_MCT. This implies
that saddles continue to exist even for T<=T_MCT. As at T_MCT the extrapolated
diffusivity goes to zero our results imply that there are saddles associated
with nondiffusional events at T<T_MCT.Comment: 5 pages, 5 ps figure
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