1,253 research outputs found
An exactly solvable toy model that mimics the mode coupling theory of supercooled liquid and glass transition
A toy model is proposed which incorporates the reversible mode coupling
mechanism responsible for ergodic-nonergodic transition with trivial
Hamiltonian in the mode coupling theory (MCT) of structural glass transition.
The model can be analyzed without relying on uncontrolled approximations
inevitable in the current MCT. The strength of hopping processes can be easily
tuned and the ideal glass transition is reproduced only in a certain range of
the strength. On the basis of the analyses of our model we discuss about a
sharp ergodic-nonergodic transition and its smearing out by "hopping".Comment: 5 pages, 2 ps-figures, inappropriate terms replace
The mean-squared displacement of a molecule moving in a glassy system
The mean-squared displacement (MSD) of a hard sphere and of a dumbbell
molecule consisting of two fused hard spheres immersed in a dense hard-sphere
system is calculated within the mode-coupling theory for ideal liquid-glass
transitions. It is proven that the velocity correlator, which is the second
time derivative of the MSD, is the negative of a completely monotone function
for times within the structural-relaxation regime. The MSD is found to exhibit
a large time interval for structural relaxation prior to the onset of the
-process which cannot be described by the asymptotic formulas for the
mode-coupling-theory-bifurcation dynamics. The -process for molecules
with a large elongation is shown to exhibit an anomalously wide cross-over
interval between the end of the von-Schweidler decay and the beginning of
normal diffusion. The diffusivity of the molecule is predicted to vary
non-monotonically as function of its elongation.Comment: 18 pages, 12 figures, Phys. Rev. E, in prin
Cooperative heterogeneous facilitation: multiple glassy states and glass-glass transition
The formal structure of glass singularities in the mode-coupling theory (MCT)
of supercooled liquids dynamics is closely related to that appearing in the
analysis of heterogeneous bootstrap percolation on Bethe lattices, random
graphs and complex networks. Starting from this observation one can build up
microscopic on lattice realizations of schematic MCT based on cooperative
facilitated spin mixtures. I discuss a microscopic implementation of the F13
schematic model including multiple glassy states and the glass-glass
transition. Results suggest that our approach is flexible enough to bridge
alternative theoretical descriptions of glassy matter based on the notions of
quenched disorder and dynamic facilitation.Comment: 4 pages, 2 figure
Self-Organized Criticality Below The Glass Transition
We obtain evidence that the dynamics of glassy systems below the glass
transition is characterized by self-organized criticality. Using molecular
dynamics simulations of a model glass-former we identify clusters of
cooperatively jumping particles. We find string-like clusters whose size is
power-law distributed not only close to T_c but for ALL temperatures below T_c,
indicating self-organized criticality which we interpret as a freezing in of
critical behavior.Comment: 4 pages, 3 figure
Critical Decay at Higher-Order Glass-Transition Singularities
Within the mode-coupling theory for the evolution of structural relaxation in
glass-forming systems, it is shown that the correlation functions for density
fluctuations for states at A_3- and A_4-glass-transition singularities can be
presented as an asymptotic series in increasing inverse powers of the logarithm
of the time t: , where
with p_n denoting some polynomial and x=ln (t/t_0). The results are
demonstrated for schematic models describing the system by solely one or two
correlators and also for a colloid model with a square-well-interaction
potential.Comment: 26 pages, 7 figures, Proceedings of "Structural Arrest Transitions in
Colloidal Systems with Short-Range Attractions", Messina, Italy, December
2003 (submitted
Vibrational origin of the fast relaxation processes in molecular glass-formers
We study the interaction of the relaxation processes with the density
fluctuations by molecular dynamics simulation of a flexible molecule model for
o-terphenyl (oTP) in the liquid and supercooled phases. We find evidence,
besides the structural relaxation, of a secondary vibrational relaxation whose
characteristic time, few ps, is slightly temperature dependent. This i)
confirms the result by Monaco et al. [Phys. Rev, E 62, 7595 (2000)] of the
vibrational nature of the fast relaxation observed in Brillouin Light
Scattering (BLS) experiments in oTP; and ii) poses a caveat on the
interpretation of the BLS spectra of molecular systems in terms of a purely
center of mass dynamics.Comment: RevTeX, 5 pages, 4 eps figure
Frustrated spin- Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the ---- model
The zero-temperature phase diagram of the spin-
---- model on an -stacked square-lattice
bilayer is studied using the coupled cluster method implemented to very high
orders. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor
Heisenberg exchange interactions, of strengths and , respectively, are included in each layer. The two layers are
coupled via a NN interlayer Heisenberg exchange interaction with a strength
. The magnetic order parameter (viz.,
the sublattice magnetization) is calculated directly in the thermodynamic
(infinite-lattice) limit for the two cases when both layers have
antiferromagnetic ordering of either the N\'{e}el or the striped kind, and with
the layers coupled so that NN spins between them are either parallel (when
) to one another. Calculations
are performed at th order in a well-defined sequence of approximations,
which exactly preserve both the Goldstone linked cluster theorem and the
Hellmann-Feynman theorem, with . The sole approximation made is to
extrapolate such sequences of th-order results for to the exact limit,
. By thus locating the points where vanishes, we calculate
the full phase boundaries of the two collinear AFM phases in the
-- half-plane with . In particular, we provide the
accurate estimate, (), for the
position of the quantum triple point (QTP) in the region . We also
show that there is no counterpart of such a QTP in the region ,
where the two quasiclassical phase boundaries show instead an ``avoided
crossing'' behavior, such that the entire region that contains the nonclassical
paramagnetic phases is singly connected
Numerical Investigation of Glassy Dynamics in Low Density Systems
Vitrification in colloidal systems typically occurs at high densities driven
by sharply varying, short-ranged interactions. The possibility of glassy
behavior arising from smoothly varying, long-ranged particle interactions has
received relatively little attention. Here we investigate the behavior of
screened charged particles, and explicitly demonstrate that these systems
exhibit glassy properties in the regime of low temperature and low density.
Properties close to this low density (Wigner) glass transition share many
features with their hard-sphere counterparts, but differ in quantitative
aspects that may be accounted for via microscopic theoretical considerations.Comment: 4 pages, 4 figures, revised versio
Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids
We extend Mode-Coupling Theory (MCT) to inhomogeneous situations, relevant
for supercooled liquid in pores, close to a surface, or in an external field.
We compute the response of the dynamical structure factor to a static
inhomogeneous external potential and provide the first direct evidence that the
standard formulation of MCT is associated with a diverging length scale. We
find in particular that the so called ``cages'' are in fact extended objects.
Although close to the transition the dynamic length grows as |T-T_c|^-1/4 in
_both_ the beta and alpha regimes, our results suggest that the fractal
dimension of correlated clusters is larger in the alpha regime. We also derive
inhomogeneous MCT equations valid to second order in gradients.Comment: 4 page
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