103 research outputs found
Are defect models consistent with the entropy and specific heat of glass-formers?
We show that point-like defect model of glasses cannot explain thermodynamic
properties of glass-formers, as for example the excess specific heat close to
the glass transition, contrary to the claim of J.P. Garrahan, D. Chandler
[Proc. Natl. Acad. Sci. 100, 9710 (2003)]. More general models and approaches
in terms of extended defects are also discussed.Comment: 4 pages, version to appear in J. Chem. Phys with a Note Adde
Super-diffusion around the rigidity transition: Levy and the Lilliputians
By analyzing the displacement statistics of an assembly of horizontally
vibrated bidisperse frictional grains in the vicinity of the jamming transition
experimentally studied before, we establish that their superdiffusive motion is
a genuine Levy flight, but with `jump' size very small compared to the diameter
of the grains. The vibration induces a broad distribution of jumps that are
random in time, but correlated in space, and that can be interpreted as
micro-crack events at all scales. As the volume fraction departs from the
critical jamming density, this distribution is truncated at a smaller and
smaller jump size, inducing a crossover towards standard diffusive motion at
long times. This interpretation contrasts with the idea of temporally
persistent, spatially correlated currents and raises new issues regarding the
analysis of the dynamics in terms of vibrational modes.Comment: 7 pages, 6 figure
Critical scaling and heterogeneous superdiffusion across the jamming/rigidity transition of a granular glass
The dynamical properties of a dense horizontally vibrated bidisperse granular
monolayer are experimentally investigated. The quench protocol produces states
with a frozen structure of the assembly, but the remaining degrees of freedom
associated with contact dynamics control the appearance of macroscopic
rigidity. We provide decisive experimental evidence that this transition is a
critical phenomenon, with increasingly collective and heterogeneous
rearrangements occurring at length scales much smaller than the grains'
diameter, presumably reflecting the contact force network fluctuations.
Dynamical correlation time and length scales soar on both sides of the
transition, as the volume fraction varies over a remarkably tiny range (). We characterize the motion of individual grains,
which becomes super-diffusive at the jamming transition , signaling
long-ranged temporal correlations. Correspondingly, the system exhibits
long-ranged four-point dynamical correlations in space that obey critical
scaling at the transition density.Comment: 4 pages, 8 figure
Critical fluctuations and breakdown of Stokes-Einstein relation in the Mode-Coupling Theory of glasses
We argue that the critical dynamical fluctuations predicted by the
mode-coupling theory (MCT) of glasses provide a natural mechanism to explain
the breakdown of the Stokes-Einstein relation. This breakdown, observed
numerically and experimentally in a region where MCT should hold, is one of the
major difficulty of the theory, for which we propose a natural resolution based
on the recent interpretation of the MCT transition as a bona fide critical
point with a diverging length scale. We also show that the upper critical
dimension of MCT is d_c=8.Comment: Proceedings of the workshop on non-equilibrium phenomena in
supercooled fluids, glasses and amorphous materials (17-22 September, 2006,
Pisa
Mode-Coupling as a Landau Theory of the Glass Transition
We derive the Mode Coupling Theory (MCT) of the glass transition as a Landau
theory, formulated as an expansion of the exact dynamical equations in the
difference between the correlation function and its plateau value. This sheds
light on the universality of MCT predictions. While our expansion generates
higher order non-local corrections that modify the standard MCT equations, we
find that the square root singularity of the order parameter, the scaling
function in the \beta regime and the functional relation between the exponents
defining the \alpha and \beta timescales are universal and left intact by these
corrections.Comment: 6 pages, 1 figure, submitted to EPL; corrected typos in the abstract;
corrected minor typo in reference
Evidence of growing spatial correlations at the glass transition from nonlinear response experiments
The ac nonlinear dielectric response of glycerol was
measured close to its glass transition temperature to investigate the
prediction that supercooled liquids respond in an increasingly non-linear way
as the dynamics slows down (as spin-glasses do). We find that
indeed displays several non trivial features. It is peaked
as a function of the frequency and obeys scaling as a function of
, with the relaxation time of the liquid. The height
of the peak, proportional to the number of dynamically correlated molecules
, increases as the system becomes glassy, and decays as a
power-law of over several decades beyond the peak. These findings
confirm the collective nature of the glassy dynamics and provide the first
direct estimate of the dependence of .Comment: 22 pages, 6 figures. With respect to v1, a few new sentences were
added in the introduction and conclusion, references were updated, some typos
corrected
Non-linear susceptibility in glassy systems: a probe for cooperative dynamical length scales
We argue that for generic systems close to a critical point, an extended
Fluctuation-Dissipation relation connects the low frequency non-linear (cubic)
susceptibility to the four-point correlation function. In glassy systems, the
latter contains interesting information on the heterogeneity and cooperativity
of the dynamics. Our result suggests that if the abrupt slowing down of glassy
materials is indeed accompanied by the growth of a cooperative length ell, then
the non-linear, 3 omega response to an oscillating field should substantially
increase and give direct information on the temperature (or density) dependence
of ell. The analysis of the non-linear compressibility or the dielectric
susceptibility in supercooled liquids, or the non-linear magnetic
susceptibility in spin-glasses, should give access to a cooperative length
scale, that grows as the temperature is decreased or as the age of the system
increases. Our theoretical analysis holds exactly within the Mode-Coupling
Theory of glasses.Comment: 12 pages, 3 figures; a careful discussion of the spin-glass case in a
field adde
Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations
We study in detail the predictions of various theoretical approaches, in
particular mode-coupling theory (MCT) and kinetically constrained models
(KCMs), concerning the time, temperature, and wavevector dependence of
multi-point correlation functions that quantify the strength of both induced
and spontaneous dynamical fluctuations. We also discuss the precise predictions
of MCT concerning the statistical ensemble and microscopic dynamics dependence
of these multi-point correlation functions. These predictions are compared to
simulations of model fragile and strong glass-forming liquids. Overall, MCT
fares quite well in the fragile case, in particular explaining the observed
crucial role of the statistical ensemble and microscopic dynamics, while MCT
predictions do not seem to hold in the strong case. KCMs provide a simplified
framework for understanding how these multi-point correlation functions may
encode dynamic correlations in glassy materials. However, our analysis
highlights important unresolved questions concerning the application of KCMs to
supercooled liquids.Comment: 23 pages, 12 fig
Spectral Density of Sparse Sample Covariance Matrices
Applying the replica method of statistical mechanics, we evaluate the
eigenvalue density of the large random matrix (sample covariance matrix) of the
form , where is an real sparse random matrix.
The difference from a dense random matrix is the most significant in the tail
region of the spectrum. We compare the results of several approximation
schemes, focusing on the behavior in the tail region.Comment: 22 pages, 4 figures, minor corrections mad
- …