354 research outputs found
Do current-density nonlinearities cut off the glass transition?
Extended mode coupling theories for dense fluids predict that nonlinear
current-density couplings cut off the singular `ideal glass transition',
present in the standard mode coupling theory where such couplings are ignored.
We suggest here that, rather than allowing for activated processes as sometimes
supposed, contributions from current-density couplings are always negligible
close to a glass transition. We discuss in schematic terms how activated
processes can nonetheless cut off the transition, by causing the memory
function to become linear in correlators at late times.Comment: 4 page
Expansion of the Gibbs potential for quantum many-body systems: General formalism with applications to the spin glass and the weakly non-ideal Bose gas
For general quantum systems the power expansion of the Gibbs potential and
consequently the power expansion of the self energy is derived in terms of the
interaction strength. Employing a generalization of the projector technique a
compact representation of the general terms of the expansion results. The
general aspects of the approach are discussed with special emphasis on the
effects characteristic for quantum systems. The expansion is systematic and
leads directly to contributions beyond mean-field of all thermodynamic
quantities. These features are explicitly demonstrated and illustrated for two
non-trivial systems, the infinite range quantum spin glass and the weakly
interacting Bose gas. The Onsager terms of both systems are calculated, which
represent the first beyond mean-field contributions. For the spin glass new
TAP-like equations are presented and discussed in the paramagnetic region. The
investigation of the Bose gas leads to a beyond mean-field thermodynamic
description. At the Bose-Einstein condensation temperature complete agreement
is found with the results presented recently by alternative techniques.Comment: 17 pages, 0 figures; revised version accepted by Phys Rev
On the Adam-Gibbs-Wolynes scenario for the viscosity increase in glasses
We reformulate the interpretation of the mean-field glass transition scenario
for finite dimensional systems, proposed by Wolynes and collaborators.
This allows us to establish clearly a temperature dependent length xi* above
which the mean-field glass transition picture has to be modified. We argue in
favor of the mosaic state introduced by Wolynes and collaborators, which leads
to the Adam-Gibbs relation between the viscosity and configurational entropy of
glass forming liquids.
Our argument is a mixture of thermodynamics and kinetics, partly inspired by
the Random Energy
Model: small clusters of particles are thermodynamically frozen in low energy
states, whereas large clusters are kinetically frozen by large activation
energies. The relevant relaxation time is that of the smallest `liquid'
clusters. Some physical consequences are discussed.Comment: 8 page
Finite size effects in the dynamics of glass-forming liquids
We present a comprehensive theoretical study of finite size effects in the
relaxation dynamics of glass-forming liquids. Our analysis is motivated by
recent theoretical progress regarding the understanding of relevant correlation
length scales in liquids approaching the glass transition. We obtain
predictions both from general theoretical arguments and from a variety of
specific perspectives: mode-coupling theory, kinetically constrained and defect
models, and random first order transition theory. In the latter approach, we
predict in particular a non-monotonic evolution of finite size effects across
the mode-coupling crossover due to the competition between mode-coupling and
activated relaxation. We study the role of competing relaxation mechanisms in
giving rise to non-monotonic finite size effects by devising a kinetically
constrained model where the proximity to the mode-coupling singularity can be
continuously tuned by changing the lattice topology. We use our theoretical
findings to interpret the results of extensive molecular dynamics studies of
four model liquids with distinct structures and kinetic fragilities. While the
less fragile model only displays modest finite size effects, we find a more
significant size dependence evolving with temperature for more fragile models,
such as Lennard-Jones particles and soft spheres. Finally, for a binary mixture
of harmonic spheres we observe the predicted non-monotonic temperature
evolution of finite size effects near the fitted mode-coupling singularity,
suggesting that the crossover from mode-coupling to activated dynamics is more
pronounced for this model. Finally, we discuss the close connection between our
results and the recent report of a non-monotonic temperature evolution of a
dynamic length scale near the mode-coupling crossover in harmonic spheres.Comment: 19 pages, 10 figures. V2: response to referees + refs added (close to
published version
Quantum fluctuations can promote or inhibit glass formation
The very nature of glass is somewhat mysterious: while relaxation times in
glasses are of sufficient magnitude that large-scale motion on the atomic level
is essentially as slow as it is in the crystalline state, the structure of
glass appears barely different than that of the liquid that produced it.
Quantum mechanical systems ranging from electron liquids to superfluid helium
appear to form glasses, but as yet no unifying framework exists connecting
classical and quantum regimes of vitrification. Here we develop new insights
from theory and simulation into the quantum glass transition that surprisingly
reveal distinct regions where quantum fluctuations can either promote or
inhibit glass formation.Comment: Accepted for publication in Nature Physics. 22 pages, 3 figures, 1
Tabl
Potential energy landscape of finite-size mean-field models for glasses
connected spin-glass models with a discontinuous transition. In the
thermodynamic limit the equilibrium properties in the high temperature phase
are described by the schematic Mode Coupling Theory of super-cooled liquids. We
show that {\it finite-size} fully connected spin-glass models do exhibit
properties typical of Lennard-Jones systems when both are near the critical
glass transition, where thermodynamics is ruled by energy minima distribution.
Our study opens the way to consider activated processes in real glasses through
finite-size corrections (i.e. calculations beyond the saddle point
approximation) in mean-field spin-glass models.Comment: 8 pages, 3 postscript figures, EPL format, improved versio
Coarsening of Disordered Quantum Rotors under a Bias Voltage
We solve the dynamics of an ensemble of interacting rotors coupled to two
leads at different chemical potential letting a current flow through the system
and driving it out of equilibrium. We show that at low temperature the
coarsening phase persists under the voltage drop up to a critical value of the
applied potential that depends on the characteristics of the electron
reservoirs. We discuss the properties of the critical surface in the
temperature, voltage, strength of quantum fluctuations and coupling to the bath
phase diagram. We analyze the coarsening regime finding, in particular, which
features are essentially quantum mechanical and which are basically classical
in nature. We demonstrate that the system evolves via the growth of a coherence
length with the same time-dependence as in the classical limit, -- the scalar curvature driven universality class. We obtain the
scaling function of the correlation function at late epochs in the coarsening
regime and we prove that it coincides with the classical one once a prefactor
that encodes the dependence on all the parameters is factorized. We derive a
generic formula for the current flowing through the system and we show that,
for this model, it rapidly approaches a constant that we compute.Comment: 53 pages, 12 figure
Numerical simulations of liquids with amorphous boundary conditions
It has recently become clear that simulations under amorphpous boundary
conditions (ABCs) can provide valuable information on the dynamics and
thermodynamics of disordered systems with no obvious ordered parameter. In
particular, they allow to detect a correlation length that is not measurable
with standard correlation functions. Here we explain what exactly is meant by
ABCs, discuss their relation with point-to-set correlations and briefly
describe some recent results obtained with this technique.Comment: Presented at STATPHYS 2
Fluctuations in the coarsening dynamics of the O(N) model: are they similar to those in glassy systems?
We study spatio-temporal fluctuations in the non-equilibrium dynamics of the
d dimensional O(N) in the large N limit. We analyse the invariance of the
dynamic equations for the global correlation and response in the slow ageing
regime under transformations of time. We find that these equations are
invariant under scale transformations. We extend this study to the action in
the dynamic generating functional finding similar results. This model therefore
falls into a different category from glassy problems in which full
time-reparametrisation invariance, a larger symmetry that emcompasses time
scale invariance, is expected to be realised asymptotically. Consequently, the
spatio-temporal fluctuations of the large N O(N) model should follow a
different pattern from that of glassy systems. We compute the fluctuations of
local, as well as spatially separated, two-field composite operators and
responses, and we confront our results with the ones found numerically for the
3d Edwards-Anderson model and kinetically constrained lattice gases. We analyse
the dependence of the fluctuations of the composite operators on the growing
domain length and we compare to what has been found in super-cooled liquids and
glasses. Finally, we show that the development of time-reparametrisation
invariance in glassy systems is intimately related to a well-defined and finite
effective temperature, specified from the modification of the
fluctuation-dissipation theorem out of equilibrium. We then conjecture that the
global asymptotic time-reparametrisation invariance is broken down to time
scale invariance in all coarsening systems.Comment: 57 pages, 5 figure
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