10 research outputs found
Jamming versus Glass Transitions
Recent ideas based on the properties of assemblies of frictionless particles
in mechanical equilibrium provide a perspective of amorphous systems different
from that offered by the traditional approach originating in liquid theory. The
relation, if any, between these two points of view, and the relevance of the
former to the glass phase, has been difficult to ascertain. In this paper we
introduce a model for which both theories apply strictly: it exhibits on the
one hand an ideal glass transition and on the other `jamming' features
(fragility, soft modes) virtually identical to that of real systems. This
allows us to disentangle the different contents and domains of applicability of
the two physical phenomena.Comment: 4 pages, 6 figures Modified content, new figur
Constraint optimization and landscapes
We describe an effective landscape introduced in [1] for the analysis of
Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph
Coloring. This geometric construction reexpresses these problems in the more
familiar terms of optimization in rugged energy landscapes. In particular, it
allows one to understand the puzzling fact that unsophisticated programs are
successful well beyond what was considered to be the `hard' transition, and
suggests an algorithm defining a new, higher, easy-hard frontier.Comment: Contribution to STATPHYS2
Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
We study first-order quantum phase transitions in models where the mean-field
traitment is exact, and the exponentially fast closure of the energy gap with
the system size at the transition. We consider exactly solvable ferromagnetic
models, and show that they reduce to the Grover problem in a particular limit.
We compute the coefficient in the exponential closure of the gap using an
instantonic approach, and discuss the (dire) consequences for quantum
annealing.Comment: 6 pages, 3 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