29,188 research outputs found
The "glass transition'' as a topological defect driven transition in a distribution of crystals and a prediction of a universal viscosity collapse
Topological defects are typically quantified relative to ordered backgrounds.
The importance of these defects to the understanding of physical phenomena
including diverse equilibrium melting transitions from low temperature ordered
to higher temperatures disordered systems (and vice versa) can hardly be
overstated. Amorphous materials such as glasses seem to constitute a
fundamental challenge to this paradigm. A long held dogma is that transitions
into and out of an amorphous glassy state are distinctly different from typical
equilibrium phase transitions and must call for radically different concepts.
In this work, we critique this belief. We examine systems that may be viewed as
simultaneous distribution of different ordinary equilibrium structures. In
particular, we focus on the analogs of melting (or freezing) transitions in
such distributed systems. The theory that we arrive at yields dynamical,
structural, and thermodynamic behaviors of glasses and supercooled fluids that,
for the properties tested thus far, are in qualitative and quantitative
agreement with experiment. We arrive at a prediction for the viscosity and
dielectric relaxations that is universally satisfied for all experimentally
measured supercooled liquids and glasses over 15 decades.Comment: 21 pages, 2 figure
Crystallization and melting of bacteria colonies and Brownian Bugs
Motivated by the existence of remarkably ordered cluster arrays of bacteria
colonies growing in Petri dishes and related problems, we study the spontaneous
emergence of clustering and patterns in a simple nonequilibrium system: the
individual-based interacting Brownian bug model. We map this discrete model
into a continuous Langevin equation which is the starting point for our
extensive numerical analyses. For the two-dimensional case we report on the
spontaneous generation of localized clusters of activity as well as a
melting/freezing transition from a disordered or isotropic phase to an ordered
one characterized by hexagonal patterns. We study in detail the analogies and
differences with the well-established Kosterlitz-Thouless-Halperin-Nelson-Young
theory of equilibrium melting, as well as with another competing theory. For
that, we study translational and orientational correlations and perform a
careful defect analysis. We find a non standard one-stage, defect-mediated,
transition whose nature is only partially elucidated.Comment: 13 Figures. 14 pages. Submitted to Phys. Rev.
Localization on the D-brane, two-dimensional gauge theory and matrix models
We consider the effective topological field theory on Euclidean D-strings
wrapping on a 2-cycle in the internal space. We evaluate the vev of a suitable
operator corresponding to the chemical potential of vortices bounded to the
D-strings, and find that it reduces to the partition function of generalized
two-dimensional Yang-Mills theory as a result of localization. We argue that
the partition function gives a grand canonical ensemble of multi-instanton
corrections for four-dimensional N=2 gauge theory in a suitable large N limit.
We find two-dimensional gauge theories that provide the instanton partition
function for four-dimensional N=2 theories with the hypermultiplets in the
adjoint and fundamental representations. We also propose a partition function
that gives the instanton contributions to four-dimensional N=2 quiver gauge
theory. We discuss the relation between Nekrasov's instanton partition function
and the Dijkgraaf-Vafa theory in terms of large N phase transitions of the
generalized two-dimensional Yang-Mills theory.Comment: 40 pages, 5 figures, LaTeX2e, typos corrected, references added,
Final version to appear in Physical Review
- …