14,776 research outputs found
Symmetry Breaking Bulk Effects in Local D-brane Models
We study symmetry breaking effects in local D-brane models that arise as a
result of compactification, taking models constructed on C^3/Z_3 as prototype.
Zero-modes of the Lichnerowicz operator in cone-like geometries have a power
law behaviour; thus the leading symmetry breaking effects are captured by the
modes with the lowest scaling dimension which transform non-trivially under the
isometry group. Combining this with the fact that global symmetries in local
models are gauged upon compactification we determine the strength and form of
the leading operators responsible for the symmetry breaking. We find a
hierarchical separation in the size of symmetry breaking parameters.Comment: 13 pages, 1 figure; v2 typos removed; v3 JHEP versio
Hierarchical Mean-Field Theories in Quantum Statistical Mechanics
We present a theoretical framework and a calculational scheme to study the
coexistence and competition of thermodynamic phases in quantum statistical
mechanics. The crux of the method is the realization that the microscopic
Hamiltonian, modeling the system, can always be written in a hierarchical
operator language that unveils all symmetry generators of the problem and,
thus, possible thermodynamic phases. In general one cannot compute the
thermodynamic or zero-temperature properties exactly and an approximate scheme
named ``hierarchical mean-field approach'' is introduced. This approach treats
all possible competing orders on an equal footing. We illustrate the
methodology by determining the phase diagram and quantum critical point of a
bosonic lattice model which displays coexistence and competition between
antiferromagnetism and superfluidity.Comment: 4 pages, 2 psfigures. submitted Phys. Rev.
Stringy Origin of Discrete R-symmetries
Discrete symmetries play a crucial role in particle physics. They appear
abundantly in string model constructions. We focus here on the case of discrete
-symmetries which are intrinsically connected to the Lorentz group in extra
dimensions and the appearance of -extended supersymmetry. In that sense,
discrete -symmetries can be understood as "fractionally" extended
supersymmetry. These symmetries reveal insight about the location of fields in
extra dimensions (in particular the Higgs boson). Applications can be found in
the solution of the -problem, suppression of proton decay and the
structure of the soft terms of broken supersymmetry.Comment: Proceedings of the Corfu Summer Institute 2016 "School and Workshops
on Elementary Particle Physics and Gravity",31 August - 23 September, 2016,
Corfu, Greec
Algebraic Approach to Interacting Quantum Systems
We present an algebraic framework for interacting extended quantum systems to
study complex phenomena characterized by the coexistence and competition of
different states of matter. We start by showing how to connect different
(spin-particle-gauge) {\it languages} by means of exact mappings (isomorphisms)
that we name {\it dictionaries} and prove a fundamental theorem establishing
when two arbitrary languages can be connected. These mappings serve to unravel
symmetries which are hidden in one representation but become manifest in
another. In addition, we establish a formal link between seemingly unrelated
physical phenomena by changing the language of our model description. This link
leads to the idea of {\it universality} or equivalence. Moreover, we introduce
the novel concept of {\it emergent symmetry} as another symmetry guiding
principle. By introducing the notion of {\it hierarchical languages}, we
determine the quantum phase diagram of lattice models (previously unsolved) and
unveil hidden order parameters to explore new states of matter. Hierarchical
languages also constitute an essential tool to provide a unified description of
phases which compete and coexist. Overall, our framework provides a simple and
systematic methodology to predict and discover new kinds of orders. Another
aspect exploited by the present formalism is the relation between condensed
matter and lattice gauge theories through quantum link models. We conclude
discussing applications of these dictionaries to the area of quantum
information and computation with emphasis in building new models of computation
and quantum programming languages.Comment: 44 pages, 14 psfigures. Advances in Physics 53, 1 (2004
Image Sampling with Quasicrystals
We investigate the use of quasicrystals in image sampling. Quasicrystals
produce space-filling, non-periodic point sets that are uniformly discrete and
relatively dense, thereby ensuring the sample sites are evenly spread out
throughout the sampled image. Their self-similar structure can be attractive
for creating sampling patterns endowed with a decorative symmetry. We present a
brief general overview of the algebraic theory of cut-and-project quasicrystals
based on the geometry of the golden ratio. To assess the practical utility of
quasicrystal sampling, we evaluate the visual effects of a variety of
non-adaptive image sampling strategies on photorealistic image reconstruction
and non-photorealistic image rendering used in multiresolution image
representations. For computer visualization of point sets used in image
sampling, we introduce a mosaic rendering technique.Comment: For a full resolution version of this paper, along with supplementary
materials, please visit at
http://www.Eyemaginary.com/Portfolio/Publications.htm
A Discrete Geometric Optimal Control Framework for Systems with Symmetries
This paper studies the optimal motion control of
mechanical systems through a discrete geometric approach. At
the core of our formulation is a discrete Lagrange-d’Alembert-
Pontryagin variational principle, from which are derived discrete
equations of motion that serve as constraints in our optimization
framework. We apply this discrete mechanical approach to
holonomic systems with symmetries and, as a result, geometric
structure and motion invariants are preserved. We illustrate our
method by computing optimal trajectories for a simple model of
an air vehicle flying through a digital terrain elevation map, and
point out some of the numerical benefits that ensue
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