2,025 research outputs found
Form-factors computation of Friedel oscillations in Luttinger liquids
We show how to analytically determine for the "Friedel
oscillations" of charge density by a single impurity in a 1D Luttinger liquid
of spinless electrons.Comment: Revtex, epsf, 4pgs, 2fig
In situ experimental study of a near-field lens at visible frequencies
Frequency dependent near-field scanning optical microscopy (NSOM) measurements of plasmon-mediated near-field focusing using a 50 nm thick Au film are presented. In these studies the tip aperture of a NSOM probe acts as a localized light source, while the near-field image formed by the metal lens is detected in situ using nanoscale scatterers placed in the image plane. By scanning the relative position of object and probe, the near-field image generated by the lens is resolved. NSOM scans performed at different illumination frequencies reveal an optimum near-field image quality at frequencies close to the surface plasmon resonance frequency
Boundary breathers in the sinh-Gordon model
We present an investigation of the boundary breather states of the
sinh-Gordon model restricted to a half-line. The classical boundary breathers
are presented for a two parameter family of integrable boundary conditions.
Restricting to the case of boundary conditions which preserve the \phi -->
-\phi symmetry of the bulk theory, the energy spectrum of the boundary states
is computed in two ways: firstly, by using the bootstrap technique and
subsequently, by using a WKB approximation. Requiring that the two descriptions
of the spectrum agree with each other allows a determination of the
relationship between the boundary parameter, the bulk coupling constant, and
the parameter appearing in the reflection factor derived by Ghoshal to describe
the scattering of the sinh-Gordon particle from the boundary.Comment: 16 pages amslate
Exact noncommutative solitons in p-adic strings and BSFT
The tachyon field of p-adic string theory is made noncommutative by replacing
ordinary products with noncommutative products in its exact effective action.
The same is done for the boundary string field theory, treated as the p -> 1
limit of the p-adic string. Solitonic lumps corresponding to D-branes are
obtained for all values of the noncommutative parameter theta. This is in
contrast to usual scalar field theories in which the noncommutative solitons do
not persist below a critical value of theta. As theta varies from zero to
infinity, the solution interpolates smoothly between the soliton of the p-adic
theory (respectively BSFT) to the noncommutative soliton.Comment: 1+14 pages (harvmac b), 1 eps figure, v2: references added, typos
correcte
Characterizing Distances of Networks on the Tensor Manifold
At the core of understanding dynamical systems is the ability to maintain and
control the systems behavior that includes notions of robustness,
heterogeneity, or regime-shift detection. Recently, to explore such functional
properties, a convenient representation has been to model such dynamical
systems as a weighted graph consisting of a finite, but very large number of
interacting agents. This said, there exists very limited relevant statistical
theory that is able cope with real-life data, i.e., how does perform analysis
and/or statistics over a family of networks as opposed to a specific network or
network-to-network variation. Here, we are interested in the analysis of
network families whereby each network represents a point on an underlying
statistical manifold. To do so, we explore the Riemannian structure of the
tensor manifold developed by Pennec previously applied to Diffusion Tensor
Imaging (DTI) towards the problem of network analysis. In particular, while
this note focuses on Pennec definition of geodesics amongst a family of
networks, we show how it lays the foundation for future work for developing
measures of network robustness for regime-shift detection. We conclude with
experiments highlighting the proposed distance on synthetic networks and an
application towards biological (stem-cell) systems.Comment: This paper is accepted at 8th International Conference on Complex
Networks 201
Boundary Reflection Matrix for Affine Toda Field Theory
We present one loop boundary reflection matrix for Toda field
theory defined on a half line with the Neumann boundary condition. This result
demonstrates a nontrivial cancellation of non-meromorphic terms which are
present when the model has a particle spectrum with more than one mass. Using
this result, we determine uniquely the exact boundary reflection matrix which
turns out to be \lq non-minimal' if we assume the strong-weak coupling \lq
duality'.Comment: 14 pages, Late
Inferring spatial source of disease outbreaks using maximum entropy
Mathematical modeling of disease outbreaks can infer the future trajectory of an epidemic, allowing for making more informed policy decisions. Another task is inferring the origin of a disease, which is relatively difficult with current mathematical models. Such frameworks, across varying levels of complexity, are typically sensitive to input data on epidemic parameters, case counts, and mortality rates, which are generally noisy and incomplete. To alleviate these limitations, we propose a maximum entropy framework that fits epidemiological models, provides calibrated infection origin probabilities, and is robust to noise due to a prior belief model. Maximum entropy is agnostic to the parameters or model structure used and allows for flexible use when faced with sparse data conditions and incomplete knowledge in the dynamical phase of disease-spread, providing for more reliable modeling at early stages of outbreaks. We evaluate the performance of our model by predicting future disease trajectories based on simulated epidemiological data in synthetic graph networks and the real mobility network of New York State. In addition, unlike existing approaches, we demonstrate that the method can be used to infer the origin of the outbreak with accurate confidence. Indeed, despite the prevalent belief on the feasibility of contact-tracing being limited to the initial stages of an outbreak, we report the possibility of reconstructing early disease dynamics, including the epidemic seed, at advanced stages
Integrable Field Theories with Defects
The structure of integrable field theories in the presence of defects is
discussed in terms of boundary functions under the Lagrangian formalism.
Explicit examples of bosonic and fermionic theories are considered. In
particular, the boundary functions for the super sinh-Gordon model is
constructed and shown to generate the Backlund transformations for its soliton
solutions.Comment: talk presented at the XVth International Colloquium on Integrable
Systems and Quantum Symmetries, to appear in Czechoslovak Journal of Physics
(2006
The stability of “Ce2O3” nanodots in ambient conditions: a study using block copolymer templated structures
The stability of reduced cerium oxide in ambient conditions is clearly demonstrated in this paper. Well-defined, crystalline, cerium oxide nanodots (predominantly Ce4+ or Ce3+ material could be selectively prepared) were defined at silicon substrate surfaces by a method of block copolymer templating. Here, selective addition of the cerium ion into one block via solvent inclusion and subsequent UV/ozone processing resulted in the formation of well-separated, size mono-dispersed, oxide nanodots having a hexagonal arrangement mimicking that of the polymer nanopattern. The size of the dots could be varied in a facile manner by controlling the metal ion content. Synthesis and processing conditions could be varied to create nanodots which have a Ce2O3 type composition. The stability of the sesquioxide type structure under processing (synthesis) conditions and calcination was explored. Surprisingly, the sesquioxide type structure appears to be reasonably stable in ambient conditions with little evidence for extensive oxidation until heating to temperatures above ambient. Room temperature fluorescence is supposed to originate from a distribution of surface or defect states and depends on preparation conditions
Zeta Nonlocal Scalar Fields
We consider some nonlocal and nonpolynomial scalar field models originated
from p-adic string theory. Infinite number of spacetime derivatives is
determined by the operator valued Riemann zeta function through d'Alembertian
in its argument. Construction of the corresponding Lagrangians L starts
with the exact Lagrangian for effective field of p-adic tachyon
string, which is generalized replacing p by arbitrary natural number n and then
taken a sum of over all n. The corresponding new objects we
call zeta scalar strings. Some basic classical field properties of these fields
are obtained and presented in this paper. In particular, some solutions of the
equations of motion and their tachyon spectra are studied. Field theory with
Riemann zeta function dynamics is interesting in its own right as well.Comment: 13 pages, submitted to Theoretical and Mathematical Physic
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