4,119 research outputs found
Dimensional Effects on Densities of States and Interactions in Nanostructures
We consider electrons in the presence of interfaces with different effective electron mass, and electromagnetic fields in the presence of a high-permittivity interface in bulk material. The equations of motion for these dimensionally hybrid systems yield analytic expressions for Green’s functions and electromagnetic potentials that interpolate between the two-dimensional logarithmic potential at short distance, and the three-dimensional r−1 potential at large distance. This also yields results for electron densities of states which interpolate between the well-known two-dimensional and three-dimensional formulas. The transition length scales for interfaces of thickness L are found to be of order Lm/2m* for an interface in which electrons move with effective mass m*, and for a dielectric thin film with permittivity in a bulk of permittivity . We can easily test the merits of the formalism by comparing the calculated electromagnetic potential with the infinite series solutions from image charges. This confirms that the dimensionally hybrid models are excellent approximations for distances r ≳ L/2
Fragmentation pathways of nanofractal structures on surface
We present a detailed systematical theoretical analysis of the post-growth
processes occurring in nanofractals grown on surface. For this study we
developed a method which accounts for the internal dynamics of particles in a
fractal. We demonstrate that particle diffusion and detachment controls the
shape of the emerging stable islands on surface. We consider different
scenarios of fractal post-growth relaxation and analyze the time evolution of
the island's morphology. The results of our calculations are compared with
available experimental observations, and experiments in which the post-growth
relaxation of deposited nanostructures can be probed are suggested.Comment: 34 pages, 11 figure
Graviton Mass or Cosmological Constant?
To describe a massive graviton in 4D Minkowski space-time one introduces a
quadratic term in the Lagrangian. This term, however, can lead to a
readjustment or instability of the background instead of describing a massive
graviton on flat space. We show that for all local Lorentz-invariant mass terms
Minkowski space is unstable. We start with the Pauli-Fierz (PF) term that is
the only local mass term with no ghosts in the linearized approximation. We
show that nonlinear completions of the PF Lagrangian give rise to instability
of Minkowski space. We continue with the mass terms that are not of a PF type.
Although these models are known to have ghosts in the linearized
approximations, nonlinear interactions can lead to background change due to
which the ghosts are eliminated. In the latter case, however, the graviton
perturbations on the new background are not massive. We argue that a consistent
theory of a massive graviton on flat space can be formulated in theories with
extra dimensions. They require an infinite number of fields or non-local
description from a 4D point of view.Comment: 16 pages; references and comments adde
DGP Cosmology with a Non-Minimally Coupled Scalar Field on the Brane
We construct a DGP inspired braneworld scenario where a scalar field
non-minimally coupled to the induced Ricci curvature is present on the brane.
First we investigate the status of gravitational potential with non-minimal
coupling and observational constraints on this non-minimal model. Then we
further deepen the idea of embedding of FRW cosmology in this non-minimal
setup. Cosmological implications of this scenario are examined with details and
the quintessence and late-time expansion of the universe within this framework
are examined. Some observational constraints imposed on this non-minimal
scenario are studied and relation of this model with dark radiation formalism
is determined with details.Comment: 26 pages, 3 eps figure
Hot new directions for quasi-Monte Carlo research in step with applications
This article provides an overview of some interfaces between the theory of
quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC
theoretical settings: first order QMC methods in the unit cube and in
, and higher order QMC methods in the unit cube. One important
feature is that their error bounds can be independent of the dimension
under appropriate conditions on the function spaces. Another important feature
is that good parameters for these QMC methods can be obtained by fast efficient
algorithms even when is large. We outline three different applications and
explain how they can tap into the different QMC theory. We also discuss three
cost saving strategies that can be combined with QMC in these applications.
Many of these recent QMC theory and methods are developed not in isolation, but
in close connection with applications
Crossing Phantom Boundary in Modified Gravity : Jordan Frame vs Einstein Frame
We study capability of gravity models to allow crossing the phantom
boundary in both Jordan and Einstein conformal frames. In Einstein frame, these
models are equivalent to Einstein gravity together with a scalar field
minimally coupled to gravity. This scalar degree of freedom appears as a
quintessence field with a coupling with the matter sector. We investigate
evolution of the equation of sate parameter for some cosmologically viable
gravity models in both conformal frames. This investigation (beyond mere
theoretical arguments) acts as an operational tool to distinguish physical
status of the two conformal frames. It shows that the two conformal frames have
not the same physical status.Comment: 13 Pages, 4 figs., To appear in Gravitation and Cosmolog
CP Violation for Leptons at Higher Energy Scales
The phase convention independent measure of CP violation for three
generations of leptons is evaluated at different energy scales. Unlike in the
quark sector, this quantity does not vary much between the weak and the grand
unification scales. The behavior of the measure of CP violation in the Standard
Model is found to be different from that in the extensions of the Standard
Model.Comment: 10 pages, 2 figures, references added, typos correcte
Perturbations of Self-Accelerated Universe
We discuss small perturbations on the self-accelerated solution of the DGP
model, and argue that claims of instability of the solution that are based on
linearized calculations are unwarranted because of the following: (1) Small
perturbations of an empty self-accelerated background can be quantized
consistently without yielding ghosts. (2) Conformal sources, such as radiation,
do not give rise to instabilities either. (3) A typical non-conformal source
could introduce ghosts in the linearized approximation and become unstable,
however, it also invalidates the approximation itself. Such a source creates a
halo of variable curvature that locally dominates over the self-accelerated
background and extends over a domain in which the linearization breaks down.
Perturbations that are valid outside the halo may not continue inside, as it is
suggested by some non-perturbative solutions. (4) In the Euclidean continuation
of the theory, with arbitrary sources, we derive certain constraints imposed by
the second order equations on first order perturbations, thus restricting the
linearized solutions that could be continued into the full nonlinear theory.
Naive linearized solutions fail to satisfy the above constraints. (5) Finally,
we clarify in detail subtleties associated with the boundary conditions and
analytic properties of the Green's functions.Comment: 39 LaTex page
Measuring Atmospheric Neutrino Oscillations with Neutrino Telescopes
Neutrino telescopes with large detection volumes can demonstrate that the
current indications of neutrino oscillation are correct or if a better
description can be achieved with non-standard alternatives. Observations of
contained muons produced by atmospheric neutrinos can better constrain the
allowed region for oscillations or determine the relevant parameters of
non-standard models. We analyze the possibility of neutrino telescopes
measuring atmospheric neutrino oscillations. We suggest adjustments to improve
this potential. An addition of four densely-instrumented strings to the AMANDA
II detector makes observations feasible. Such a configuration is competitive
with current and proposed experiments.Comment: 36 pages, 21 figures, revte
Recovery of the Schwarzschild Metric in Theories with Localized Gravity Beyond Linear Order
We solve the Einstein equations in the Randall-Sundrum framework with a
static, spherically symmetric matter distribution on the {\it physical brane}
and obtain an approximate expression for the gravitational field outside the
source to second order in the gravitational coupling. This expression when
confined on the {\it physical brane} coincides with the standard form of the
Schwarzschild metric. Therefore, the Randall-Sundrum scenario is consistent
with the Mercury precession test of General Relativity.Comment: 17 pages, plain Tex, references added, typos correcte
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