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 $[0,1]^s$ and in $\mathbb{R}^s$, and higher order QMC methods in the unit cube. One important feature is that their error bounds can be independent of the dimension $s$ 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 $s$ 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 f(R)f(R) Modified Gravity : Jordan Frame vs Einstein Frame

We study capability of $f(R)$ 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 $f(R)$ 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