Large Deviations Principle for a Large Class of One-Dimensional Markov Processes

We study the large deviations principle for one dimensional, continuous, homogeneous, strong Markov processes that do not necessarily behave locally as a Wiener process. Any strong Markov process $X_{t}$ in $\mathbb{R}$ that is continuous with probability one, under some minimal regularity conditions, is governed by a generalized elliptic operator $D_{v}D_{u}$, where $v$ and $u$ are two strictly increasing functions, $v$ is right continuous and $u$ is continuous. In this paper, we study large deviations principle for Markov processes whose infinitesimal generator is $\epsilon D_{v}D_{u}$ where $0<\epsilon\ll 1$. This result generalizes the classical large deviations results for a large class of one dimensional "classical" stochastic processes. Moreover, we consider reaction-diffusion equations governed by a generalized operator $D_{v}D_{u}$. We apply our results to the problem of wave front propagation for these type of reaction-diffusion equations.Comment: 23 page

Horava Gravity and Gravitons at a Conformal Point

Recently Horava proposed a renormalizable gravity theory with higher derivatives by abandoning the Lorenz invariance in UV. Here, I study the Horava model at $\lambda=1/3$, where an anisotropic Weyl symmetry exists in the UV limit, in addition to the foliation-preserving diffeomorphism. By considering linear perturbations around Minkowski vacuum, I show that the scalar graviton mode is completely disappeared and only the usual tensor graviton modes remain in the physical spectrum. The existence of the UV conformal symmetry is unique to the theory with the detailed balance and it is quite probable that $\lambda=1/3$ be the UV fixed point. This situation is analogous to $\lambda=1$, which is Lorentz invariant in the IR limit and is believed to be the IR fixed point.Comment: Added comments and references, Accepted in GER

Absorption cross section in the topologically massive gravity at the critical point

The absorption cross section for the the warped AdS$_3$ black hole background shows that it is larger than the area even if the s-wave limit is considered. It raises some question whether the deviation from the areal cross section is due to the warped configuration of the geometry or the rotating coordinate system, where these two effects are mixed up in the warped AdS$_3$ black hole. So, we study the low-frequency scattering dynamics of propagating scalar fields under the warped AdS$_3$ background at the critical point which reduces to the BTZ black hole in the rotating frame without the warped factor, which shows that the deformation effect at the critical point does not appear.Comment: 12 pages, LaTe

Quasi-multi-Regge Processes with a Quark Exchange in the t-channel

The QCD amplitudes for particle's production in the quasi-multi-Regge kinematics with a quark exchange in crossing channels are calculated in the Born approximation. In particular they are needed to find next-to-leading corrections to the quark Regge trajectory and to the integral kernel of the Bethe-Salpeter equation for the t-channel partial wave with fermion quantum numbers and a negative signature. The gauge-invariant action for the interaction of the reggeized quarks and gluons with the usual particles is constructed.Comment: LaTeX, 10 page

Electromagnetic properties of graphene junctions

A resonant chiral tunneling (CT) across a graphene junction (GJ) induced by an external electromagnetic field (EF) is studied. Modulation of the electron and hole wavefunction phases $\varphi$ by the external EF during the CT processes strongly impacts the CT directional diagram. Therefore the a.c. transport characteristics of GJs depend on the EF polarization and frequency considerably. The GJ shows great promises for various nanoelectronic applications working in the THz diapason.Comment: 4 pages 3 figure

Autonomous stochastic resonance in fully frustrated Josephson-junction ladders

We investigate autonomous stochastic resonance in fully frustrated Josephson-junction ladders, which are driven by uniform constant currents. At zero temperature large currents induce oscillations between the two ground states, while for small currents the lattice potential forces the system to remain in one of the two states. At finite temperatures, on the other hand, oscillations between the two states develop even below the critical current; the signal-to-noise ratio is found to display array-enhanced stochastic resonance. It is suggested that such behavior may be observed experimentally through the measurement of the staggered voltage.Comment: 6 pages, 11 figures, to be published in Phys. Rev.

On the Calculation of the NLO Virtual Photon Impact Factor

The definition of the virtual photon impact factor involves the integration of the s-channel discontinuity of the photon-Reggeon scattering amplitude over the right cut. It permits to formulate a new approach for the calculation of the impact factor based on analytical properties of the amplitude in question. In the next-to-leading order it may give a possibility for considerable simplification of the calculation. We have shown that a part of the diagrams contributing to the impact factor can be treated without their real calculation.Comment: 18 pages, latex, axodraw.sty for figures, version to appear in Nucl. Phys.

Capacitance of MnO2 Micro-Flowers Decorated CNFs in Alkaline Electrolyte and Its Bi-Functional Electrocatalytic Activity toward Hydrazine Oxidation

Well-dispersed MnO2 micro-flowers were grown directly on carbon nanofibers via a simple hydrothermal technique without any template. Structure and morphology were characterized by X-ray diffraction (XRD) and field-emission scanning electron microscopy (FESEM) equipped with rapid energy dispersive analysis X-ray (EDX). The appealed characterization techniques specified that the obtained material is carbon nanofibers decorated by MnO2 micro-flowers. Super capacitive performance of the MnO2 micro-flowers decorated CNFs as active electrode material was evaluated by cyclic voltammetry (CV) in alkaline medium and yield a reasonable specific capacitance of 120 Fg−1 at 5 mV s−1. As an electrocatalyst for hydrazine oxidation, the MnO2 micro-flowers decorated CNFs showed high current density. The impressive bi-functional electrochemical activity of MnO2 micro-flowers decorated CNFs is mainly attributed to its unique architectural structure.This Research was financially supported by National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIP) (No. 2014R1A4A1008140

Extremal black holes in the Ho\v{r}ava-Lifshitz gravity

We study the near-horizon geometry of extremal black holes in the $z=3$ Ho\v{r}ava-Lifshitz gravity with a flow parameter $\lambda$. For $\lambda>1/2$, near-horizon geometry of extremal black holes are AdS$_2 \times S^2$ with different radii, depending on the (modified) Ho\v{r}ava-Lifshitz gravity. For $1/3\le \lambda \le 1/2$, the radius $v_2$ of $S^2$ is negative, which means that the near-horizon geometry is ill-defined and the corresponding Bekenstein-Hawking entropy is zero. We show explicitly that the entropy function approach does not work for obtaining the Bekenstein-Hawking entropy of extremal black holes.Comment: 18 pages, v2:some points on Lifshitz black holes claified, v3: version to appear in EJP

Thermodynamics of a black hole based on a generalized uncertainty principle

We study thermodynamic quantities and the stability of a black hole in a cavity using the Euclidean action formalism by Gibbons and Hawking based on the generalized uncertainty relation which is extended in a symmetric way with respect to the space and momentum without loss of generality. Two parameters in the uncertainty relation affect the thermodynamical quantities such as energy, entropy, and the heat capacity. In particular, it can be shown that the small black hole is unstable and it may decay either into a minimal black hole or a large black hole. We discuss a constraint for a large black hole comparable to the size of the cavity in connection with the critical mass.Comment: 12 pages, 4 figures; v2. to appear in JHE