An interesting deformation of the Jackiw-Teitelboim (JT) gravity has been proposed by Witten by adding a potential term $U(phi)$ as a self-coupling of the scalar dilaton field. During calculating the path integral over fields, a constraint comes from
integration over $phi$ as $R(x)+2=2alpha delta(vec{x}-vec{x})$. The resulting Euclidean metric suffered from a conical singularity at $vec{x}=vec{x}$. A possible geometry modeled locally in polar coordinates $(r,varphi)$ by $ds^2=dr^2+r^2dvarphi^2,varphi cong varphi+2pi-alpha$. In this letter we showed that there exists another family of exact geometries for arbitrary values of the $alpha$. A pair of exact solutions are found for the case of $alpha=0$. One represents the static patch of the AdS and the other one is the non static patch of the AdS metric. These solutions were used to construct the Green function for the inhomogeneous model with $alpha eq 0$. We address a type of the phase transition between different patches of the AdS in theory because of the discontinuity in the first derivative of the metric at $x=x$. We extended the study to the exact space of metrics satisfying the constraint $R(x)+2=2sum_{i=1}^{k}alpha_idelta^{(2)}(x-x_i)$ as a modulo diffeomorphisms for an arbitrary set of the deficit parameters $(alpha_1,alpha_2,..,alpha_k)$. The space is the moduli space of Riemann surfaces of genus $g$ with $k$ conical singularities located at $x_k$ denoted by $mathcal{M}_{g,k}$.
The classical Einstein-Hilbert (EH) action for general relativity (GR) is shown to be formally analogous to the classical system with position-dependent mass (PDM) models. The analogy is developed and used to build the covariant classical Hamiltonian
as well as defining an alternative phase portrait for GR. The set of associated Hamiltons equations in the phase space is presented as a first-order system dual to the Einstein field equations. Following the principles of quantum mechanics, I build a canonical theory for the classical general. A fully consistent quantum Hamiltonian for GR is constructed based on adopting a high dimensional phase space. It is observed that the functional wave equation is timeless. As a direct application, I present an alternative wave equation for quantum cosmology. In comparison to the standard Arnowitt-Deser-Misner(ADM) decomposition and quantum gravity proposals, I extended my analysis beyond the covariant regime when the metric is decomposed into the $3+1$ dimensional ADM decomposition. I showed that an equal dimensional phase space can be obtained if one applies ADM decomposed metric.
In a primordial universe pre(post)-inflationary era , there could be phases of early universe made of cold gas baryons, radiation and early post inflationary cosmological constant. I showed that in the baryonic epoch, the quantum vacuum is unique. By
using the standard quantization scheme for a massive minimally coupled scalar field with maximal conformal symmetry in the classical spacetime, I demonstrated that the scalar modes had an effective mass $m_{eff}^2approx 0$ (or $m_{eff}^2approx constant$). This argument validated when the conformal time $eta$ kept so close to the inflation ending time $eta=eta_c$. The energy density of the baryonic matter diverged at the inflation border and vanishes at the late time future. Furthermore I argued that at very early accelerating epoch when the radiation was the dominant part in the close competition with the early time cosmological constant, fine tuned mass of the scalar field $mpropto sqrt{Lambda}$ also provided a unique quantum vacuum. The reason is that the effective mass eventually is vanished. A remarkable observation was that all the other possible vacuum states squeezed eternally.
Fabrication, characterization and comparison of gold and graphene micro- and nano-size Hall sensors for room temperature scanning magnetic field microscopy applications is presented. The Hall sensors with active areas from 5 $mu$m down to 50 nm were
fabricated by electron-beam lithography. The calibration of the Hall sensors in an external magnetic field revealed a sensitivity of 3.2 mV/(AT) $pm$ 0.3 % for gold and 1615 V/(AT) $pm$ 0.5 % for graphene at room temperature. The gold sensors were fabricated on silicon nitride cantilever chips suitable for integration into commercial scanning probe microscopes, allowing scanning Hall microscopy (SHM) under ambient conditions and controlled sensor-sample distance. The height dependent stray field distribution of a magnetic scale was characterized using a 5 $mu$m gold Hall sensor. The uncertainty of the entire Hall sensor based scanning and data acquisition process was analyzed allowing traceably calibrated SHM measurements. The measurement results show good agreement with numerical simulations within the uncertainty budget.
Based on the Stueckelberg-Horwitz-Piron theory of covariant quantum mechanics on curved spacetime, we solved wave equation for a charged covariant harmonic oscillator in the background of charged static spherically symmetric black hole. Using Greens
functions , we found asymptotic form for the wave function in the lowest mode (s-mode) and in higher moments. It has been proven that for s-wave, in a definite range of solid angles, the differential cross section depends effectively to the magnetic and electric charges of the black hole.
I show how Bose-Einstein condensation (BEC) in a non interacting bosonic system with exponential density of states function yields to a new class of Lerch zeta functions. By looking on the critical temperature, I suggest that a possible strategy to p
rove the Riemann hypothesis problem. In a theorem and a lemma I suggested that the classical limit $hbarto 0$ of BEC can be used as a tool to find zeros of real part of the Riemann zeta function with complex argument. It reduces the Riemann hypothesis to a softer form. Furthermore I propose a pair of creation-annihilation operators for BEC phenomena. This set of creation-annihilation operators is defined on a complex Hilbert space. They build a set up to interpret this type of BEC as a creation-annihilation phenomenon for a virtual hypothetical particle.
We found exact solutions for canonical classical and quantum dynamics for general relativity in Horwitz general covarience theory. These solutions can be obtained by solving the generalized geodesic equation and Schr{o}dinger-Stueckelberg -Horwitz-Pi
ron (SHP) wave equation for a simple harmonic oscilator in the background of a two dimensional dilaton black hole spacetime metric. We proved the existence of an orthonormal basis of eigenfunctions for generalized wave equation. This basis functions form an orthogonanl and normalized (orthonormal) basis for an appropriate Hilbert space. The energy spectrum has a mixed spectrum with one conserved momentum $p$ according to a quantum number $n$. To find the ground state energy we used a variational method with appropriate boundary conditions. A set of mode decomposed wave functions and calculated for the Stueckelberg-Schrodinger equation on a general five dimensional blackhole spacetime in Hamilton gauge.
In this study, we first show that the argon flow during epitaxial graphene growth is an important parameter to control the quality of the buffer and the graphene layer. Atomic force microscopy (AFM) and low-energy electron diffraction (LEED) measurem
ents reveal that the decomposition of the SiC substrate strongly depends on the Ar mass flow rate while pressure and temperature are kept constant. Our data are interpreted by a model based on the competition of the SiC decomposition rate, controlled by the Ar flow, with a uniform graphene buffer layer formation under the equilibrium process at the SiC surface. The proper choice of a set of growth parameters allows the growth of defect-free, ultra-smooth and coherent graphene-free buffer layer and bilayer-free monolayer graphene sheets which can be transformed into large-area high-quality quasi-freestanding monolayer and bilayer graphene (QFMLG and QFBLG) by hydrogen intercalation. AFM, scanning tunneling microscopy (STM), Raman spectroscopy and electronic transport measurements underline the excellent homogeneity of the resulting quasi-freestanding layers. Electronic transport measurements in four-point probe configuration reveal a homogeneous low resistance anisotropy on both {mu}m- and mm scales.
As quantum optical phenomena are based on Maxwells equations, and it is becoming important to understand quantum optical phenomena at short distances, so it is important to analyze quantum optics using short distance corrected Maxwells equation. Maxw
ells action can be obtained from quantum electrodynamics using the framework of effective field theory, and so the leading order short distance corrections to Maxwells action can also be obtained from the derivative expansion of the same effective field theory. Such short distance corrections will be universal for all quantum optical systems, and they will effect all short distance quantum optical phenomena. In this paper, we will analyze the form of such corrections, and demonstrate the standard formalism of quantum optics can still be used (with suitable modifications), to analyze quantum optical phenomena from this short distance corrected Maxwells actions.
In this paper, we will analyze the connection between the fidelity susceptibility, the holographic complexity and the thermodynamic volume. We will regularize the fidelity susceptibility and the holographic complexity by subtracting the contribution
of the background AdS spacetime from the deformation of the AdS spacetime. It will be demonstrated that this regularized fidelity susceptibility has the same behavior as the thermodynamic volume and that the regularized complexity has a very different behavior. As the information dual to different volumes in the bulk would be measured by the fidelity susceptibility and the holographic complexity, this paper will establish a connection between thermodynamics and information dual to a volume.
