Analysis of an FRW cosmological model

The Einstein field equations for the Friedmann universe reduce to a system of three first-order equations for the space-like components and a constraint from the temporal component. We analyse the system from the viewpoints of symmetry and singularity analyses. The solutions of particular relevance to Cosmology are highlighted.      

Effect of ZnO doping on the structural and optical properties of BaWO<Subscript>4</Subscript> thin films prepared using pulsed laser ablation technique

BaWO₄ doped with ZnO (2, 3, 5, 7 and 10 wt%) nanostructured films are prepared on quartz substrates by pulsed laser ablation. The films are post annealed at 900°C. GIXRD analysis of the post-annealed films reveal the change of orientation of scheelite tetragonal crystal growth from 1 1 2 reflection plane to 0 0 4 planes when doping concentration is more than 3 wt%. The AFM images show that film with 7 wt% ZnO doping concentration has good ceramic pattern with surface features giving a minimum value of rms surface roughness suitable for optoelectronic device applications. The optical transmittance and band-gap energy of the films are found to decrease considerably on postannealing which can be due to the increase in grain size of the crystallites on annealing. Thus doping with ZnO improves the surface features of the films and increases the optical band-gap energy.     

Asymptotics of the Farey Fraction Spin Chain Free Energy at the Critical Point

We consider the Farey fraction spin chain in an external field h. Using ideas from dynamical systems and functional analysis, we show that the free energy f in the vicinity of the second-order phase transition is given, exactly, by $$f\sim\frac{t}{\log t}-\frac{1}{2}\frac{h^2}{t}\quad\mbox{for }h^2\ll t\ll1.$$ Here $t=\lambda_{G}\log(2)(1-\frac{\beta}{\beta_{c}})$ is a reduced temperature, so that the deviation from the critical point is scaled by the Lyapunov exponent of the Gauss map, λ _G . It follows that λ _G determines the amplitude of both the specific heat and susceptibility singularities. To our knowledge, there is only one other microscopically defined interacting model for which the free energy near a phase transition is known as a function of two variables. Our results confirm what was found previously with a cluster approximation, and show that a clustering mechanism is in fact responsible for the transition. However, the results disagree in part with a renormalisation group treatment.     

Quantum-confined electronic states in atomically well-defined graphene nanostructures

Despite the enormous interest in the properties of graphene and the potential of graphene nanostructures in electronic applications, the study of quantum-confined states in atomically well-defined graphene nanostructures remains an experimental challenge. Here, we study graphene quantum dots (GQDs) with well-defined edges in the zigzag direction, grown by chemical vapor deposition on an Ir(111) substrate by low-temperature scanning tunneling microscopy and spectroscopy. We measure the atomic structure and local density of states of individual GQDs as a function of their size and shape in the range from a couple of nanometers up to ca. 20 nm. The results can be quantitatively modeled by a relativistic wave equation and atomistic tight-binding calculations. The observed states are analogous to the solutions of the textbook "particle-in-a-box" problem applied to relativistic massless fermions.     

Preparation, IR spectroscopy, and time-of-flight mass spectrometry of halogenated and methylated Si(111)

The preparation of chlorine-, bromine-, and iodine-terminated silicon surfaces (Si(111):Cl, Br, and I) using atomically flat Si(111)-(1×1):H is described. The halogenated surfaces were obtained by photochemically induced radical substitution reactions with the corresponding dihalogen in a Schlenk tube by conventional inert gas chemistry. The nucleophilic substitution of the Si-Cl functionality with the Grignard reagent (CH₃MgCl) resulted in the unreconstructed methylated Si(111)-(1×1):CH₃ surface. The halogenated and methylated silicon surfaces were characterized by Fourier transform infrared (FTIR) spectroscopy and laser-induced desorption of monolayers (LIDOM). Calibration of the desorption temperature via analysis of time-of-flight (TOF) distributions as a function of laser fluence allowed the determination of the originally emitted neutral fragments by TOF mass spectrometry using electron-impact ionization. The halogens were desorbed atomically and as SiX _n (X = Cl, Br) clusters. The methyl groups mainly desorbed as methyl and ethyl fragments and a small amount of ⁺SiCH₃.     

Low-loss coupling between two single-mode optical fibers with different mode-field diameters using a graded-index multimode optical fiber

We present a method for ultra-low-loss coupling between two single-mode optical fibers with different mode-field diameters using multimode interference in a graded-index multimode optical fiber. We perform a detailed analysis of the interference effects and show that the graded-index fiber can also be used as a beam expander or condenser. The results are important for devices in which optical fibers with different mode-field diameters are coupled in series, such as in ultra-short-pulse fiber ring lasers, or in optical fiber communication links.     

On the averaged quantum dynamics by white-noise hamiltonians with and without dissipation

Exact results are derived on the averaged dynamics of a class of random quantum-dynamical systems in continuous space. Each member of the class is characterized by a Hamiltonian which is the sum of two parts. While one part is deterministic, time-independent and quadratic, the Weyl-Wigner symbol of the other part is a homogeneous Gaussian random field which is delta correlated in time, but smoothly correlated in position and momentum. The averaged dynamics of the resulting white-noise system is shown to be a monotone mixing increasing quantum-dynamical semigroup. Its generator is computed explicitly. Typically, in the course of time the mean energy of such a system grows linearly to infinity. In the second part of the paper an extended model is studied, which, in addition, accounts for dissipation by coupling the white-noise system linearly to a quantum-mechanical harmonic heat bath. It is demonstrated that, under suitable assumptions on the spectral density of the heat bath, the mean energy then saturates for long times.