Feynman Diagrams and Differential Equations

We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of one- and two-loop corrections to the photon propagator in QED, by computing the Vacuum Polarization tensor exactly in D. Finally, we treat two cases of less trivial differential equations, respectively associated to a two-loop three-point, and a four-loop two-point integral. These two examples are the playgrounds for showing more technical aspects about: Laurent expansion of the differential equations in D (around D=4); the choice of the boundary conditions; and the link among differential and difference equations for Feynman integrals.Comment: invited review article from Int. J. Mod. Phys.

Fabrication of integrated planar gunn diode and micro-cooler on GaAs substrate

We demonstrate fabrication of an integrated micro cooler with the planar Gunn diode and characterise its performance. First experimental results have shown a small cooling at the surface of the micro cooler. This is first demonstration of an integrated micro-cooler with a planar Gunn diode

Simple isatin derivatives as free radical scavengers: Synthesis, biological evaluation and structure-activity relationship

To develop more potent small molecules with enhanced free radical scavenger properties, a series of N-substituted isatin derivatives was synthesized, and the cytoprotective effect on the apoptosis of PC12 cells induced by H2O2 was screened. All these compounds were found to be active, and N-ethyl isatin was found with the most potent activity of 69.7% protective effect on PC12 cells. Structure-activity relationship analyses showed the bioactivity of N-alkyl isatins decline as the increasing of the chain of the alkyl group, furthermore odd-even effect was found in the activity, which is interesting for further investigation

Planar gunn diode characterisation and resonators elements to realise oscillator circuits

The paper describes the planar Gunn diode, which is well suited to providing milli-metric and tera hertz sources using microwave monolithic integrated circuit (MMIC) technologies. Different planar Gunn electrode geometries are described along with DC, RF and thermal characterisation. To realize the planar high frequency sources there is requirement for high frequency planar resonators, the paper will describe both the radial and new diamond shaped geometries

The formation of the first galaxies and the transition to low-mass star formation

The formation of the first galaxies at redshifts z ~ 10-15 signaled the transition from the simple initial state of the universe to one of ever increasing complexity. We here review recent progress in understanding their assembly process with numerical simulations, starting with cosmological initial conditions and modelling the detailed physics of star formation. In this context we emphasize the importance and influence of selecting appropriate initial conditions for the star formation process. We revisit the notion of a critical metallicity resulting in the transition from primordial to present-day initial mass functions and highlight its dependence on additional cooling mechanisms and the exact initial conditions. We also review recent work on the ability of dust cooling to provide the transition to present-day low-mass star formation. In particular, we highlight the extreme conditions under which this transition mechanism occurs, with violent fragmentation in dense gas resulting in tightly packed clusters.Comment: 16 pages, 7 figures, appeared in the conference proceedings for IAU Symposium 255: Low-Metallicity Star Formation: From the First Stars to Dwarf Galaxies, a high resolution version (highly recommended) can be found at http://www.ita.uni-heidelberg.de/~tgreif/files/greif08.pd

Bond length contraction in Au nanocrystals formed by ion implantation into thin SiO[sub 2]

Au nanocrystals (NCs) fabricated by ion implantation into thin SiO₂ and annealing were investigated by means of extended x-rayabsorption fine structure (EXAFS)spectroscopy and transmission electron microscopy. A bond length contraction was observed and can be explained by surface tension effects in a simple liquid-drop model. Such results are consistent with previous reports on nonembedded NCs implying a negligible influence of the SiO₂ matrix. Cumulant analysis of the EXAFS data suggests surface reconstruction or relaxation involving a further shortened bond length. A deviation from the octahedral closed shell structure is apparent for NCs of size 25Å.P. K. is grateful to the Humboldt Foundation in Germany for support. P.K., B.J., A.C., C.J.G., G.d.M.A., G.J.F., and M.C.R. were supported by the Australian Synchrotron Research Program

An estimate of the QCD corrections to the decay Z --> W u d

We present an estimate of perturbative QCD corrections to the decay $Z \to Wu\bar d$. A simple approximate approach is described in detail. The difference of masses of $M_Z$ and $M_W$ is used as an expansion parameter. A complete analytical formula for a part of the corrections is also presented.Comment: 9 pages, late

Terahertz oscillations in an In_0.53Ga_0.47As submicron planar gunn diode

The length of the transit region of a Gunn diode determines the natural frequency at which it operates in fundamental mode – the shorter the device, the higher the frequency of operation. The long-held view on Gunn diode design is that for a functioning device the minimum length of the transit region is about 1.5μm, limiting the devices to fundamental mode operation at frequencies of roughly 60 GHz. Study of these devices by more advanced Monte Carlo techniques that simulate the ballistic transport and electron-phonon interactions that govern device behaviour, offers a new lower bound of 0.5μm, which is already being approached by the experimental evidence that has shown planar and vertical devices exhibiting Gunn operation at 600nm and 700nm, respectively. The paper presents results of the first ever THz submicron planar Gunn diode fabricated in In<sub>0.53</sub>Ga<sub>0.47</sub>A on an InP substrate, operating at a fundamental frequency above 300 GHz. Experimentally measured rf power of 28 µW was obtained from a 600 nm long ×120 µm wide device. At this new length, operation in fundamental mode at much higher frequencies becomes possible – the Monte Carlo model used predicts power output at frequencies over 300 GHz

Long-range interactions of metastable helium atoms

Polarizabilities, dispersion coefficients, and long-range atom-surface interaction potentials are calculated for the n=2 triplet and singlet states of helium using highly accurate, variationally determined, wave functions.Comment: RevTeX, epsf, 4 fig

The Triple Higgs Boson Self-Coupling at Future Linear e+e- Colliders Energies: ILC and CLIC

We analyzed the triple Higgs boson self-coupling at future $e^{+}e^{-}$ colliders energies, with the reactions $e^{+}e^{-}\to b \bar b HH, t \bar t HH$. We evaluate the total cross-sections for both $b\bar bHH$ and $t\bar tHH$, and calculate the total number of events considering the complete set of Feynman diagrams at tree-level. We vary the triple coupling $\kappa\lambda_{3H}$ within the range $\kappa=-1$ and +2. The numerical computation is done for the energies expected to be available at a possible Future Linear $e^{+}e^{-}$ Collider with a center-of-mass energy $800, 1000, 1500$ $GeV$ and a luminosity 1000 $fb^{-1}$. Our analysis is also extended to a center-of-mass energy 3 $TeV$ and luminosities of 1000 $fb^{-1}$ and 5000 $fb^{-1}$. We found that for the process $e^{+}e^{-}\to b \bar b HH$, the complete calculation differs only by 3% from the approximate calculation $e^{+}e^{-}\to ZHH(Z\to b\bar b)$, while for the process $e^{+}e^{-}\to t \bar tHH$, the expected number of events, considering the decay products of both $t$ and $H$, is not enough to obtain an accurate determination of the triple Higgs boson self-coupling.Comment: 19 pages, 12 figure