Exact renormalization group equations and the field theoretical approach to critical phenomena

After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general Wilson (nonperturbative) approach. Notions such as the continuum limit and the renormalizability and the presence of singularities in the perturbative series are discussed.Comment: 15 pages, 7 figures, to appear in the Proceedings of the 2nd Conference on the Exact Renormalization Group, Rome 200

The Energy Spectrum of Primary Cosmic Ray Electrons in Clusters of Galaxies and Inverse Compton Emission

Models for the evolution of the integrated energy spectrum of primary cosmic ray electrons in clusters of galaxies have been calculated, including the effects of losses due to inverse Compton (IC), synchrotron, and bremsstrahlung emission, and Coulomb losses to the intracluster medium (ICM). The combined time scale for these losses reaches a maximum of ~3e9 yr for electrons with a Lorentz factor ~300. Only clusters in which there has been a substantial injection of relativistic electrons since z <~ 1 will have any significant population of primary cosmic ray electrons at present. In typical models, there is a broad peak in the electron energy distribution extending to gamma~300, and a steep drop in the electron population beyond this. In clusters with current particle injection, there is a power-law tail of higher energy electrons with an abundance determined by the current rate of injection. A significant population of electrons with gamma~300, associated with the peak in the particle loss time, is a generic feature of the models. The IC and synchrotron emission from these models was calculated. In the models, EUV and soft X-ray emission are nearly ubiquitous. This emission is produced by electrons with gamma~300. The spectra are predicted to drop rapidly in going from the EUV to the X-ray band. The IC emission also extends down the UV, optical, and IR bands with a fairly flat spectrum. Hard X-ray (HXR) and diffuse radio emission due to high energy electrons (gamma~10e4) is present only in clusters which have current particle acceleration. Assuming that the electrons are accelerated in ICM shocks, one would only expect diffuse HXR/radio emission in clusters which are currently undergoing a large merger.Comment: Accepted for publication in the Astrophysical Journal, with minor revisons to wording for clarity and one additional reference. 19 pages with 16 embedded Postscript figures in emulateapj.sty. Abbreviated abstract belo

Molecular dark matter in galaxies

Clouds containing molecular dark matter in quantities relevant for star formation may exist in minihaloes of the type of cold dark matter included in many cosmological simulations or in the regions of some galaxies extending far beyond their currently known boundaries. We have systematically explored parameter space to identify conditions under which plane-parallel clouds contain sufficient column densities of molecular dark matter that they could be reservoirs for future star formation. Such clouds would be undetected or at least appear by current observational criteria to be uninteresting from the perspective of star formation. We use a time-dependent PDR code to produce theoretical models of the chemistry and emission arising in clouds for our chosen region of parameter space. We then select a subset of model clouds with levels of emission that are low enough to be undetectable or at least overlooked by current surveys. The existence of significant column densities of cold molecular dark matter requires that the background radiation field be several or more orders of magnitude weaker than that in the solar neighbourhood. Lower turbulent velocities and cosmic ray induced ionization rates than typically associated with molecular material within a kpc of the Sun are also required for the molecular matter to be dark. We find that there is a large region within the parameter space that results in clouds that might contain a significant mass of molecular gas whilst remaining effectively undetectable or at least not particularly noticeable in surveys. We note briefly conditions under which molecular dark matter may contain a dynamically interesting mass.Comment: 9 pages, 2 figures, accepted for publication in A&A; additional concluding paragraph added at proof stag

On Renormalization Group Flows and Polymer Algebras

In this talk methods for a rigorous control of the renormalization group (RG) flow of field theories are discussed. The RG equations involve the flow of an infinite number of local partition functions. By the method of exact beta-function the RG equations are reduced to flow equations of a finite number of coupling constants. Generating functions of Greens functions are expressed by polymer activities. Polymer activities are useful for solving the large volume and large field problem in field theory. The RG flow of the polymer activities is studied by the introduction of polymer algebras. The definition of products and recursive functions replaces cluster expansion techniques. Norms of these products and recursive functions are basic tools and simplify a RG analysis for field theories. The methods will be discussed at examples of the $\Phi^4$-model, the $O(N)$ $\sigma$-model and hierarchical scalar field theory (infrared fixed points).Comment: 32 pages, LaTeX, MS-TPI-94-12, Talk presented at the conference ``Constructive Results in Field Theory, Statistical Mechanics and Condensed Matter Physics'', 25-27 July 1994, Palaiseau, Franc

Composition profiles of InAs–GaAs quantum dots determined by medium-energy ion scattering

The composition profile along the [001] growth direction of low-growth-rate InAs–GaAs quantum dots (QDs) has been determined using medium-energy ion scattering (MEIS). A linear profile of In concentration from 100% In at the top of the QDs to 20% at their base provides the best fit to MEIS energy spectra

Is graphene on copper doped?

Angle-resolved photoemission spectroscopy (ARPES) and X-ray photoemission spectroscopy have been used to characterise epitaxially ordered graphene grown on copper foil by low-pressure chemical vapour deposition. A short vacuum anneal to 200 °C allows observation of ordered low energy electron diffraction patterns. High quality Dirac cones are measured in ARPES with the Dirac point at the Fermi level (undoped graphene). Annealing above 300 °C produces n-type doping in the graphene with up to 350 meV shift in Fermi level, and opens a band gap of around 100 meV. Dirac cone dispersion for graphene on Cu foil after vacuum anneals (left: 200 °C, undoped; right: 500 °C, n-doped). Centre: low energy electron diffraction from graphene on Cu foil after 200 °C anneal. Data from Antares (SOLEIL)

Exact Renormalization Group Equations. An Introductory Review

We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.Comment: Final version to appear in Phys. Rep.; Many references added, section 4.2 added, minor corrections. 65 pages, 6 fig

NLO QCD Corrections to BcB_c-to-Charmonium Form Factors

The $B_c(^1S_0)$ meson to S-wave Charmonia transition form factors are calculated in next-to-leading order(NLO) accuracy of Quantum Chromodynamics(QCD). Our results indicate that the higher order corrections to these form factors are remarkable, and hence are important to the phenomenological study of the corresponding processes. For the convenience of comparison and use, the relevant expressions in asymptotic form at the limit of $m_c\rightarrow0$ for the radiative corrections are presented