Gauge dependence of effective action and renormalization group functions in effective gauge theories

The Caswell-Wilczek analysis on the gauge dependence of the effective action and the renormalization group functions in Yang-Mills theories is generalized to generic, possibly power counting non renormalizable gauge theories. It is shown that the physical coupling constants of the classical theory can be redefined by gauge parameter dependent contributions of higher orders in $\hbar$ in such a way that the effective action depends trivially on the gauge parameters, while suitably defined physical beta functions do not depend on those parameters.Comment: 13 pages Latex file, additional comments in section

Wigner Crystals Phases in Bilayer Quantum Hall Systems

(This is a substantially shortened version of the original abstract:) The Wigner crystal phase diagram of the bilayer systems have been studied using variational methods. Five crystal phases are obtained. As the layer spacing increases, the system will undergo a sequence of phase transitions. A common feature of most bilayer Wigner crystals is that they have mixed (pseudo-spin) ferromagnetic and antiferromagnetic order.Comment: 19 figures. Figures will be provided upon request. Submitted in PRB in Nov 94

Quantum Correlated Interstitials and the Hall Resistivity of the Magnetically Induced Wigner Crystal

We study a trial wavefunction for an interstitial in a Wigner crystal. We find that the electron correlations, ignored in a conventional Hartree-Fock treatment, dramatically lower the interstitial energy, especially at fillings close to an incompressible liquid state. The correlation between the interstitial electron and the lattice electrons at $\nu <1/m$ is introduced by constructing a trial wave- function which bears a Jastrow factor of a Laughlin state at $\nu=1/m$. For fillings close to but just below $\nu=1/m$, we find that a perfect Wigner crystal becomes unstable against formation of such interstitials. It is argued that conduction due to correlated interstitials in the presence of weak disorder leads to the {\it classical} Hall resistivity, as seen experimentally.Comment: 10 pages, RevTe

Competition between quantum-liquid and electron-solid phases in intermediate Landau levels

On the basis of energy calculations we investigate the competition between quantum-liquid and electron-solid phases in the Landau levels n=1,2, and 3 as a function of their partial filling factor. Whereas the quantum-liquid phases are stable only in the vicinity of quantized values 1/(2s+1) of the partial filling factor, an electron solid in the form of a triangular lattice of clusters with a few number of electrons (bubble phase) is energetically favorable between these fillings. This alternation of electron-solid phases, which are insulating because they are pinned by the residual impurities in the sample, and quantum liquids displaying the fractional quantum Hall effect explains a recently observed reentrance of the integral quantum Hall effect in the Landau levels n=1 and 2. Around half-filling of the last Landau level, a uni-directional charge density wave (stripe phase) has a lower energy than the bubble phase.Comment: 12 pages, 9 figures; calculation of exact exchange potential for n=1,2,3 included, energies of electron-solid phases now calculated with the help of the exact potential, and discussion of approximation include

Working paper analysing the economic implications of the proposed 30% target for areal protection in the draft post-2020 Global Biodiversity Framewor

58 pages, 5 figures, 3 tables- The World Economic Forum now ranks biodiversity loss as a top-five risk to the global economy, and the draft post-2020 Global Biodiversity Framework proposes an expansion of conservation areas to 30% of the earth’s surface by 2030 (hereafter the “30% target”), using protected areas (PAs) and other effective area-based conservation measures (OECMs). - Two immediate concerns are how much a 30% target might cost and whether it will cause economic losses to the agriculture, forestry and fisheries sectors. - Conservation areas also generate economic benefits (e.g. revenue from nature tourism and ecosystem services), making PAs/Nature an economic sector in their own right. - If some economic sectors benefit but others experience a loss, high-level policy makers need to know the net impact on the wider economy, as well as on individual sectors. [...]A. Waldron, K. Nakamura, J. Sze, T. Vilela, A. Escobedo, P. Negret Torres, R. Button, K. Swinnerton, A. Toledo, P. Madgwick, N. Mukherjee were supported by National Geographic and the Resources Legacy Fund. V. Christensen was supported by NSERC Discovery Grant RGPIN-2019-04901. M. Coll and J. Steenbeek were supported by EU Horizon 2020 research and innovation programme under grant agreement No 817578 (TRIATLAS). D. Leclere was supported by TradeHub UKRI CGRF project. R. Heneghan was supported by Spanish Ministry of Science, Innovation and Universities, Acciones de Programacion Conjunta Internacional (PCIN-2017-115). M. di Marco was supported by MIUR Rita Levi Montalcini programme. A. Fernandez-Llamazares was supported by Academy of Finland (grant nr. 311176). S. Fujimori and T. Hawegawa were supported by The Environment Research and Technology Development Fund (2-2002) of the Environmental Restoration and Conservation Agency of Japan and the Sumitomo Foundation. V. Heikinheimo was supported by Kone Foundation, Social Media for Conservation project. K. Scherrer was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 682602. U. Rashid Sumaila acknowledges the OceanCanada Partnership, which funded by the Social Sciences and Humanities Research Council of Canada (SSHRC). T. Toivonen was supported by Osk. Huttunen Foundation & Clare Hall college, Cambridge. W. Wu was supported by The Environment Research and Technology Development Fund (2-2002) of the Environmental Restoration and Conservation Agency of Japan. Z. Yuchen was supported by a Ministry of Education of Singapore Research Scholarship Block (RSB) Research FellowshipPeer reviewe