Temperature reducing coating for metals subject to flame exposure Patent

Anodizing method for providing metal surfaces with temperature reducing coatings against flame

Quantum Hall Physics - hierarchies and CFT techniques

The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past thirty years, has generated many groundbreaking new ideas and concepts. Very early on it was realized that the zoo of emerging states of matter would need to be understood in a systematic manner. The first attempts to do this, by Haldane and Halperin, set an agenda for further work which has continued to this day. Since that time the idea of hierarchies of quasiparticles condensing to form new states has been a pillar of our understanding of fractional quantum Hall physics. In the thirty years that have passed since then, a number of new directions of thought have advanced our understanding of fractional quantum Hall states, and have extended it in new and unexpected ways. Among these directions is the extensive use of topological quantum field theories and conformal field theories, the application of the ideas of composite bosons and fermions, and the study of nonabelian quantum Hall liquids. This article aims to present a comprehensive overview of this field, including the most recent developments.Comment: added section on experimental status, 59 pages+references, 3 figure

A Typology for Quantum Hall Liquids

There is a close analogy between the response of a quantum Hall liquid (QHL) to a small change in the electron density and the response of a superconductor to an externally applied magnetic flux - an analogy which is made concrete in the Chern-Simons Landau-Ginzburg (CSLG) formulation of the problem. As the Types of superconductor are distinguished by this response, so too for QHLs: a typology can be introduced which is, however, richer than that in superconductors owing to the lack of any time-reversal symmetry relating positive and negative fluxes. At the boundary between Type I and Type II behavior, the CSLG action has a "Bogomol'nyi point," where the quasi-holes (vortices) are non-interacting - at the microscopic level, this corresponds to the behavior of systems governed by a set of model Hamiltonians which have been constructed to render exact a large class of QHL wavefunctions. All Types of QHLs are capable of giving rise to quantized Hall plateaux.Comment: 4 +epsilon pages, 1 figure; v2 has added references and minor changes, version published in Phys. Rev. B. (Rapid Communications

Paired composite fermion wavefunctions

We construct a family of BCS paired composite fermion wavefunctions that generalize, but remain in the same topological phase as, the Moore-Read Pfaffian state for the half-filled Landau level. It is shown that for a wide range of experimentally relevant inter-electron interactions the groundstate can be very accurately represented in this form.Comment: 4 pages, 2 figure

Response Function of the Fractional Quantized Hall State on a Sphere II: Exact Diagonalization

We study the excitation spectra and the dynamical structure factor of quantum Hall states in a finite size system through exact diagonalization. Comparison is made between the numerical results so obtained and the analytic results obtained from a modified RPA in the preceding companion paper. We find good agreement between the results at low energies.Comment: 22 pages (REVTeX 3.0). 10 figures available on request. Complete postscript file (including figures) for this paper are available on the World Wide Web at http://cmtw.harvard.edu/~simon/ ; Preprint number HU-CMT-94S0

Hamilton's Turns for the Lorentz Group

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by ``turns'', which are equivalence classes of directed great circle arcs on the unit sphere $S^2$, in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group. It is only recently that this construction has been generalized to the simplest noncompact group $SU(1,1) = Sp(2, R) = SL(2,R)$, the double cover of SO(2,1). The present work develops a theory of turns for $SL(2,C)$, the double and universal cover of SO(3,1) and $SO(3,C)$, rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics. The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late

Phase transitions in three-dimensional topological lattice models with surface anyons

We study the phase diagrams of a family of 3D "Walker-Wang" type lattice models, which are not topologically ordered but have deconfined anyonic excitations confined to their surfaces. We add a perturbation (analogous to that which drives the confining transition in Z_p lattice gauge theories) to the Walker-Wang Hamiltonians, driving a transition in which all or some of the variables associated with the loop gas or string-net ground states of these models become confined. We show that in many cases the location and nature of the phase transitions involved is exactly that of a generalized Z_p lattice gauge theory, and use this to deduce the basic structure of the phase diagram. We further show that the relationship between the phases on opposite sides of the transition is fundamentally different than in conventional gauge theories: in the Walker-Wang case, the number of species of excitations that are deconfined in the bulk can increase across a transition that confines only some of the species of loops or string-nets. The analogue of the confining transition in the Walker-Wang models can therefore lead to bulk deconfinement and topological order

A comparison of the excess mass around CFHTLenS galaxy-pairs to predictions from a semi-analytic model using galaxy-galaxy-galaxy lensing

The matter environment of galaxies is connected to the physics of galaxy formation and evolution. Utilising galaxy-galaxy-galaxy lensing as a direct probe, we map out the distribution of correlated surface mass-density around galaxy pairs for different lens separations in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). We compare, for the first time, these so-called excess mass maps to predictions provided by a recent semi-analytic model, which is implanted within the dark-matter Millennium Simulation. We analyse galaxies with stellar masses between $10^9-10^{11}\,{\rm M}_\odot$ in two photometric redshift bins, for lens redshifts $z\lesssim0.6$, focusing on pairs inside groups and clusters. To allow us a better interpretation of the maps, we discuss the impact of chance pairs, i.e., galaxy pairs that appear close to each other in projection only. Our tests with synthetic data demonstrate that the patterns observed in the maps are essentially produced by correlated pairs that are close in redshift ($\Delta z\lesssim5\times10^{-3}$). We also verify the excellent accuracy of the map estimators. In an application to the galaxy samples in the CFHTLenS, we obtain a $3\sigma-6\sigma$ significant detection of the excess mass and an overall good agreement with the galaxy model predictions. There are, however, a few localised spots in the maps where the observational data disagrees with the model predictions on a $\approx3.5\sigma$ confidence level. Although we have no strong indications for systematic errors in the maps, this disagreement may be related to the residual B-mode pattern observed in the average of all maps. Alternatively, misaligned galaxy pairs inside dark matter halos or lensing by a misaligned distribution of the intra-cluster gas might also cause the unanticipated bulge in the distribution of the excess mass between lens pairs.Comment: 21 pages, 12 figures; abridged abstract; revised version for A&A after addressing all comments by the refere