On the theory of composition in physics

We develop a theory for describing composite objects in physics. These can be static objects, such as tables, or things that happen in spacetime (such as a region of spacetime with fields on it regarded as being composed of smaller such regions joined together). We propose certain fundamental axioms which, it seems, should be satisfied in any theory of composition. A key axiom is the order independence axiom which says we can describe the composition of a composite object in any order. Then we provide a notation for describing composite objects that naturally leads to these axioms being satisfied. In any given physical context we are interested in the value of certain properties for the objects (such as whether the object is possible, what probability it has, how wide it is, and so on). We associate a generalized state with an object. This can be used to calculate the value of those properties we are interested in for for this object. We then propose a certain principle, the composition principle, which says that we can determine the generalized state of a composite object from the generalized states for the components by means of a calculation having the same structure as the description of the generalized state. The composition principle provides a link between description and prediction.Comment: 23 pages. To appear in a festschrift for Samson Abramsky edited by Bob Coecke, Luke Ong, and Prakash Panangade

Intensive variables in the framework of the non-extensive thermostatistics

By assuming an appropriate energy composition law between two systems governed by the same non-extensive entropy, we revisit the definitions of temperature and pressure, arising from the zeroth principle of thermodynamics, in a manner consistent with the thermostatistics structure of the theory. We show that the definitions of these quantities are sensitive to the composition law of entropy and internal energy governing the system. In this way, we can clarify some questions raised about the possible introduction of intensive variables in the context of non-extensive statistical mechanics.Comment: 14 pages, elsart style, version accepted on Physics Letters

Paramagnetism in the kagome compounds (Zn,Mg,Cd)Cu3_{3}(OH)6_{6}Cl2_{2}

Frustrated magnetism on the kagome lattice has been a fertile ground for rich and fascinating physics, ranging from experimental evidence of a spin liquid to theoretical predictions of exotic superconductivity. Among experimentally realized spin-$\frac{1}{2}$ kagome magnets, herbertsmithite, kapellasite, and haydeeite [(Zn,Mg)Cu$_{3}$(OH)$_{6}$Cl$_{2}$] are all well described by a three-parameter Heisenberg model, but they exhibit distinctly different physics. We address the problem using a pseudofermion functional renormalization-group approach and analyze the low-energy physics in the experimentally accessible parameter range. Our analysis places kapellasite and haydeeite near the boundaries between magnetically ordered and disordered phases, implying that slight modifications could dramatically affect their magnetic properties. Inspired by this, we perform \textit{ab initio} density functional theory calculations of (Zn,Mg,Cd)Cu$_{3}$ (OH)$_{6}$Cl$_{2}$ at various pressures. Our results suggest that by varying pressure and composition one can traverse a paramagnetic regime between different magnetically ordered phases.Comment: Published version. Main paper (7 pages, 5 figures) and Supplemental material (7 pages, 4 figures, 3 tables). Change in titl

Composition, volume, and aspect ratio dependence of the strain distribution, band lineups and electron effective masses in self-assembled pyramidal In1-xGaxAs/GaAs and SixGe1-x/Si quantum dots

We present a systematic investigation of the strain distribution of self-assembled pyramidal In1-xGaxAs/GaAs and SixGe1-x/Si quantum dots for the case of growth on a (001) substrate. The dependence of the biaxial and hydrostatic components of the strain on the quantum dot volume, aspect ratio, composition, and percentage of alloying x is studied using a method based on a Green's function technique. The dependence of the carriers' confining potentials and the electronic effective mass on the same parameters is then calculated in the framework of eight-band k .p theory. The results for which comparable published data are available are in good agreement with the theoretical values for strain profiles, confining potentials, and electronic effective mass. © 2002 American Institute of Physics

The Inner Rim of YSO Disks: Effects of dust grain evolution

Dust-grain growth and settling are the first steps towards planet formation. An understanding of dust physics is therefore integral to a complete theory of the planet formation process. In this paper, we explore the possibility of using the dust evaporation front in YSO disks (`the inner rim') as a probe of the dust physics operating in circumstellar disks. The geometry of the rim depends sensitively on the composition and spatial distribution of dust. Using radiative transfer and hydrostatic equilibrium calculations we demonstrate that dust growth and settling can curve the evaporation front dramatically (from a cylindrical radius of about 0.5 AU in the disk mid-plane to 1.2 AU in the disk upper layers for an A0 star). We compute synthetic images and interferometric visibilities for our representative rim models and show that the current generation of near-IR long-baseline interferometers (VLTI, CHARA) can strongly constrain the dust properties of circumstellar disks, shedding light on the relatively poorly understood processes of grain growth, settling and turbulent mixing.Comment: 26 pages, 9 figures. Accepted for publication in Ap

Role of Dirac cones in magnetotransport properties of REFeAsO (RE=rare earth) oxypnictides

In this work we study the effect of the rare earth element in iron oxypnictides of composition REFeAsO (RE=rare earth). On one hand we carry out Density Functional Theory calculations of the band structure, which evidence the multiband character of these compounds and the presence of Dirac cones along the Y-{\Gamma} and Z-R directions of the reciprocal space. On the other hand, we explore transport behavior by means of resistivity, Hall resistance and magnetoresistance measurements, which confirm the dominant role of Dirac cones. By combining our theoretical and experimental approaches, we extract information on effective masses, scattering rates and Fermi velocities for different rare earth elements.Comment: 13 pages, 5 figures accepted for publication on European Journal of Physics

Synthesis of the elements in stars: forty years of progress

Forty years ago Burbidge, Burbidge, Fowler, and Hoyle combined what we would now call fragmentary evidence from nuclear physics, stellar evolution and the abundances of elements and isotopes in the solar system as well as a few stars into a synthesis of remarkable ingenuity. Their review provided a foundation for forty years of research in all of the aspects of low energy nuclear experiments and theory, stellar modeling over a wide range of mass and composition, and abundance studies of many hundreds of stars, many of which have shown distinct evidence of the processes suggested by B2FH. In this review we summarize progress in each of these fields with emphasis on the most recent developments

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