Fractal index, central charge and fractons

We introduce the notion of fractal index associated with the universal class $h$ of particles or quasiparticles, termed fractons, which obey specific fractal statistics. A connection between fractons and conformal field theory(CFT)-quasiparticles is established taking into account the central charge $c[\nu]$ and the particle-hole duality $\nu\longleftrightarrow\frac{1}{\nu}$, for integer-value $\nu$ of the statistical parameter. In this way, we derive the Fermi velocity in terms of the central charge as $v\sim\frac{c[\nu]}{\nu+1}$. The Hausdorff dimension $h$ which labelled the universal classes of particles and the conformal anomaly are therefore related. Following another route, we also established a connection between Rogers dilogarithm function, Farey series of rational numbers and the Hausdorff dimension.Comment: latex, 12 pages, To appear in Mod. Phys. Lett. A (2000

A Remark on Unconditional Uniqueness in the Chern-Simons-Higgs Model

The solution of the Chern-Simons-Higgs model in Lorenz gauge with data for the potential in $H^{s-1/2}$ and for the Higgs field in $H^s \times H^{s-1}$ is shown to be unique in the natural space $C([0,T];H^{s-1/2} \times H^s \times H^{s-1})$ for $s \ge 1$, where $s=1$ corresponds to finite energy. Huh and Oh recently proved local well-posedness for $s > 3/4$, but uniqueness was obtained only in a proper subspace $Y^s$ of Bourgain type. We prove that any solution in $C([0,T];H^{1/2} \times H^1 \times L^2)$ must in fact belong to the space $Y^{3/4+\epsilon}$, hence it is the unique solution obtained by Huh and Oh

From the ecology of the human spirit to the development of the orchestral theory of communication: the inclusion of the medium-message axiom

The contributions of the biologist, anthropologist and communication theorist Gregory Bateson (1904- 1980) form the nucleus of the cross-disciplinary theoretical principles which led to the founding of the web of thought spun by Watzlawick, Weakland, Beavin, Fish, Jackson, Erickson, Foster, Haley and Satir, amongst others. These authors were united by a common theoretical standpoint which foregrounded the ecology of the human spirit and saw communication as process, a system of transactional interaction. They were also similarly influenced by cybernetics, systems theory and constructivism. Energised by the clash of the ideas in their exchanges, they constructed the orchestral theory of communication, formalised by Paul Watzlawick, Donald Jackson and Janet Beavin. Today, Watzlawick (1967) is regarded as a seminal publication in the annals of interpersonal communication studies. Moving beyond the confines of the original object of study – face-to-face communication – this theory has been increasingly applied to the analysis of institutionally mediated communication and to the understanding of the construction of learning and change in organisations. However, in current circumstances, its set of axiomatic principles would benefit from the inclusion of a medium-message axiom to allow a fuller understanding of the realities of the mediated communication process that the process contains. This paper proposes the inclusion of this new axiom, medium-message; a proposal which is based on the work of Gregory Bateson, the ecology of the human spirit, the orchestral theory of communication and the thinking of the Media Ecology Association. It aims to help build a more profound insight into the realities of the process of human communication

Global Analytic Solutions for the Nonlinear Schr\"odinger Equation

We prove the existence of global analytic solutions to the nonlinear Schr\"odinger equation in one dimension for a certain type of analytic initial data in $L^2$.Comment: Corrected errors in proofs in section

Conformal Klein-Gordon equations and quasinormal modes

Using conformal coordinates associated with conformal relativity -- associated with de Sitter spacetime homeomorphic projection into Minkowski spacetime -- we obtain a conformal Klein-Gordon partial differential equation, which is intimately related to the production of quasi-normal modes (QNMs) oscillations, in the context of electromagnetic and/or gravitational perturbations around, e.g., black holes. While QNMs arise as the solution of a wave-like equation with a Poschl-Teller potential, here we deduce and analytically solve a conformal radial d'Alembert-like equation, from which we derive QNMs formal solutions, in a proposed alternative to more completely describe QNMs. As a by-product we show that this radial equation can be identified with a Schrodinger-like equation in which the potential is exactly the second Poschl-Teller potential, and it can shed some new light on the investigations concerning QNMs.Comment: 13 pages, 10 figure

Model studies of fluctuations in the background for jets in heavy ion collisions

Jets produced in high energy heavy ion collisions are quenched by the production of the quark gluon plasma. Measurements of these jets are influenced by the methods used to suppress and subtract the large, fluctuating background and the assumptions inherent in these methods. We compare the measurements of the background in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV by the ALICE collaboration to calculations in TennGen (a data-driven random background generator) and PYTHIA Angantyr. The standard deviation of the energy in random cones in TennGen is approximately in agreement with the form predicted in the ALICE paper, with deviations of 1-6 $\%$. The standard deviation of energy in random cones in Angantyr exceeds the same predictions by approximately 40 $\%$. Deviations in both models can be explained by the assumption that the single particle $d^2N/dydp_T$ is a Gamma distribution in the derivation of the prediction. This indicates that model comparisons are potentially sensitive to the treatment of the background