Absence of a consistent classical equation of motion for a mass-renormalized point charge

The restrictions of analyticity, relativistic (Born) rigidity, and negligible O(a) terms involved in the evaluation of the self electromagnetic force on an extended charged sphere of radius "a" are explicitly revealed and taken into account in order to obtain a classical equation of motion of the extended charge that is both causal and conserves momentum-energy. Because the power-series expansion used in the evaluation of the self force becomes invalid during transition time intervals immediately following the application and termination of an otherwise analytic externally applied force, transition forces must be included during these transition time intervals to remove the noncausal pre-acceleration and pre-deceleration from the solutions to the equation of motion without the transition forces. For the extended charged sphere, the transition forces can be chosen to maintain conservation of momentum-energy in the causal solutions to the equation of motion within the restrictions of relativistic rigidity and negligible O(a) terms under which the equation of motion is derived. However, it is shown that renormalization of the electrostatic mass to a finite value as the radius of the charge approaches zero introduces a violation of momentum-energy conservation into the causal solutions to the equation of motion of the point charge if the magnitude of the external force becomes too large. That is, the causal classical equation of motion of a point charge with renormalized mass experiences a high acceleration catastrophe.Comment: 13 pages, No figure

Self-forces on extended bodies in electrodynamics

In this paper, we study the bulk motion of a classical extended charge in flat spacetime. A formalism developed by W. G. Dixon is used to determine how the details of such a particle's internal structure influence its equations of motion. We place essentially no restrictions (other than boundedness) on the shape of the charge, and allow for inhomogeneity, internal currents, elasticity, and spin. Even if the angular momentum remains small, many such systems are found to be affected by large self-interaction effects beyond the standard Lorentz-Dirac force. These are particularly significant if the particle's charge density fails to be much greater than its 3-current density (or vice versa) in the center-of-mass frame. Additional terms also arise in the equations of motion if the dipole moment is too large, and when the `center-of-electromagnetic mass' is far from the `center-of-bare mass' (roughly speaking). These conditions are often quite restrictive. General equations of motion were also derived under the assumption that the particle can only interact with the radiative component of its self-field. These are much simpler than the equations derived using the full retarded self-field; as are the conditions required to recover the Lorentz-Dirac equation.Comment: 30 pages; significantly improved presentation; accepted for publication in Phys. Rev.

Students\u27 use of personal technology in the classroom: analyzing the perceptions of the digital generation

Faculty frequently express concerns about students’ personal use of information and communication technologies in today’s university classrooms. As a requirement of a graduate research methodology course in a university in Ontario, Canada, the authors conducted qualitative research to gain an in-depth understanding of students’ perceptions of this issue. Their findings reveal students’ complex considerations about the acceptability of technology use. Their analysis of the broader contexts of students’ use reveals that despite a technological revolution, university teaching practices have remained largely the same, resulting in ‘cultural lag’ within the classroom. While faculty are technically ‘in charge’, students wield power through course evaluations, surveillance technologies and Internet postings. Neoliberalism and the corporatisation of the university have engendered an ‘entrepreneurial student’ customer who sees education as a means to a career. Understanding students’ perceptions and their technological, social and political contexts offers insights into the tensions within today’s classrooms

Experimental determination of the degree of quantum polarisation of continuous variable states

We demonstrate excitation-manifold resolved polarisation characterisation of continuous-variable (CV) quantum states. In contrast to traditional characterisation of polarisation that is based on the Stokes parameters, we experimentally determine the Stokes vector of each excitation manifold separately. Only for states with a given photon number does the methods coincide. For states with an indeterminate photon number, for example Gaussian states, the employed method gives a richer and more accurate description. We apply the method both in theory and in experiment to some common states to demonstrate its advantages.Comment: 5 page

Self-forces from generalized Killing fields

A non-perturbative formalism is developed that simplifies the understanding of self-forces and self-torques acting on extended scalar charges in curved spacetimes. Laws of motion are locally derived using momenta generated by a set of generalized Killing fields. Self-interactions that may be interpreted as arising from the details of a body's internal structure are shown to have very simple geometric and physical interpretations. Certain modifications to the usual definition for a center-of-mass are identified that significantly simplify the motions of charges with strong self-fields. A derivation is also provided for a generalized form of the Detweiler-Whiting axiom that pointlike charges should react only to the so-called regular component of their self-field. Standard results are shown to be recovered for sufficiently small charge distributions.Comment: 21 page

High energy neutrino yields from astrophysical sources II: Magnetized sources

We calculate the yield of high energy neutrinos produced in astrophysical sources for arbitrary interaction depths $\tau_0$ and magnetic field strengths $B$. We take into account energy loss processes like synchrotron radiation and diffusion of charged particles in turbulent magnetic fields as well as the scattering of secondaries on background photons and the direct production of charm neutrinos. Meson-photon interactions are simulated with an extended version of the SOPHIA model. Diffusion leads to an increased path-length before protons leave the source of size R_s and therefore magnetized sources lose their transparency below the energy $E\sim 10^{18}{\rm eV} (R_s/{\rm pc}) (B/{\rm mG}) \tau_0^{1/\alpha}$, with $\alpha=1/3$ and 1 for Kolmogorov and Bohm diffusion, respectively. Moreover, the neutrino flux is suppressed above the energy where synchrotron energy losses become important for charged particles. As a consequence, the energy spectrum and the flavor composition of neutrinos are strongly modified both at low and high energies even for sources with \tau_0\lsim 1.Comment: 15 pages, 16 figure

Finite-Dimensional Calculus

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement in finite terms Rota's "finite operator calculus".Comment: 26 pages. Added material on Krawtchouk polynomials. Additional references include

Energy versus Angular Momentum in Black Hole Binaries

Using accurate numerical relativity simulations of (nonspinning) black-hole binaries with mass ratios 1:1, 2:1 and 3:1 we compute the gauge invariant relation between the (reduced) binding energy $E$ and the (reduced) angular momentum $j$ of the system. We show that the relation $E(j)$ is an accurate diagnostic of the dynamics of a black-hole binary in a highly relativistic regime. By comparing the numerical-relativity $E^{\rm NR} (j)$ curve with the predictions of several analytic approximation schemes, we find that, while the usual, non-resummed post-Newtonian-expanded $E^{\rm PN} (j)$ relation exhibits large and growing deviations from $E^{\rm NR} (j)$, the prediction of the effective one-body formalism, based purely on known analytical results (without any calibration to numerical relativity), agrees strikingly well with the numerical-relativity results.Comment: 4 pages, 2 figure

Internal Friction and Vulnerability of Mixed Alkali Glasses

Based on a hopping model we show how the mixed alkali effect in glasses can be understood if only a small fraction c_V ofthe available sites for the mobile ions is vacant. In particular, we reproduce the peculiar behavior of the internal friction and the steep fall (''vulnerability'') of the mobility of the majority ion upon small replacements by the minority ion. The single and mixed alkali internal friction peaks are caused by ion-vacancy and ion-ion exchange processes. If c_V is small, they can become comparable in height even at small mixing ratios. The large vulnerability is explained by a trapping of vacancies induced by the minority ions. Reasonable choices of model parameters yield typical behaviors found in experiments.Comment: 4 pages, 4 figure