8,636 research outputs found
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 and magnetic field strengths
. 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 , with 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 and the (reduced) angular
momentum of the system. We show that the relation is an accurate
diagnostic of the dynamics of a black-hole binary in a highly relativistic
regime. By comparing the numerical-relativity curve with the
predictions of several analytic approximation schemes, we find that, while the
usual, non-resummed post-Newtonian-expanded relation exhibits
large and growing deviations from , 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
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