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J. Franklin

Publications and source records attributed to J. Franklin.

At least 19 recordsLinked to original sources
arXiv2025

Neutrinos from Stored Muons (nuSTORM)

The Neutrinos from Stored Muons, nuSTORM, facility has been designed to deliver a definitive neutrino-nucleus scattering programme using beams of ,{\nu}e- and ,{\nu}{\mu}- from the decay of muons confined within a storage ring. The facility is unique, it will be capable of storing {\mu} beams with a central momentum of between 1 GeV/c and 6 GeV/c and a momentum spread of 16%. This specification will allow neutrino-scattering measurements to be made over the kinematic range of interest to the DUNE and Hyper-K collaborations. At nuSTORM, the flavour composition of the beam and the neutrino-energy spectrum are both precisely known. The storage-ring instrumentation will allow the neutrino flux to be determined to a precision of 1% or better. With its existing proton-beam infrastructure, CERN is uniquely well-placed to implement nuSTORM. A summary of the proposed implementation of nuSTORM at CERN is presented below.

hep-ex↗
arXiv2020

A Magnetic Velocity Verlet Method

We discuss an extension of the velocity Verlet method that accurately approximates the kinetic-energy-conserving charged particle motion that comes from magnetic forcing. For a uniform magnetic field, the method is shown to conserve both particle kinetic energy and magnetic dipole moment better than midpoint Runge-Kutta. We then use the magnetic velocity Verlet method to generate trapped particle trajectories, both in a cylindrical magnetic mirror machine setup, and for dipolar fields like the earth's magnetic field. Finally, the method is used to compute an example of (single) mirror motion in the presence of a magnetic monopole field, where the trajectory can be described in closed form.

physics.class-ph↗
arXiv2017

The (Weak) Gravitational Field of a Dirac Monopole

We establish the gravitational detectability of a Dirac monopole using a weak-field limit of general relativity, which can be developed from the Newtonian gravitational potential by including energy as a source. The resulting potential matches (by construction) the weak-field limit of two different solutions to Einstein's equations of general relativity: one associated with the magnetically monopolar spray of field lines emerging from the half-infinite solenoid that makes up the Dirac monopole, the other associated with the field-energetic source of the solenoid itself (the Dirac string). The string's gravitational effect dominates, and we suggest that the primary strong-field contribution of the Dirac configuration is that of a half-infinite line of energy, whose GR solution is known.

gr-qc↗
arXiv2016

The Dynamics of the Schrodinger-Newton System with Self-Field Coupling

We probe the dynamics of a modified form of the Schrodinger-Newton system of gravity coupled to single particle quantum mechanics. At the masses of interest here, the ones associated with the onset of "collapse" (where the gravitational attraction is competitive with the quantum mechanical dissipation), we show that the Schrodinger ground state energies match the Dirac ones with an error of ~ 10%. At the Planck mass scale, we predict the critical mass at which a potential collapse could occur for the self-coupled gravitational case, m ~ 3.3 Planck mass, and show that gravitational attraction opposes Gaussian spreading at around this value, which is a factor of two higher than the one predicted (and verified) for the Schrodinger-Newton system. Unlike the Schrodinger-Newton dynamics, we do not find that the self-coupled case tends to decay towards its ground state; there is no collapse in this case.

gr-qc↗
arXiv2016

Classical and Quantum Mechanical Motion in Magnetic Fields

We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds depend, classically, on a gauge-fixed magnetic vector potential, and demonstrate some trajectories associated with this special type of magnetic field. Then we show that some of the geometric features of the classical trajectory (perpendicular exit from the field region, trapped and escape behavior) are reproduced quantum mechanically using a numerical method that extends the norm-preserving Crank-Nicolson method to problems involving magnetic fields. While there are similarities between the classical trajectory and the position expectation value of the quantum mechanical solution, there are also differences, and we demonstrate some of these.

quant-ph↗
arXiv2015

Bel-Robinson as stress-tensor gradients and their extensions to massive spin (0,1,2)

We show that the Bel-Robinson (BR) tensor is - generically, as well as in its original GR setting - an autonomously conserved part of the, manifestly conserved, double gradient of a system's stress-tensor. This suggests its natural extension from GR to matter models, first to (known) massless scalars and vectors, then to massive ones, including tensors. These massive versions are to be expected, given that they arise upon KK reduction of massless D+1 ones. We exhibit the resulting spin (0, 1, 2) "massive" BR.

gr-qc↗
arXiv2015

The Schrodinger-Newton System with Self-Field Coupling

We study the Schrodinger-Newton system of equations with the addition of gravitational field energy sourcing - such additional nonlinearity is to be expected from a theory of gravity (like general relativity), and its appearance in this simplified scalar setting (one of Einstein's precursors to general relativity) leads to significant changes in the spectrum of the self-gravitating theory. Using an iterative technique, we compare the mass dependence of the ground state energies of both Schrodinger-Newton and the new, self-sourced system and find that they are dramatically different. The Bohr method approach from old quantization provides a qualitative description of the difference, which comes from the additional nonlinearity introduced in the self-sourced case. In addition to comparison of ground state energies, we calculate the transition energy between the ground state and first excited state to compare emission frequencies between Schrodinger-Newton and the self-coupled scalar case.

gr-qc↗
arXiv2013

The Motion of a Pair of Charged Particles

We re-visit the problem of two (oppositely) charged particles interacting electromagnetically in one dimension with retarded potentials and no radiation reaction. The specific quantitative result of interest is the time it takes for the particles to fall in towards one another. Starting with the non-relativistic form, we answer this question while adding layers of complexity until we arrive at the full relativistic delay differential equation that governs this problem. That case can be solved using the Synge method, which we describe and discuss.

physics.class-ph↗
arXiv2012

Symmetrically reduced Galileon equations and solutions

The maximally complicated arbitrary-dimensional "maximal" Galileon field equations simplify dramatically for symmetric configurations. Thus, spherical symmetry reduces the equations from the D- to the two-dimensional Monge-Ampere equation, axial symmetry to its cubic extension etc. We can then obtain explicit solutions, such as spherical or axial waves, and relate them to the (known) general, but highly implicit, lower-D solutions.

gr-qc↗
arXiv2012

Relativistic Linear Restoring Force

We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right of the relativistic expressions: dp/dt or dp/dtau . Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we introduce a form of retardation appropriate for the description of a linear (in displacement) force arising from the interaction of a pair of particles with a relativistic field. The procedure is akin to replacing Coulomb's law in E&M with a retarded form (the first correction in the full relativistic case). This retardation leads to the expected oscillation, but with amplitude growth in both its relativistic and non-relativistic incarnations.

physics.class-ph↗
arXiv2012

Canonical Analysis and Stability of Lanczos-Lovelock Gravity

We perform a space-time analysis of the D>4 quadratic curvature Lanczos-Lovelock (LL) model, exhibiting its dependence on intrinsic/extrinsic curvatures, lapse and shifts. As expected from general covariance, the field equations include D constraints, of zeroth and first time derivative order. In the "linearized" - here necessarily cubic - limit, we give an explicit formulation in terms of the usual ADM metric decomposition, incidentally showing that time derivatives act only on its transverse-traceless spatial components. Unsurprisingly, pure LL has no Hamiltonian formulation, nor are even its - quadratic - weak field constraints easily soluble. Separately, we point out that the extended, more physical R+LL, model is stable - its energy is positive - due to its supersymmetric origin and ghost-freedom.

gr-qc↗
arXiv2011

No Bel-Robinson Tensor for Quadratic Curvature Theories

We attempt to generalize the familiar covariantly conserved Bel-Robinson tensor B_{mnab} ~ R R of GR and its recent topologically massive third derivative order counterpart B ~ RDR, to quadratic curvature actions. Two very different models of current interest are examined: fourth order D=3 "new massive", and second order D>4 Lanczos-Lovelock, gravity. On dimensional grounds, the candidates here become B ~ DRDR+RRR. For the D=3 model, there indeed exist conserved B ~ dRdR in the linearized limit. However, despite a plethora of available cubic terms, B cannot be extended to the full theory. The D>4 models are not even linearizable about flat space, since their field equations are quadratic in curvature; they also have no viable B, a fact that persists even if one includes cosmological or Einstein terms to allow linearization about the resulting dS vacua. These results are an unexpected, if hardly unique, example of linearization instability.

gr-qc↗
arXiv2011

Approximate Born-Infeld Effects on the Relativistic Hydrogen Spectrum

The Born-Infeld form of the hydrogen atom has a spectrum that can be used to determine the physical viability of the theory, and place an experimentally relevant bound on the single parameter found in it. We compute this spectrum using the relativistic Dirac equation, and a form of the Born-Infeld potential that approximates the self-field corrections of the electron. Using these together, we can establish that if the Born-Infeld nonlinear electrodynamics is to be physically relevant, it must contain a fundamental constant that is well below the original value proposed by Born. This work extends the original Schrodinger spectrum from Carley and Kiessling (2006) [1] for the self-field correction, and shows that using the Dirac equation introduces minor corrections - but also gives access to a range for the fundamental constant that is below that attainable from non-relativistic considerations.

quant-ph↗
arXiv2011

Charged Radial Infall for Spherical Central Bodies

A massive, charged, spherical central body can be neutralized by attracting particles of opposite charge. We calculate the time it takes to neutralize these central bodies using classical mechanics, special relativistic mechanics, and finally, the "forced" trajectories of general relativity. While we can compare the classical and (special) relativistic times, and find, predictably, that the special relativistic neutralization time is longer, a comparison of these times with the general relativistic result is not as directly possible. We offer the final calculation as a demonstration of dynamics in a general setting and in particular, the structural similarity of the (general) relativistic problem to the other cases.

physics.class-ph↗
arXiv2010

Is BTZ a separate superselection sector of CTMG?

We exhibit exact solutions of (positive) matter coupled to cosmological TMG; they necessarily evolve to conical singularity/negative mass, rather than physical black hole, BTZ. By providing evidence that the latter constitutes a separate, "superselection", sector not reachable from the physical one, they also provide justification for retaining TMG's original "wrong" G-sign to ensure excitation stability here as well.

hep-th↗
arXiv2010

Circular Symmetry in Topologically Massive Gravity

We re-derive, compactly, a TMG decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We can then generalize it to include matter, which is necessarily null.

gr-qc↗
arXiv2010

De/re-constructing the Kerr Metric

We derive the Kerr solution in a pedagogically transparent way, using physical symmetry and gauge arguments to reduce the candidate metric to just two unknowns. The resulting field equations are then easy to obtain, and solve. Separately, we transform the Kerr metric to Schwarzschild frame to exhibit its limits in that familiar setting.

gr-qc↗