arXiv subjects

A. D. Jackson

Publications and source records attributed to A. D. Jackson.

At least 19 recordsLinked to original sources

arXiv2016

Understanding the LIGO GW150914 event

We present a simplified method for the extraction of meaningful signals from Hanford and Livingstone 32 seconds data for the GW150914 event made publicly available by the LIGO collaboration and demonstrate its ability to reproduce the LIGO collaboration's own results quantitatively given the assumption that all narrow peaks in the power spectrum are a consequence of physically uninteresting signals and can be removed. After the clipping of these peaks and return to the time domain, the GW150914 event is readily distinguished from broadband background noise. This simple technique allows us to identify the GW150914 event without any assumption regarding its physical origin and with minimal assumptions regarding its shape. We also confirm that the LIGO GW150914 event is uniquely correlated in the Hanford and Livingston detectors for 4096 second data at the level of $6-7\,σ$ with a temporal displacement of $τ=6.9 \pm 0.4\,$ms. We have also identified a few events that are morphologically close to GW150914 but less strongly cross correlated with it.

astro-ph.CO↗

arXiv2015

Hysteresis and metastability of Bose-Einstein condensed clouds of atoms confined in ring potentials

We consider a Bose-Einstein condensed cloud of atoms which rotate in a toroidal/annular potential. Assuming one-dimensional motion, we evaluate the critical frequencies associated with the effect of hysteresis and the critical coupling for stability of the persistent currents. We perform these calculations using both the mean-field approximation and the method of numerical diagonalization of the many-body Hamiltonian which includes corrections due to the finiteness of the atom number.

cond-mat.quant-gas↗

arXiv2015

Rotating Bose-Einstein condensates: Closing the gap between exact and mean-field solutions

When a Bose-Einstein condensed cloud of atoms is given some angular momentum, it forms vortices arranged in structures with a discrete rotational symmetry. For these vortex states, the Hilbert space of the exact solution separates into a "primary" space related to the mean-field Gross-Pitaevskii solution and a "complementary" space including the corrections beyond mean-field. Considering a weakly-interacting Bose-Einstein condensate of harmonically-trapped atoms, we demonstrate how this separation can be used to close the conceptual gap between exact solutions for systems with only a few atoms and the thermodynamic limit for which the mean-field is the correct leading-order approximation. Although we illustrate this approach for the case of weak interactions, it is expected to be more generally valid.

cond-mat.quant-gas↗

arXiv2012

Solitary-wave solutions in binary mixtures of Bose-Einstein condensates under periodic boundary conditions

We derive solitary-wave solutions within the mean-field approximation in quasi-one-dimensional binary mixtures of Bose-Einstein condensates under periodic boundary conditions, for the case of an effective repulsive interatomic interaction. The particular gray-bright solutions that give the global energy minima are determined. Their characteristics and the associated dispersion relation are derived. In the case of weak coupling, we diagonalize the Hamiltonian analytically to obtain the full excitation spectrum of "quantum" solitary-wave solutions.

cond-mat.quant-gas↗

arXiv2012

Excitation spectrum of a two-component Bose-Einstein condensate in a ring potential

A mixture of two distinguishable Bose-Einstein condensates confined in a ring potential has numerous interesting properties under rotational and solitary-wave excitation. The lowest-energy states for a fixed angular momentum coincide with a family of solitary-wave solutions. In the limit of weak interactions, exact diagonalization of the many-body Hamiltonian is possible and permits evaluation of the complete excitation spectrum of the system.

cond-mat.quant-gas↗

arXiv2011

Solitary waves and yrast states in Bose-Einstein condensed gases of atoms

Considering a Bose-Einstein condensed gas confined in one dimension with periodic boundary conditions, we demonstrate that, very generally, solitary-wave and rotational excitations coincide. This exact equivalence allows us to establish connections between a number of effects that are present in these two problems, many of which have been studied using the mean-field approximation.

cond-mat.quant-gas↗

arXiv2010

Solitary waves of Bose-Einstein condensed atoms confined in finite rings

Motivated by recent progress in trapping Bose-Einstein condensed atoms in toroidal potentials, we examine solitary-wave solutions of the nonlinear Schrödinger equation subject to periodic boundary conditions. When the circumference of the ring is much larger than the size of the wave, the density profile is well approximated by that of an infinite ring, however the density and the velocity of propagation cannot vanish simultaneously. When the size of the ring becomes comparable to the size of the wave, the density variation becomes sinusoidal and the velocity of propagation saturates to a constant value.

cond-mat.quant-gas↗

arXiv2009

Solitary waves in mixtures of Bose gases confined in annular traps

A two-component Bose-Einstein condensate that is confined in a one-dimensional ring potential supports solitary-wave solutions, which we evaluate analytically. The derived solutions are shown to be unique. The corresponding dispersion relation that generalizes the case of a single-component system shows interesting features.

cond-mat.quant-gas↗

arXiv2008

The absence of fragmentation in Bose-Einstein condensates

A Bose-Einstein condensate produced by a Hamiltonian which is rotationally or translationally symmetric is fragmented as a direct result of these symmetries. A corresponding mean-field unfragmented state, with an identical energy to leading order in the number of particles, can generally be constructed. As a consequence, vanishingly weak symmetry-breaking perturbations destabilize the fragmented state, which would thus be extremely difficult to realize experimentally, and lead to an unfragmented condensate.

cond-mat.other↗

arXiv2008

Bright solitary waves in a Bose-Einstein condensate and their interactions

We examine the dynamics of two bright solitary waves with a negative nonlinear term. The observed repulsion between two solitary waves -- when these are in an antisymmetric combination -- is attributed to conservation laws. Slight breaking of parity, in combination with weak relaxation of energy, leads the two solitary waves to merge. The effective repulsion between solitary waves requires certain nearly ideal conditions and is thus fragile.

cond-mat.other↗

arXiv2007

A quantitative analysis of measures of quality in science

Condensing the work of any academic scientist into a one-dimensional measure of scientific quality is a difficult problem. Here, we employ Bayesian statistics to analyze several different measures of quality. Specifically, we determine each measure's ability to discriminate between scientific authors. Using scaling arguments, we demonstrate that the best of these measures require approximately 50 papers to draw conclusions regarding long term scientific performance with usefully small statistical uncertainties. Further, the approach described here permits the value-free (i.e., statistical) comparison of scientists working in distinct areas of science.

physics.soc-ph↗

arXiv2006

Manipulating Bose-Einstein condensed atoms in toroidal traps

We consider Bose-Einstein condensed atoms confined in a toroidal trap. We demonstrate that under conditions of one-dimensional behavior, the density distribution of the atoms may be exponentially localized/delocalized, even for very small variations in the trapping potential along the torus. This observation allows one to control the atom density externally via slight modifications of the trapping potential. For similar reasons, small irregularities of the trap may also have a very pronounced effect on the density of the cloud.

cond-mat.other↗

arXiv2005

The stability of solitons in biomembranes and nerves

We examine the stability of a class of solitons, obtained from a generalization of the Boussinesq equation, which have been proposed to be relevant for pulse propagation in biomembranes and nerves. These solitons are found to be stable with respect to small amplitude fluctuations. They emerge naturally from non-solitonic initial excitations and are robust in the presence of dissipation.

physics.bio-ph↗

arXiv2005

Stability of the solutions of the Gross-Pitaevskii equation

We examine the static and dynamic stability of the solutions of the Gross-Pitaevskii equation and demonstrate the intimate connection between them. All salient features related to dynamic stability are reflected systematically in static properties. We find, for example, the obvious result that static stability always implies dynamic stability and present a simple explanation of the fact that dynamic stability can exist even in the presence of static instability.

cond-mat.other↗

arXiv2005

Solitary waves in elongated clouds of strongly-interacting bosons

We examine the propagation of solitary waves in elongated clouds of trapped bosonic atoms as the confinement, the strength of the interatomic interaction, and the atom density are varied. We identify three different physical regimes and develop a general formalism that allows us to interpolate between them. Finally we pay special attention to the transition to the Tonks-Girardeau limit of strongly-interacting bosons.

cond-mat.other↗

arXiv2005

Multi-channel scattering and Feshbach resonances: Effective theory, phenomenology, and many-body effects

A low energy effective theory based on a microscopic multi-channel description of the atom-atom interaction is derived for the scattering of alkali atoms in different hyperfine states. This theory describes all scattering properties, including medium effects, in terms of the singlet and triplet scattering lengths and the range of the atom-atom potential and provides a link between a microscopic description of Feshbach scattering and more phenomenological approaches. It permits the calculation of medium effects on the resonance coming from the occupation of closed channel states. The examination of such effects are demonstrated to be of particular relevance to an experimentally important Feshbach resonance for $^{40}$K atoms. We analyze a recent rethermalization rate experiment on $^{40}$K and demonstrate that a measurement of the temperature dependence of this rate can determine the magnetic moment of the Feshbach molecule. Finally, the energy dependence of the Feshbach interaction is shown to introduce a negative effective range inversely proportional to the width of the resonance. Since our theory is based on a microscopic multi-channel picture, it allows the explicit calculation of corrections to commonly used approximations such as the neglect of the effective range and the treatment of the Feshbach molecule as a point boson.

cond-mat.other↗

arXiv2005

Live and Dead Nodes

In this paper, we explore the consequences of a distinction between `live' and `dead' network nodes; `live' nodes are able to acquire new links whereas `dead' nodes are static. We develop an analytically soluble growing network model incorporating this distinction and show that it can provide a quantitative description of the empirical network composed of citations and references (in- and out-links) between papers (nodes) in the SPIRES database of scientific papers in high energy physics. We also demonstrate that the death mechanism alone can result in power law degree distributions for the resulting network.

physics.soc-ph↗

arXiv2005

Random matrix models for chiral and diquark condensation

We consider random matrix models for the thermodynamic competition between chiral symmetry breaking and diquark condensation in QCD at finite temperature and finite baryon density. The models produce mean field phase diagrams whose topology depends solely on the global symmetries of the theory. We discuss the block structure of the interactions that is imposed by chiral, spin, and color degrees of freedom and comment on the treatment of density and temperature effects. Extension of the coupling parameters to a larger class of theories allows us to investigate the robustness of the phase topology with respect to variations in the dynamics of the interactions. We briefly study the phase structure as a function of coupling parameters and the number of colors.

hep-ph↗