3,913 research outputs found
Analytic solutions of the 1D finite coupling delta function Bose gas
An intensive study for both the weak coupling and strong coupling limits of
the ground state properties of this classic system is presented. Detailed
results for specific values of finite are given and from them results for
general are determined. We focus on the density matrix and concomitantly
its Fourier transform, the occupation numbers, along with the pair correlation
function and concomitantly its Fourier transform, the structure factor. These
are the signature quantities of the Bose gas. One specific result is that for
weak coupling a rational polynomial structure holds despite the transcendental
nature of the Bethe equations. All these new results are predicated on the
Bethe ansatz and are built upon the seminal works of the past.Comment: 23 pages, 0 figures, uses rotate.sty. A few lines added. Accepted by
Phys. Rev.
Massive spinor fields in flat spacetimes with non-trivial topology
The vacuum expectation value of the stress-energy tensor is calculated for
spin massive fields in several multiply connected flat spacetimes.
We examine the physical effects of topology on manifolds such as , , , the Mobius strip and the Klein bottle.
We find that the spinor vacuum stress tensor has the opposite sign to, and
twice the magnitude of, the scalar tensor in orientable manifolds. Extending
the above considerations to the case of Misner spacetime, we calculate the
vacuum expectation value of spinor stress-energy tensor in this space and
discuss its implications for the chronology protection conjecture.Comment: 18 pages, Some of the equations in section VI as well as
typographical errors corrected, 5 figures, Revtex
We Could, but Should We? Ethical Considerations for Providing Access to GeoCities and Other Historical Digital Collections
We live in an era in which the ways that we can make sense of our past are evolving as more artifacts from that past become digital. At the same time, the responsibilities of traditional gatekeepers who have negotiated the ethics of historical data collection and use, such as librarians and archivists, are increasingly being sidelined by the system builders who decide whether and how to provide access to historical digital collections, often without sufficient reflection on the ethical issues at hand. It is our aim to better prepare system builders to grapple with these issues. This paper focuses discussions around one such digital collection from the dawn of the web, asking what sorts of analyses can and should be conducted on archival copies of the GeoCities web hosting platform that dates to 1994.This research was supported by the Natural Sciences and Engineering Research Council of Canada, the Social Sciences and Humanities Research Council of Canada, the US National Science Foundation (grants 1618695 and 1704369), the Andrew W. Mellon Foundation, Start Smart Labs, and Compute Canada
Eigenvalue Separation in Some Random Matrix Models
The eigenvalue density for members of the Gaussian orthogonal and unitary
ensembles follows the Wigner semi-circle law. If the Gaussian entries are all
shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in
the large N limit a single eigenvalue will separate from the support of the
Wigner semi-circle provided c > 1. In this study, using an asymptotic analysis
of the secular equation for the eigenvalue condition, we compare this effect to
analogous effects occurring in general variance Wishart matrices and matrices
from the shifted mean chiral ensemble. We undertake an analogous comparative
study of eigenvalue separation properties when the size of the matrices are
fixed and c goes to infinity, and higher rank analogues of this setting. This
is done using exact expressions for eigenvalue probability densities in terms
of generalized hypergeometric functions, and using the interpretation of the
latter as a Green function in the Dyson Brownian motion model. For the shifted
mean Gaussian unitary ensemble and its analogues an alternative approach is to
use exact expressions for the correlation functions in terms of classical
orthogonal polynomials and associated multiple generalizations. By using these
exact expressions to compute and plot the eigenvalue density, illustrations of
the various eigenvalue separation effects are obtained.Comment: 25 pages, 9 figures include
Geometry of the energy landscape of the self-gravitating ring
We study the global geometry of the energy landscape of a simple model of a
self-gravitating system, the self-gravitating ring (SGR). This is done by
endowing the configuration space with a metric such that the dynamical
trajectories are identified with geodesics. The average curvature and curvature
fluctuations of the energy landscape are computed by means of Monte Carlo
simulations and, when possible, of a mean-field method, showing that these
global geometric quantities provide a clear geometric characterization of the
collapse phase transition occurring in the SGR as the transition from a flat
landscape at high energies to a landscape with mainly positive but fluctuating
curvature in the collapsed phase. Moreover, curvature fluctuations show a
maximum in correspondence with the energy of a possible further transition,
occurring at lower energies than the collapse one, whose existence had been
previously conjectured on the basis of a local analysis of the energy landscape
and whose effect on the usual thermodynamic quantities, if any, is extremely
weak. We also estimate the largest Lyapunov exponent of the SGR using
the geometric observables. The geometric estimate always gives the correct
order of magnitude of and is also quantitatively correct at small
energy densities and, in the limit , in the whole homogeneous
phase.Comment: 20 pages, 12 figure
Taylor dispersion of gyrotactic swimming micro-organisms in a linear flow
The theory of generalized Taylor dispersion for suspensions of Brownian particles is developed to study the dispersion of gyrotactic swimming micro-organisms in a linear shear flow. Such creatures are bottom-heavy and experience a gravitational torque which acts to right them when they are tipped away from the vertical. They also suffer a net viscous torque in the presence of a local vorticity field. The orientation of the cells is intrinsically random but the balance of the two torques results in a bias toward a preferred swimming direction. The micro-organisms are sufficiently large that Brownian motion is negligible but their random swimming across streamlines results in a mean velocity together with diffusion. As an example, we consider the case of vertical shear flow and calculate the diffusion coefficients for a suspension of the alga <i>Chlamydomonas nivalis</i>. This rational derivation is compared with earlier approximations for the diffusivity
Spherical Vesicles Distorted by a Grafted Latex Bead: An Exact Solution
We present an exact solution to the problem of the global shape description
of a spherical vesicle distorted by a grafted latex bead. This solution is
derived by treating the nonlinearity in bending elasticity through the
(topological) Bogomol'nyi decomposition technique and elastic compatibility. We
recover the ``hat-model'' approximation in the limit of a small latex bead and
find that the region antipodal to the grafted latex bead flattens. We also
derive the appropriate shape equation using the variational principle and
relevant constraints.Comment: 12 pages, 2 figures, LaTeX2e+REVTeX+AmSLaTe
Some integrals ocurring in a topology change problem
In a paper presented a few years ago, De Lorenci et al. showed, in the
context of canonical quantum cosmology, a model which allowed space topology
changes (Phys. Rev. D 56, 3329 (1997)). The purpose of this present work is to
go a step further in that model, by performing some calculations only estimated
there for several compact manifolds of constant negative curvature, such as the
Weeks and Thurston spaces and the icosahedral hyperbolic space (Best space).Comment: RevTeX article, 4 pages, 1 figur
Variational formulation of ideal fluid flows according to gauge principle
On the basis of the gauge principle of field theory, a new variational
formulation is presented for flows of an ideal fluid. The fluid is defined
thermodynamically by mass density and entropy density, and its flow fields are
characterized by symmetries of translation and rotation. The rotational
transformations are regarded as gauge transformations as well as the
translational ones. In addition to the Lagrangians representing the translation
symmetry, a structure of rotation symmetry is equipped with a Lagrangian
including the vorticity and a vector potential bilinearly. Euler's
equation of motion is derived from variations according to the action
principle. In addition, the equations of continuity and entropy are derived
from the variations. Equations of conserved currents are deduced as the Noether
theorem in the space of Lagrangian coordinate \ba. Without , the
action principle results in the Clebsch solution with vanishing helicity. The
Lagrangian yields non-vanishing vorticity and provides a source
term of non-vanishing helicity. The vorticity equation is derived as an
equation of the gauge field, and the characterizes topology of the
field. The present formulation is comprehensive and provides a consistent basis
for a unique transformation between the Lagrangian \ba space and the Eulerian
\bx space. In contrast, with translation symmetry alone, there is an
arbitrariness in the ransformation between these spaces.Comment: 34 pages, Fluid Dynamics Research (2008), accepted on 1st Dec. 200
Short Wavelength Analysis of the Evolution of Perturbations in a Two-component Cosmological Fluid
The equations describing a two-component cosmological fluid with linearized
density perturbations are investigated in the small wavelength or large
limit. The equations are formulated to include a baryonic component, as well as
either a hot dark matter (HDM) or cold dark matter (CDM) component. Previous
work done on such a system in static spacetime is extended to reveal some
interesting physical properties, such as the Jeans wavenumber of the mixture,
and resonant mode amplitudes. A WKB technique is then developed to study the
expanding universe equations in detail, and to see whether such physical
properties are also of relevance in this more realistic scenario. The Jeans
wavenumber of the mixture is re-interpreted for the case of an expanding
background spacetime. The various modes are obtained to leading order, and the
amplitudes of the modes are examined in detail to compare to the resonances
observed in the static spacetime results. It is found that some conclusions
made in the literature about static spacetime results cannot be carried over to
an expanding cosmology.Comment: 42 pages, 12 figure
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