1,006 research outputs found
Solution of the Percus-Yevick equation for hard discs
We solve the Percus-Yevick equation in two dimensions by reducing it to a set
of simple integral equations. We numerically obtain both the pair correlation
function and the equation of state for a hard disc fluid and find good
agreement with available Monte-Carlo calculations. The present method of
resolution may be generalized to any even dimension.Comment: 9 pages, 3 figure
Structure of hard-hypersphere fluids in odd dimensions
The structural properties of single component fluids of hard hyperspheres in
odd space dimensionalities are studied with an analytical approximation
method that generalizes the Rational Function Approximation earlier introduced
in the study of hard-sphere fluids [S. B. Yuste and A. Santos, Phys. Rev. A
{\bf 43}, 5418 (1991)]. The theory makes use of the exact form of the radial
distribution function to first order in density and extends it to finite
density by assuming a rational form for a function defined in Laplace space,
the coefficients being determined by simple physical requirements. Fourier
transform in terms of reverse Bessel polynomials constitute the mathematical
framework of this approximation, from which an analytical expression for the
static structure factor is obtained. In its most elementary form, the method
recovers the solution of the Percus-Yevick closure to the Ornstein-Zernike
equation for hyperspheres at odd dimension. The present formalism allows one to
go beyond by yielding solutions with thermodynamic consistency between the
virial and compressibility routes to any desired equation of state. Excellent
agreement with available computer simulation data at and is
obtained. As a byproduct of this study, an exact and explicit polynomial
expression for the intersection volume of two identical hyperspheres in
arbitrary odd dimensions is given.Comment: 18 pages, 7 figures; v2: new references added plus minor changes; to
be published in PR
Photon bremsstrahlung and diffusive broadening of a hard jet
The photon bremsstrahlung rate from a quark jet produced in deep-inelastic
scattering (DIS) off a large nucleus is studied in the collinear limit. The
leading medium-enhanced higher twist corrections which describe the multiple
scattering of the jet in the nucleus are re-summed to all orders of twist. The
propagation of the jet in the absence of further radiative energy loss is shown
to be governed by a transverse momentum diffusion equation. We compute the
final photon spectrum in the limit of soft photons, taking into account the
leading and next-to-leading terms in the photon momentum fraction y. In this
limit, the photon spectrum in a physical gauge is shown to arise from two
interfering sources: one where the initial hard scattering produces an
off-shell quark which immediately radiates the photon and then undergoes
subsequent soft re-scattering; alternatively the quark is produced on-shell and
propagates through the medium until it is driven off-shell by re-scattering and
radiates the photon. Our result has a simple formal structure as a product of
the photon splitting function, the quark transverse momentum distribution
coming from a diffusion equation and a dimensionless factor which encodes the
effect of the interferences encountered by the propagating quark over the
length of the medium. The destructive nature of such interferences in the small
y limit are responsible for the origin of the Landau-Pomeranchuck-Migdal (LPM)
effect. Along the way we also discuss possible implications for quark jets in
hot nuclear matter.Comment: 24 pages, 3 figures, Revtex
Hard collinear gluon radiation and multiple scattering in a medium
The energy loss of hard jets produced in the Deep-Inelastic scattering (DIS)
off a large nucleus is considered in the collinear limit. In particular, the
single gluon emission cross section due to multiple scattering in the medium is
calculated. Calculations are carried out in the higher-twist scheme, which is
extended to include contributions from multiple transverse scatterings on both
the produced quark and the radiated gluon. The leading length enhanced parts of
these power suppressed contributions are resummed. Various interferences
between such diagrams lead to the Landau-Pomeranchuk-Migdal (LPM) effect. We
resum the corrections from an arbitrary number of scatterings and isolate the
leading contributions which are suppressed by one extra power of the hard scale
. All powers of the emitted gluon forward momentum fraction are
retained. We compare our results with the previous calculation of single
scattering per emission in the higher-twist scheme as well as with multiple
scattering resummations in other schemes. It is found that the leading
() contribution to the double differential gluon production cross
section, in this approach, is equivalent to that obtained from the single
scattering calculation once the transverse momentum of the final quark is
integrated out. We comment on the generalization of this formalism to
Monte-Carlo routines.Comment: 30 pages, 7 figures, revtex4, typos correcte
Higher twist jet broadening and classical propagation
The transverse broadening of jets produced in deep-inelastic scattering (DIS)
off a large nucleus is studied in the collinear limit. A class of medium
enhanced higher twist corrections are re-summed to calculate the transverse
momentum distribution of the produced collinear jet. In contrast to previous
approaches, resummation of the leading length enhanced higher twist corrections
is shown to lead to a two dimensional diffusion equation for the transverse
momentum of the propagating jet. Results for the average transverse momentum
obtained from this approach are then compared to the broadening expected from a
classical Langevin analysis for the propagation of the jet under the action of
the fluctuating color Lorentz force inside the nucleons. The set of
approximations that lead to identical results from the two approaches are
outlined. The relationship between the momentum diffusion constant and the
transport coefficient is explicitly derived.Comment: 17 pages, 6 figures, revtex4, references added, typos corrected,
discussion update
The Quantum Mellin transform
We uncover a new type of unitary operation for quantum mechanics on the
half-line which yields a transformation to ``Hyperbolic phase space''. We show
that this new unitary change of basis from the position x on the half line to
the Hyperbolic momentum , transforms the wavefunction via a Mellin
transform on to the critial line . We utilise this new transform
to find quantum wavefunctions whose Hyperbolic momentum representation
approximate a class of higher transcendental functions, and in particular,
approximate the Riemann Zeta function. We finally give possible physical
realisations to perform an indirect measurement of the Hyperbolic momentum of a
quantum system on the half-line.Comment: 23 pages, 6 Figure
Cognitive demands of face monitoring: Evidence for visuospatial overload
Young children perform difficult communication tasks better face to face than when they cannot see one another (e.g., Doherty-Sneddon & Kent, 1996). However, in recent studies, it was found that children aged 6 and 10 years, describing abstract shapes, showed evidence of face-to-face interference rather than facilitation. For some communication tasks, access to visual signals (such as facial expression and eye gaze) may hinder rather than help children’s communication. In new research we have pursued this interference effect. Five studies are described with adults and 10- and 6-year-old participants. It was found that looking at a face interfered with children’s abilities to listen to descriptions of abstract shapes. Children also performed visuospatial memory tasks worse when they looked at someone’s face prior to responding than when they looked at a visuospatial pattern or at the floor. It was concluded that performance on certain tasks was hindered by monitoring another person’s face. It is suggested that processing of visual communication signals shares certain processing resources with the processing of other visuospatial information
Measuring subdiffusion parameters
We propose a method to extract from experimental data the subdiffusion
parameter and subdiffusion coefficient which are defined by
means of the relation where
denotes a mean square displacement of a random walker starting from
at the initial time . The method exploits a membrane system where a
substance of interest is transported in a solvent from one vessel to another
across a thin membrane which plays here only an auxiliary role. Using such a
system, we experimentally study a diffusion of glucose and sucrose in a gel
solvent. We find a fully analytic solution of the fractional subdiffusion
equation with the initial and boundary conditions representing the system under
study. Confronting the experimental data with the derived formulas, we show a
subdiffusive character of the sugar transport in gel solvent. We precisely
determine the parameter , which is smaller than 1, and the subdiffusion
coefficient .Comment: 17 pages, 9 figures, revised, to appear in Phys. Rev.
The rotation curve and mass-distribution in highly flattened galaxies
A new method is developed which permits the reconstruction of the
surface-density distribution in the galactic disk of finite radius from an
arbitrary smooth distribution of the angular velocity via two simple
quadratures. The existence of upper limits for disk's mass and radius during
the analytic continuation of rotation curves into the hidden (non-radiating)
part of the disk is demonstrated.Comment: 13 pages, 2 figure
Universal Parametric Correlations of Eigenvalues of Random Matrix Ensemble
Eigenvalue correlations of random matrix ensembles as a function of an
external perturbation are investigated vis the Dyson Brownian Motion Model in
the situation where the level density has a hard edge singularity. By solving a
linearized hydrodynamical equation, a universal dependence of the
density-density correlator on the external field is found. As an application we
obtain a formula for the variance of linear statistics with the parametric
dependence exhibited as a Laplace transform.Comment: 23 pages, late
- …