175 research outputs found
Steady state existence of passive vector fields under the Kraichnan model
The steady state existence problem for Kraichnan advected passive vector
models is considered for isotropic and anisotropic initial values in arbitrary
dimension. The model includes the magnetohydrodynamic (MHD) equations, linear
pressure model (LPM) and linearized Navier-Stokes (LNS) equations. In addition
to reproducing the previously known results for the MHD and linear pressure
model, we obtain the values of the Kraichnan model roughness parameter
for which the LNS steady state exists.Comment: Improved text & figures, added references & other correction
High-Order Coupled Cluster Method Calculations for the Ground- and Excited-State Properties of the Spin-Half XXZ Model
In this article, we present new results of high-order coupled cluster method
(CCM) calculations, based on a N\'eel model state with spins aligned in the
-direction, for both the ground- and excited-state properties of the
spin-half {\it XXZ} model on the linear chain, the square lattice, and the
simple cubic lattice. In particular, the high-order CCM formalism is extended
to treat the excited states of lattice quantum spin systems for the first time.
Completely new results for the excitation energy gap of the spin-half {\it XXZ}
model for these lattices are thus determined. These high-order calculations are
based on a localised approximation scheme called the LSUB scheme in which we
retain all -body correlations defined on all possible locales of
adjacent lattice sites (). The ``raw'' CCM LSUB results are seen to
provide very good results for the ground-state energy, sublattice
magnetisation, and the value of the lowest-lying excitation energy for each of
these systems. However, in order to obtain even better results, two types of
extrapolation scheme of the LSUB results to the limit (i.e.,
the exact solution in the thermodynamic limit) are presented. The extrapolated
results provide extremely accurate results for the ground- and excited-state
properties of these systems across a wide range of values of the anisotropy
parameter.Comment: 31 Pages, 5 Figure
Governance factors in the identification of global conservation priorities for mammals
Global conservation priorities have often been identified based on the combination of species richness and threat information. With the development of the field of systematic conservation planning, more attention has been given to conservation costs. This leads to prioritizing developing countries, where costs are generally low and biodiversity is high. But many of these countries have poor governance, which may result in ineffective conservation or in larger costs than initially expected. We explore how the consideration of governance affects the selection of global conservation priorities for the world's mammals in a complementarity-based conservation prioritization. We use data on Control of Corruption (Worldwide Governance Indicators project) as an indicator of governance effectiveness, and gross domestic product per capita as an indicator of cost. We show that, while core areas with high levels of endemism are always selected as important regardless of governance and cost values, there are clear regional differences in selected sites when biodiversity, cost or governance are taken into account separately. Overall, the analysis supports the concentration of conservation efforts in most of the regions generally considered of high priority, but stresses the need for different conservation approaches in different continents owing to spatial patterns of governance and economic development
Single-Particle Green Functions in Exactly Solvable Models of Bose and Fermi Liquids
Based on a class of exactly solvable models of interacting bose and fermi
liquids, we compute the single-particle propagators of these systems exactly
for all wavelengths and energies and in any number of spatial dimensions. The
field operators are expressed in terms of bose fields that correspond to
displacements of the condensate in the bose case and displacements of the fermi
sea in the fermi case.
Unlike some of the previous attempts, the present attempt reduces the answer
for the spectral function in any dimension in both fermi and bose systems to
quadratures.
It is shown that when only the lowest order sea-displacement terms are
included, the random phase approximation in its many guises is recovered in the
fermi case, and Bogoliubov's theory in the bose case. The momentum distribution
is evaluated using two different approaches, exact diagonalisation and the
equation of motion approach.
The novelty being of course, the exact computation of single-particle
properties including short wavelength behaviour.Comment: Latest version to be published in Phys. Rev. B. enlarged to around 40
page
An extension of the coupled-cluster method: A variational formalism
A general quantum many-body theory in configuration space is developed by
extending the traditional coupled cluter method (CCM) to a variational
formalism. Two independent sets of distribution functions are introduced to
evaluate the Hamiltonian expectation. An algebraic technique for calculating
these distribution functions via two self-consistent sets of equations is
given. By comparing with the traditional CCM and with Arponen's extension, it
is shown that the former is equivalent to a linear approximation to one set of
distribution functions and the later is equivalent to a random-phase
approximation to it. In additional to these two approximations, other
higher-order approximation schemes within the new formalism are also discussed.
As a demonstration, we apply this technique to a quantum antiferromagnetic spin
model.Comment: 15 pages. Submitted to Phys. Rev.
High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States
In this article, we prove that exact representations of dimer and plaquette
valence-bond ket ground states for quantum Heisenberg antiferromagnets may be
formed via the usual coupled cluster method (CCM) from independent-spin product
(e.g. N\'eel) model states. We show that we are able to provide good results
for both the ground-state energy and the sublattice magnetization for dimer and
plaquette valence-bond phases within the CCM. As a first example, we
investigate the spin-half -- model for the linear chain, and we show
that we are able to reproduce exactly the dimerized ground (ket) state at
. The dimerized phase is stable over a range of values for
around 0.5. We present evidence of symmetry breaking by considering
the ket- and bra-state correlation coefficients as a function of . We
then consider the Shastry-Sutherland model and demonstrate that the CCM can
span the correct ground states in both the N\'eel and the dimerized phases.
Finally, we consider a spin-half system with nearest-neighbor bonds for an
underlying lattice corresponding to the magnetic material CaVO (CAVO).
We show that we are able to provide excellent results for the ground-state
energy in each of the plaquette-ordered, N\'eel-ordered, and dimerized regimes
of this model. The exact plaquette and dimer ground states are reproduced by
the CCM ket state in their relevant limits.Comment: 34 pages, 13 figures, 2 table
Phase Transitions in the Spin-Half J_1--J_2 Model
The coupled cluster method (CCM) is a well-known method of quantum many-body
theory, and here we present an application of the CCM to the spin-half J_1--J_2
quantum spin model with nearest- and next-nearest-neighbour interactions on the
linear chain and the square lattice. We present new results for ground-state
expectation values of such quantities as the energy and the sublattice
magnetisation. The presence of critical points in the solution of the CCM
equations, which are associated with phase transitions in the real system, is
investigated. Completely distinct from the investigation of the critical
points, we also make a link between the expansion coefficients of the
ground-state wave function in terms of an Ising basis and the CCM ket-state
correlation coefficients. We are thus able to present evidence of the
breakdown, at a given value of J_2/J_1, of the Marshall-Peierls sign rule which
is known to be satisfied at the pure Heisenberg point (J_2 = 0) on any
bipartite lattice. For the square lattice, our best estimates of the points at
which the sign rule breaks down and at which the phase transition from the
antiferromagnetic phase to the frustrated phase occurs are, respectively, given
(to two decimal places) by J_2/J_1 = 0.26 and J_2/J_1 = 0.61.Comment: 28 pages, Latex, 2 postscript figure
Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers
This paper is a detailed report on a programme of simulations used to settle
a long-standing issue in the dynamo theory and demonstrate that the fluctuation
dynamo exists in the limit of large magnetic Reynolds number Rm>>1 and small
magnetic Prandtl number Pm<<1. The dependence of the critical Rm_c vs. the
hydrodynamic Reynolds number Re is obtained for 1<Re<6700. In the limit Pm<<1,
Rm_c is ~3 times larger than for Pm>1. The stability curve Rm_c(Re) (and, it is
argued, the nature of the dynamo) is substantially different from the case of
the simulations and liquid-metal experiments with a mean flow. It is not as yet
possible to determine numerically whether the growth rate is ~Rm^{1/2} in the
limit Re>>Rm>>1, as should be the case if the dynamo is driven by the
inertial-range motions. The magnetic-energy spectrum in the low-Pm regime is
qualitatively different from the Pm>1 case and appears to develop a negative
spectral slope, although current resolutions are insufficient to determine its
asymptotic form. At 1<Rm<Rm_c, the magnetic fluctuations induced via the
tangling by turbulence of a weak mean field are investigated and the
possibility of a k^{-1} spectrum above the resistive scale is examined. At low
Rm<1, the induced fluctuations are well described by the quasistatic
approximation; the k^{-11/3} spectrum is confirmed for the first time in direct
numerical simulations.Comment: IoP latex, 27 pages, 25 figures, 3 tables. Accepted by New J. Physic
Connected Green function approach to ground state symmetry breaking in -theory
Using the cluster expansions for n-point Green functions we derive a closed
set of dynamical equations of motion for connected equal-time Green functions
by neglecting all connected functions higher than order for the
-theory in dimensions. We apply the equations to the
investigation of spontaneous ground state symmetry breaking, i.e. to the
evaluation of the effective potential at temperature . Within our momentum
space discretization we obtain a second order phase transition (in agreement
with the Simon-Griffith theorem) and a critical coupling of
as compared to a first order phase transition and
from the Gaussian effective potential approach.Comment: 25 Revtex pages, 5 figures available via fpt from the directory
ugi-94-11 of [email protected] as one postscript file (there
was a bug in our calculations, all numerical results and figures have changed
significantly), ugi-94-1
Many-body theory of gamma spectra from positron-atom annihilation
A many-body theory approach to the calculation of gamma spectra of positron
annihilation on many-electron atoms is developed. We evaluate the first-order
correlation correction to the annihilation vertex and perform numerical
calculations for the noble gas atoms. Extrapolation with respect to the maximal
orbital momentum of the intermediate electron and positron states is used to
achieve convergence. The inclusion of correlation corrections improves
agreement with experimental gamma spectra.Comment: 25 pages, 9 figures, submitted to J. Phys.
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