483 research outputs found
Calculation of electron density of periodic systems using non-orthogonal localised orbitals
Methods for calculating an electron density of a periodic crystal constructed
using non-orthogonal localised orbitals are discussed. We demonstrate that an
existing method based on the matrix expansion of the inverse of the overlap
matrix into a power series can only be used when the orbitals are highly
localised (e.g. ionic systems). In other cases including covalent crystals or
those with an intermediate type of chemical bonding this method may be either
numerically inefficient or fail altogether. Instead, we suggest an exact and
numerically efficient method which can be used for orbitals of practically
arbitrary localisation. Theory is illustrated by numerical calculations on a
model system.Comment: 12 pages, 4 figure
Fr\'echet frames, general definition and expansions
We define an {\it -frame} with Banach spaces , , and a -space (\Theta, \snorm[\cdot]).
Then by the use of decreasing sequences of Banach spaces
and of sequence spaces , we define a general Fr\'
echet frame on the Fr\' echet space . We give
frame expansions of elements of and its dual , as well of some of
the generating spaces of with convergence in appropriate norms. Moreover,
we give necessary and sufficient conditions for a general pre-Fr\' echet frame
to be a general Fr\' echet frame, as well as for the complementedness of the
range of the analysis operator .Comment: A new section is added and a minor revision is don
Numerical solution and spectrum of boundary-domain integral equation for the Neumann BVP with variable coefficient
This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 Taylor & Francis.In this paper, a numerical implementation of a direct united boundary-domain integral equation (BDIE) related to the Neumann boundary value problem for a scalar elliptic partial differential equation with a variable coefficient is discussed. The BDIE is reduced to a uniquely solvable one by adding an appropriate perturbation operator. The mesh-based discretization of the BDIEs with quadrilateral domain elements leads to a system of linear algebraic equations (discretized BDIE). Then, the system is solved by LU decomposition and Neumann iterations. Convergence of the iterative method is discussed in relation to the distribution of eigenvalues of the corresponding discrete operators calculated numerically.The work was supported by the grant EP/H020497/1 "Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients" of the EPSRC, UK
Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion
We show that the transfer of the angular spectrum of the pump beam to the
two-photon state in spontaneous parametric down-conversion enables the
generation of entangled Hermite-Gaussian modes. We derive an analytical
expression for the two-photon state in terms of these modes and show that there
are restrictions on both the parity and order of the down-converted
Hermite-Gaussian fields. Using these results, we show that the two-photon state
is indeed entangled in Hermite-Gaussian modes. We propose experimental methods
of creating maximally-entangled Bell states and non-maximally entangled pure
states of first order Hermite-Gaussian modes.Comment: 9 pages, 4 figures. Corrections made as per referee comments,
references updated. Submitted PR
On completeness of description of an equilibrium canonical ensemble by reduced s-particle distribution function
In this article it is shown that in a classical equilibrium canonical
ensemble of molecules with -body interaction full Gibbs distribution can be
uniquely expressed in terms of a reduced s-particle distribution function. This
means that whenever a number of particles and a volume are fixed the
reduced -particle distribution function contains as much information about
the equilibrium system as the whole canonical Gibbs distribution. The latter is
represented as an absolutely convergent power series relative to the reduced
-particle distribution function. As an example a linear term of this
expansion is calculated. It is also shown that reduced distribution functions
of order less than don't possess such property and, to all appearance,
contain not all information about the system under consideration.Comment: This work was reported on the International conference on statistical
physics "SigmaPhi2008", Crete, Greece, 14-19 July 200
The Hilbert-Schmidt Theorem Formulation of the R-Matrix Theory
Using the Hilbert-Schmidt theorem, we reformulate the R-matrix theory in
terms of a uniformly and absolutely convergent expansion. Term by term
differentiation is possible with this expansion in the neighborhood of the
surface. Methods for improving the convergence are discussed when the
R-function series is truncated for practical applications.Comment: 16 pages, Late
Modelling charge self-trapping in wide-gap dielectrics: Localization problem in local density functionals
We discuss the adiabatic self-trapping of small polarons within the density
functional theory (DFT). In particular, we carried out plane-wave
pseudo-potential calculations of the triplet exciton in NaCl and found no
energy minimum corresponding to the self-trapped exciton (STE) contrary to the
experimental evidence and previous calculations. To explore the origin of this
problem we modelled the self-trapped hole in NaCl using hybrid density
functionals and an embedded cluster method. Calculations show that the
stability of the self-trapped state of the hole drastically depends on the
amount of the exact exchange in the density functional: at less than 30% of the
Hartree-Fock exchange, only delocalized hole is stable, at 50% - both
delocalized and self-trapped states are stable, while further increase of exact
exchange results in only the self-trapped state being stable. We argue that the
main contributions to the self-trapping energy such as the kinetic energy of
the localizing charge, the chemical bond formation of the di-halogen quasi
molecule, and the lattice polarization, are represented incorrectly within the
Kohn-Sham (KS) based approaches.Comment: 6 figures, 1 tabl
Monge Distance between Quantum States
We define a metric in the space of quantum states taking the Monge distance
between corresponding Husimi distributions (Q--functions). This quantity
fulfills the axioms of a metric and satisfies the following semiclassical
property: the distance between two coherent states is equal to the Euclidean
distance between corresponding points in the classical phase space. We compute
analytically distances between certain states (coherent, squeezed, Fock and
thermal) and discuss a scheme for numerical computation of Monge distance for
two arbitrary quantum states.Comment: 9 pages in LaTex - RevTex + 2 figures in ps. submitted to Phys. Rev.
Adiabatic description of nonspherical quantum dot models
Within the effective mass approximation an adiabatic description of
spheroidal and dumbbell quantum dot models in the regime of strong dimensional
quantization is presented using the expansion of the wave function in
appropriate sets of single-parameter basis functions. The comparison is given
and the peculiarities are considered for spectral and optical characteristics
of the models with axially symmetric confining potentials depending on their
geometric size making use of the total sets of exact and adiabatic quantum
numbers in appropriate analytic approximations
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