
	Where results make sense

Topic: Wannier function

Related Topics

Orthogonal functions

Pontryagin duality

Reciprocal lattice

Eigenfunction

Spectral theorem

Differential operator

Hilbert space

Conjugate transpose

Eigenvector

Amorphous solid

Eigenvalue

Nanometer

Diagonal matrix

Aarti

In the News (Sun 15 Nov 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	The Australian Partnership for Advanced Computing National Facility Annual Report
		Wannier functions provide a means of obtaining maximally localised representations of the electron states in solids.
		The location of the function is represented by the coordinates of its centre and the degree to which the state is localised is measured by a spread parameter.
		The Wannier functions have been used to study the details of the bonding in the silicon carbon alloys.
	nf.apac.edu.au /annual_reports/2001/data/project_reports/Bilek_M_M_d94.html (863 words)

	Real-space localized representation for electrons: generalized Wannier functions for amorphous Si (Site not responding. Last check: 2007-11-03)
		Vanderbilt demonstrated that these localized functions are ideal for computing the surprisingly subtle electric polarization in the solid state[27] and also showed how to construct optimally localized Wannier functions for crystals[28](with a computational costs scaling cubically with the number of atoms).
		Nevertheless, the function is clearly localized and bonding at the originating bond, and is antibonding to the neighboring atom to fulfill the orthonormality constraint.
		Therefore, explicit computations of Wannier functions together with their tails also opens a way to a better understanding of the fundamental properties of these functions and the entire question of how best to formulate electronic structure calculations implemented in real space.
	www.phy.ohiou.edu /~drabold/czech/node9.html (1299 words)

	Charge density and total electronic energy with Non-orthogonal Generalised Wannier functions
		The delta function basis is equivalent to the plane-waves that can be represented by the real-space grid since it is related to them via a unitary transformation.
		From equation (10) we see that the charge density is a fine grid delta function expansion, thus the same should be true for the Hartree potential, which is a convolution of the charge density with the Coulomb potential.
		However, in the case of the exchange-correlation energy, the exchange-correlation functionals usually contain highly non-linear expressions that can not be represented without any aliasing even when we use the delta functions of the fine grid.
	www.tcm.phy.cam.ac.uk /~pdh1001/papers/paper11/node2.html (837 words)

	The functional equation of Riemann's zeta function
		the functional equation of the Riemann zeta function
		In a recent lecture, Marek Wolf stated that the functional equation "is analogous to the Kramers-Wannier duality for the partition function of the two dimensional Ising model with parameter J expressed in units of kT (i.e.
		In the example of the two dimensional (canonical) Ising model we have a (grand-canonical) lattice gas model where the chemical potential is the exterior magnetic field and the nearest neighbour coupling a short range interaction, the spin is essentially the occupation number.
	www.maths.ex.ac.uk /~mwatkins/zeta/fnleqn.htm (1061 words)

	[No title]
		For information on the implementation of the Green's function transport scheme as well as the construction of the Hamiltonian in terms of a Wannier function basis set see the paper: `Molecular transport calculations with Wannier functions`_, Thygesen and Jacobsen, Chem.
		To make sure that unoccupied states (to be used for constructing partly occupied Wannier functions) are properly converged, the calculation should be a Harris calculation, i.e.
		We refer to the output of the Wannier function construction as `zibloch_lead.pickle` and `Wannier_lead`.
	dcwww.camp.dtu.dk /campos/ASE/tut/transport.txt (1607 words)

	Exstrom Laboratories - Electronic Band Structure Calculations (Site not responding. Last check: 2007-11-03)
		When the site-potential function and one of the wavefunctions are centered on one atom and the other wavefunction is centered on a different atom the integral will be called a two center integral.
		Evaluation of the integrals can be further simplified by assuming that the site-potential functions are spherically symmetric (this assumption holds better for ionic solids such as NaCl than it does for metals and covalent solids such as the diamond lattice semiconductors).
		functions must also be angular momentum eigenfunctions and they can therefore be written as the product of a radial function and a spherical harmonic.
	www.exstrom.com /journal/tbtut/tbtut.html (1487 words)

	Proc. of SPIE 5733 - Photonic Crystal Materials and Devices III, 324-335 (Mar 2005) (Site not responding. Last check: 2007-11-03)
		Within this approach, the electromagnetic field is expanded into an orthogonal basis of highly localized Wannier functions, which reduces Maxwell's equations to low-rank eigenvalue problems (for defect mode and waveguide dispersion calculations) or to sparse systems of linear equations (for transmission/reflection calculations through/from functional elements).
		We illustrate the construction of Wannier functions as well as the subsequent determination of defect modes, waveguide dispersion relations, and the characterization of functional elements for realistic two-dimensional photonic crystal structures consisting of square and triangular lattices of air pores in a high-index matrix.
		Moreover, on the basis of our Wannier function calculations we suggest a novel type of broad-band integrated photonic crystal circuits based on the infiltration of low-index materials such as liquid crystals or polymers into individual pores of these systems.
	www-tfp.physik.uni-karlsruhe.de /~smino/papers/abs/SPIE_2005_5733_00324.shtml (252 words)

	About WanT
		The core methodology combines state-of-the-art Density Functional Theory (DFT), plane-wave, norm-conserving pseudopotentials calculations with a Green's functions method based on the Landauer formalism to describe quantum conductance.
		The essential connection between the two, and a crucial step in the calculation, is the use of the maximally-localized Wannier function representation to introduce naturally the ground-state electronic structure into the lattice Green's function approach at the basis of the evaluation of the quantum conductance.
		Moreover, the knowledge of the Wannier functions of the system allows for the direct link between the electronic transport properties of the device with the nature of the chemical bonds, providing insight onto the mechanisms that govern electron flow at the nanoscale.
	www.wannier-transport.org /about.html (303 words)

	Tutorial 5 Transport
		For information on the implementation of the Green's function transport scheme as well as the construction of the Hamiltonian in terms of a Wannier function basis set see the paper: Molecular transport calculations with Wannier functions, Thygesen and Jacobsen, Chem.
		The first line shows that after the basis change (from hydrogen orbitals to bonding/anti-bonding states) the new basis functions have the same indices as the original ones (this will always be the case).
		The first step in setting up a Wannier function Hamiltonian for transport calculation is to perform a DFT calculation for the scattering region.
	dcwww.camp.dtu.dk /campos/ASE/tut/transport.html (1915 words)

	cent (Site not responding. Last check: 2007-11-03)
		The illustration that follows is of a particular generalized Wannier function associated with an especially strained site (Wannier functions are a set of orbitals which are localized in real space, span the occupied electronic subspace, and are (usually) mutually orthonormal).
		This function was computed with the approximate ab initio Sankey et al.
		B 57 6391 (1998) (see that paper for a similar illustration of a Wannier function for crystalline diamond).
	www.phy.ohiou.edu /~drabold/cent.html (242 words)

	Wannier function analysis of silicon-carbon alloys
		Maximally localized Wannier functions are the basis of a new technique for resolving ambiguous bonding issues for amorphous materials.
		Central to these methods is the notion of treating the Wannier function centres as a virtual atomic species with a well-defined degree of localization.
		Using Wannier function methods, we classify and quantify the types of bonding present in a sample of the ternary alloy hydrogenated amorphous silicon carbide, C
	stacks.iop.org /0953-8984/15/165 (278 words)

	Infrared Spectroscopy of N-Methylacetamide Revisited by ab Initio Molecular Dynamics Simulations (Site not responding. Last check: 2007-11-03)
		The density functional theory based molecular dynamics simulation method ("Car-Parrinello") was applied in a numerical study of the electronic properties, hydrogen bonding, and infrared spectroscopy of the trans and cis isomer of N-methylacetamide in aqueous solution.
		A detailed analysis of the electronic structure of the solvated molecules, in terms of localized Wannier functions and Born atomic charges, is presented.
		Two schemes for the computation of the solute infrared absorption spectrum are investigated: In the first method the spectrum is determined by Fourier transforming the time correlation function of the solute dipole as determined from the Wannier function analysis.
	pubs.acs.org /cgi-bin/abstract.cgi/jctcce/2005/1/i05/abs/ct050029z.html (248 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		Each occupied Wannier function can be associated with two paired protons, defining a ''Wannier molecule.'' The sum of the dipole moments of these ''molecules'' always gives the correct macroscopic polarization, even under strong compression, when the overlap between nearby Wannier functions becomes significant.
		We find that at megabar pressures the contributions to the dipoles arising from the overlapping tails of the Wannier functions are very large.
		The strong vibron infrared absorption experimentally observed in phase III, above{approx}150GPa, is analyzed in terms of the vibron-induced fluctuations of the Wannier dipoles.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=40205671 (278 words)

	enolskii seminar 2004 (Site not responding. Last check: 2007-11-03)
		The Wannier functions for the 1D Schrodinger equation with elliptic finite gap potential are explicitly constructed.
		In particular, the exact value for the amplitude of the function in the origin, a power series valid in the vicinity of the origin and the asymptotic expansion characterising the decay of the function at large distances are explicitly derived.
		Using these expansions we construct approximate analytcal expression of the Wannier function which are in good agreement with expressions obtained with numericcal methods.
	amsta.leeds.ac.uk /cnls/research/integrable/seminar/2004/enolskii.html (122 words)

	Photonics Group: Publications
		Highly localized Wannier functions for the efficient modeling of photonic crystal circuits
		We illustrate the construction of Wannier functions as well
		and the characterization of functional elements for realistic two-dimensional photonic
	photonics.tfp.uni-karlsruhe.de /publications/detail/38.html (155 words)

	Walter Kohn web page
		He played the leading role in the development of the density functional theory, which has revolutionized scientists' approach to the electronic structure of atoms, molecules and solid materials in physics, chemistry and materials science.
		Density Functional Theory of Metal Surfaces and of Chemisorption on Metals, in The Physical Basis for Heterogeneous Catalysis, E. Drauglis and R. Jaffee, eds., Plenum Press (1975).
		Density Functional Theory of Electronic Structure, Proceedings of the 6th IFC Symposium, Institute for Fundamental Chemistry, Kyoto, Japan.
	gabriel.physics.ucsb.edu /~kohn (2549 words)

	Multigrid Methods (Site not responding. Last check: 2007-11-03)
		As an alternate to current approaches, we have investigated a charge partitioning scheme that is based on the maximally-localized Wannier functions.
		Tests on isolated molecules and water dimers, show that the molecular electrostatic potentials generated by such a Wannier-function based approach are in excellent agreement with the density functional-based calculations.
		Molecular electronic potential surfaces (MEPS) as generated with a classical representation based on multipoles computed by using Wannier functions.
	nemo.physics.ncsu.edu /virgil/projects/Abinitio_calculation_of_electrostatic_multipoles.htm (270 words)

	INFM MODENA S3
		Wannier functions are then obtained from plane wave coefficients and used to compute the Green’s function and in turn the quantum conductance after Landauer.
		Several post-processing routines allow for the calculation of various response functions related to experimental spectroscopies, and of the carrier-carrier correlation properties.
		GAMESS is a quantum chemistry code based on Gaussian functions that performs several kinds of calculations (e.g., electronic structure, energy, geometry optimization, electric response properties, harmonic vibrational frequencies) at different levels of theory (HF, MP2, DFT with different xc functionals, MCSCF, CI, CC).
	www.s3.infm.it /software.html (1667 words)

	APS - 2006 APS March Meeting - Event - DFT Study of the Single-Band Layered TMO LiNbO$_2$ (Site not responding. Last check: 2007-11-03)
		We will present the Nb-centered Wannier function, which provides insight into this unusual electronic structure.
		Calculations of the Born effective charges for the metal ions are also found to have anisotropy that reflects the layered nature of the electronic bonding.
		Their deviation from formal charge values indicates important covalent character, which is also evident in the Wannier function.
	meetings.aps.org /Meeting/MAR06/Event/43270 (206 words)

	Annual Report on 2003 Project (Site not responding. Last check: 2007-11-03)
		The approach here is to use density-functional molecular dynamics and the novel approach to Wannier Function centres in amorphous materials to investigate bonding and subsequent properties at the atomic level.
		Figure 2: Shows an example of a Wannier Function Centre about delineating a bond between two carbon atoms (see http://www.physics.usyd.edu.au/~merchant/wanniers/wanniers.html for details.
		Wannier function analysis for understanding disordered structures generated using Car-Parrinello molecular dynamics, MOLECULAR SIMULATIONS, 28 (10-11), 2002, 971-979.
	nf.apac.edu.au /annual_reports/2003/data/project_reports/Merchant_A_R_e36.html (426 words)

	Photonics Group: Publications
		This approach is based on an expansion of the electromagnetic field into optimally adapted photonicWannier functions, which leads to effective lattice models of the PC structures.
		Calculations for eigenmode frequencies of simple and complex cavities as well as the dispersion relations for straight waveguides agree extremely well with the results from numerically exact supercell calculations.
		Besides being substantially more efficient than standard simulation tools, the Wannier function approach offers considerable insight into the nature of defect modes in PCs.
	photonics.tfp.uni-karlsruhe.de /publications/detail/13.html (208 words)

	Wei Ku's Home Page
		The linear response function (or dynamical structure factor, S) gives valuable information about the dynamical electronic/magnetic excitations and screening processes in materials, and it can be directly compared with experiments like EELS, IXS, dielectric function, optical conductivity, reflectivity measurement, and inelastic neutron scattering.
		Numerical quantities like transition probability amplitude matrix elements and Physical quantities like density response function, self-energy, Green's function and Wannier function are then calculated using my own codes.
		Wei Ku, and Adolfo G. Eguiluz, to be submitted to Phys.
	www.cmth.bnl.gov /~weiku (1429 words)

	My Details \| College of Optics & Photonics at the University of Central Florida
		From 2000 to 2003 he headed a junior research group (Emmy-Noether fellowship of the DFG) at the Institut fÃ¼r Theorie der Kondensierten Materie (lead by Peter WÃ¶lfle) of the UniversitÃ¤t Karlsruhe and worked on wave propagation and light-matter interaction in micro- and nano-structured materials.
		In particular, he introduced the Wannier function approach to the modelling of Photonic Crystals.
		In 2001 he became a founding member, principal investigator, and spokesperson for Research Area A: Nano-Photonics of the Center for Functional Nanostructures (CFN) of the DFG at the UniversitÃ¤t Karlsruhe.
	www.creol.ucf.edu /People/Details.aspx?peopleID=3557 (283 words)

	Wannier Functions in Compressed Hydrogen (Site not responding. Last check: 2007-11-03)
		In particular, each Wannier function can be associated with one molecule in the solid, and the displacement of its center of charge in forming the solid defines an effective ``dipole moment'' for that molecule.
		This set of ``dipole moments'' provides a correct description of the bulk polarization even at high pressures, when the molecules are strongly overlapping and the Clausius-Mossotti picture of insulators is not valid.
		Finally, the spatial extent of the Wannier functions gives a measure of the localization of the electronic states, which is investigated as a function of the crystal structure and pressure.
	flux.aps.org /meetings/YR99/CENT99/abs/S5550011.html (197 words)

	Physik: DPG Tagungen - Sitzung TT 28 (Site not responding. Last check: 2007-11-03)
		We propose a method for calculating the explicit form of the Wannier functions and also a procedure of projecting the full-orbital Hamiltonian on the Wannier function subspace defined for the partially filled bands of interest.
		The self-energy operator defined in Wannier function basis obtained in such calculations is converted back into the full-orbital Hilbert space and is used for the calculation of the total and partial densities of states of real materials.
		In particular, we discuss the enhancement of correlation effects due to orbital polarization induced by Peierls distortion, the enhancement of correlations at surfaces due to band narrowing, and the possibility of observing multi-gapped Mott insulators.
	www.dpg-tagungen.de /archive/2004/tt_28.html (1045 words)

	Wave collapse Text - Physics Forums Library
		From what I understand, the wave function of a system is collapsed automatically by interaction with another, macroscopic system.
		In solid state physics, we now have to construct what is known as the Wannier function to preserve some degree of orthorgonality].
		I think what he was trying to convey is the concept of decoherence whereby the act of measurement simply induces a larger degree of freedom to the whole overall system (which now includes the orginal system and the instrument).
	www.physicsforums.com /archive/index.php/t-16023.html (1444 words)

	Theory
		is the Green function of the reservoir unconnected to the device (
		) and a is the corresponding spectral function,
		(3) and (4) by any matrix inversion technique, but we find the recursive Green function algorithm [14] to be the most efficient.
	www.cfdrc.com /nemo/pubs/apl95_html/node2.html (638 words)

Try your search on: Qwika (all wikis)