
	Where results make sense

Topic: Density matrix

Related Topics

Statistical ensemble

Wave function

Fock state

Grand canonical ensemble

Phase space

Quantum harmonic oscillator

Eigenvalue

Microcanonical ensemble

Boson

	density matrix
		The significance of the density matrix in statistical physics is described in detail in Laudau and Lifshitz, vol.
		Ballentines poses as a postulate that the mathematical expression of the notion of state is the state operator or density matrix, which is defined by the expectation value of an operator.
		are orthonormal, therefore the density matrix is not necessarily diagonal.
	dpwww.epfl.ch /cours/spin_dyn_final/density_matrix.htm (720 words)

	The Density Matrix
		The density matrix is our saviour, for it does not require a complete wavefunction for a system.
		The density operator can be written in the form of a matrix, the density matrix.
		The terminology is used interchangeably in the literature, for in Heisenberg's matrix mechanics a matrix is an operator.
	webphysics.davidson.edu /Projects/AnAntonelli/node12.html (359 words)

	The Density Matrix
		Another two-state quantum system that can be analyzed in the same way is the polarization state of a beam of light, the basis states being polarization in the x-direction and polarization in the y-direction, for a beam traveling parallel to the z-axis.
		are all zero except for the ground state: the system is in a pure state, and the density matrix has every element zero except for a single element on the diagonal.
		are equal: the density matrix is just 1/N times the unit matrix, where N is the total number of states available to the system.
	galileo.phys.virginia.edu /classes/752.mf1i.spring03/DensityMatrix.htm (1437 words)

	7.3 The density matrix and natural orbitals
		The one-body density matrix, defined in equation 7.1, is conventionally expanded in a basis of orbitals,
		Therefore a plot of the eigenvalues of the density matrix would be indistinguishable from figure 7.1, which shows the diagonal elements of the density matrix in the basis of LDA orbitals.
		In this section, the zero momentum component of the momentum density for bulk silicon is determined from the density matrix and compared with previous results for the momentum density and Compton profile.
	www.physics.uc.edu /~pkent/thesis/pkthnode58.html (1993 words)

	NationMaster - Encyclopedia: Density matrix
		A density matrix is a self-adjoint (or Hermitian) positive-semidefinite matrix, (possibly infinite dimensional), of trace one, that describes the statistical state of a quantum system.
		Thus the act of measurement induces a fundamental irreversible change on the density matrix; this is analogous to the "collapse" of the state vector, or wavefunction collapse.
		A density matrix is a self-adjoint or Hermitian, non-negative matrix, (possibly infinite dimensional), of trace one, that describes the statistical state of a quantum system.
	www.nationmaster.com /encyclopedia/Density-matrix (2771 words)

	Density matrix
		A density matrix is used in quantum theory to describe the statistical state of a quantum system[?].
		It is the quantum-mechanical analogue to a phase-space density[?] (probability distribution of position and momentum) in classical statistical mechanics.
		For the density matrix, this means that ρ is a positive semidefinite hermitian operator (its eigenvalues are nonnegative) and the trace of ρ (the sum of its eigenvalues) is equal to one.
	www.ebroadcast.com.au /lookup/encyclopedia/de/Density_matrix.html (236 words)

	Quantum Density Matrix (Site not responding. Last check: )
		The density matrix is Hermitian with all its eigenvalues between 0 and 1.
		The density matrix for an ensemble of particles prepared in the pure state Y) is Y)(Y.
		The density matrix for an ensemble that is an incoherent mixture of pure states is the weighted sum of the density matrices for the pure states.
	members.aol.com /jmtsgibbs/qdensity.htm (388 words)

	Local Density Approximation
		Approximation of the many-body energy (58) by a functional of the one-body density matrix (70) can be further simplified in the coordinate representation.
		Indeed, the nuclear density is almost constant inside the nucleus, and then falls down to zero within the region called the nuclear surface, which has a typical width of about 3fm.
		Such energy density depends on the local density, on derivatives of the local density, and on several other densities that represent properties of the one-body density matrix in the non-local direction.
	www.fuw.edu.pl /~dobaczew/maub-42w/node26.html (2065 words)

	About
		In a certain sense, the density matrix formulation is a return to Von Neumann's program for an algebraic foundation for quantum mechanics.
		The primary advantage of choosing the density matrix formalism for geometrization is that it avoids unphysical gauge freedom, a subject of some debate and or confusion.
		For example, instead of working with the (single particle) density matrix for an electron, we can consider a single particle density matrix for a lepton, a particle that is either an electron, a muon, a tau, or one of the neutrinos.
	www.brannenworks.com /about.html (1546 words)

	livre the fundamentals of electron density, density matrix and density functional theory in atoms, molecules and the ...
		McWeeny discusses some unsolved problems in density matrix theory and density functional theory and Bader discusses the use of the electron density in explaining the structure and properties of atoms and molecules.
		Density Functional Theory is widely used in studies of molecular and solid state systems.
		The fundamental of electron density, density matrix and density functional theory for atoms, molecules and the solid state, B.T. Sutcliffe.
	www.lavoisier.fr /notice/fr404121.html (545 words)

	Quantum crystallography, a developing area of computational chemistry extending to macromolecules
		Their density matrix for a full molecule is obtained from subsystem contributions in a fashion consistent with Mulliken population analysis.
		Zero elements of the density matrix also occur in a way that is analogous to the definitions used in an investigation of ours [5] and one by Walker and Mezey [6].
		The electron density for a molecule of interest is obtained by placing each lego piece into its appropriate position and orientation in the molecule and summing the numerical densities associated with all of the lego pieces.
	www.research.ibm.com /journal/rd/453/huang.html (3174 words)

	Convergence in SCF Calculation
		Thus a trial Fock gives rise to a trial density matrix, which in turn is used to generate a better Fock matrix.
		If, on any two consecutive iterations, a density matrix element changes by more than 0.05, then the density matrix element is set equal to the old element shifted by 0.05 in the direction of the calculated element.
		The density matrix from iteration 4 would then be used in the construction of the next Fock matrix.
	www.cachesoftware.com /mopac/Mopac2002manual/node476.html (645 words)

	Short Range Action
		First, one factorizes the density matrix into a center-of-mass term and a term depending on the relative coordinates.
		The latter term is equivalent to the density matrix for a particle with the reduced mass
		The six dimensional pair density matrix is reduced to a sum of two dimensional objects.
	militzer.gl.ciw.edu /diss/node16.html (294 words)

	Reduced Density Matrix Text - Physics Forums Library
		The reduced density matrix appears in the frame of composed systems, say, A and B, each with their hilbert space Ha and Hb ; so the total hilbert space of the composed system is Ha x Hb.
		If you then recalculated the reduced density matrix for the second qubit, it would simply be \left0\right\rangle\left\langle0\right, telling you that the particle now has probability p_0=1 of being in state \left0\right\rangle and probability p_1=0 of being in state \left1\right\rangle.
		The matrix rho_A being made up only of partial traces over B, this means that every individual element of the matrix rho_A remains intact, whether we perform a measurement or not, and in that case, no matter in what basis we perform a measurement.
	www.physicsforums.com /archive/index.php/t-81735.html (2201 words)

	Mopac_Density
		The dimension of the density matrix in the file does not correspond to the current definition in the program.
		The number of density matrices in the file does not correspond to the current number defined in the program.
		There will be errors if the dimensions and the number of density matrices in the file do not correspond to those of the system currently defined in the program.
	www.psc.edu /biomed/dynamo/www_v2/Modules/mopac_density.html (136 words)

	Comparison Of A Variety Of Gamma Attenuation Correction Techniques for Different Waste Matrices - CANBERRA, An AREVA ...
		The basic assumptions which have been traditionally applied to this technique are that the matrix is uniform over the vertical segment being measured, and that the sample activity is uniformly distributed in the segment and does not contain lumps.
		To obtain a matrix correction with this technique, the ratios of two or more peaks from different gamma lines of a single nuclide are initially measured with no attenuating material present.
		Correction algorithms are then used to determine the matrix density based on the variation in the peak ratios.
	www.canberra.com /literature/1024.asp (2127 words)

	Density Matrix Construction
		The only elements of the density matrix which need to be evaluated are those relating to atoms which are separated by less than
		Having stated that the construction of the density matrix is the same in principle as that used in conventional M.O. theory, the way in which LMOs are stored does introduce a technical difference.
		This unpredictable nature of the composition of the LMOs means that the order in which density matrix elements are calculated is determined by the LMOs, and not by the sequence of atoms in the molecule.
	www.cachesoftware.com /mopac/Mopac2002manual/node540.html (297 words)

	The Helicity Density Matrix
		Knowing how pure particle helicity states may be transformed from one frame to another, a formalism may now be devised to connect the scattering matrix, and the superposition of incoming and outing particle states describing a scattering experiment.
		The natural method when working with helicity states is to use the helicity density matrix.
		This density matrix describes all the physically observable quantities for the specified particles with momentum
	www.maths.tcd.ie /~rb/masters/node5.html (334 words)

	Mathematical Properties
		This implies that the corresponding density matrix is Hermitian, as required.
		The density operator is, in effect, a spatial correlation function.
		In summary, one cannot rigorously derive a Wigner function from a density operator and vice versa on a finite, and particularly on a discrete, domain.
	www.utdallas.edu /~frensley/technical/opensyst/node20.html (2633 words)

	Density matrix - RecipeFacts (Site not responding. Last check: )
		The need for a statistical description via density matrices arises when one considers either an ensemble of systems, or one system when its preparation history is uncertain.
		The operator ρ is the density operator of the mixed system.
		The von Neumann entropy $S$ of a mixture can be expressed in terms of the probabilities $p_i$ or in terms of the trace and logarithm of the density matrix $\rho$ :
	www.recipeland.com /facts/Density_matrix (1222 words)

	Density Matrix Derivation of the Semiclassical Equations
		Notice that the elements on the diagonal of the density matrix are real numbers which correspond to the probability of being in the upper or lower states.
		The density matrix is obviously related to these amplitudes.
		The density matrix is hermitian, and this fact will be used again and again to simplify the numerical algorithms presented in this text.
	webphysics.davidson.edu /Projects/AnAntonelli/node13.html (411 words)

	Adjustable Density Matrix Assembler
		For these, conventional quantum chemical calculations are performed using moderate-sized parent molecules, which contain both the fragment and all the local interactions of the fuzzy fragment with its surroundings within a pre-selected distance.
		The electron density matrices for the fragments are then recombined to approximate the electron density of the target molecule, from which properties like the electron density, the electrostatic potential, and the total energy can be calculated.
		The big advantage of this approach is that the computer time scales linearly with the system size due to the fact that the computer time needed for each fragment calculation is almost constant and the number of fragments increases linearly with the size of the target molecule.
	www.tcd.uni-konstanz.de /research/adma.php (628 words)

	Amazon.com: "matrix crack density": Key Phrase page (Site not responding. Last check: )
		By the edge observation and the X-ray observation, the matrix crack density which is defined as the number of cracks observed per unit length was measured as a function of the number...
		Matrix cracking is the predominant mechanism at the initial stage of degradation of cross-ply composite laminates under mechanical loading.
		The matrix crack density increases as a consequence of increasing applied strain or increasing number of...
	www.amazon.com /phrase/matrix-crack-density (545 words)

	[No title]
		Calculate the trace of the density matrix and the trace of the square of the density matrix.
		If those conditions are satisfied then the density matrix is built only of energy eigenstates so can describe an equilibrium system.
		If the trace of (2 is less than unity then the density matrix describes a mixed state (or ensemble average).
	www.colorado.edu /physics/phys7230/phys7230_sp04/homework/HW2solution.doc (1145 words)

	Density-matrix renormalization group (Site not responding. Last check: )
		The Density Matrix Renormalization Group (DMRG) is one of the most powerful numerical techniques for studying many-body systems.
		In DMRG the states kept to construct a renormalization group transformation are the most probable eigenstates of a reduced density matrix instead of the lowest energy states kept in a standard NRG calculation.
		K. Hallberg, Density Matrix Renormalization: A Review of the Method and its Applications, published in David Senechal, Andre-Marie Tremblay and Claude Bourbonnais (eds.), Theoretical Methods for Strongly Correlated Electrons, CRM Series in Mathematical Physics, Springer, New York, 2003; E-print: cond-mat/0303557.
	www.itp.uni-hannover.de /~jeckelm/dmrg (899 words)

Try your search on: Qwika (all wikis)