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Published
**1977** by Pergamon Press in Oxford, New York .

Written in English

Read online- Matrices.,
- Optical pumping.

**Edition Notes**

Statement | Alain Omont. |

Series | Progress in quantum electronics -- v. 5, pt. 2 |

The Physical Object | |
---|---|

Pagination | p. 69-138 : |

Number of Pages | 138 |

ID Numbers | |

Open Library | OL22089373M |

**Download Irreducible components of the density matrix**

Abstract. As discussed in Chapters 1 and 2 it is often useful to expand ρ in terms of a conveniently chosen operator set Q method has two main advantages. First of all, it gives a more satisfactory definition of ρ (see, for example, Section ), and secondly by using explicitly Irreducible components of the density matrix book algebraic properties of the basis operators the calculations are often greatly simplified (see Cited by: 5.

Cite this chapter as: Blum K. () Irreducible Components of the Density Matrix. In: Density Matrix Theory and Applications. Springer Series on Atomic, Optical, and Plasma Physics, vol Cited by: 5.

Irreducible components of the density matrix. Application to optical pumping. Author links open overlay panel Alain Omont. Show moreCited by: A density matrix is a matrix that describes the statistical state, whether pure or mixed, of a system in quantum probability for any outcome of any well-defined measurement upon a system can be calculated from the density matrix for that system.

The extreme points in the set of density matrices are the pure states, which can also be written as. Angular Momentum Density Matrix Irreducible Component Orientation Vector Tensor Operator These keywords were added by machine and not by the authors.

This process is experimental and the keywords may be updated as the learning algorithm by: 5. Written in a clear pedagogic style, this book deals with the application of density matrix theory to atomic and molecular physics.

The aim is to precisely characterize sates by a vector and to construct general formulas and proofs of general theorems. The basic concepts and quantum mechanical fundamentals (reduced density matrices, entanglement, quantum correlations).

Irreducible Components of the Density Matrix. Karl Blum. Pages Radiation from Polarized Atoms. Quantum Beats. Karl Blum. Pages Some Applications. Karl Blum. Written in a clear pedagogic style, this book deals with the application of density matrix theory to atomic and molecular physics.

The aim is to precisely characterize. Written in a clear pedagogic style, this book deals with the application of density matrix theory to atomic and molecular physics. The aim is to precisely characterize sates by a vector and to construct general formulas and proofs of general theorems.

The basic concepts and quantum mechanical Irreducible Components of the Density Matrix. The density matrix was introduced by J. von Neumann in to describe statistical concepts in quantum mechanics. The main virtue of the density matrix is its analytical power in the construction of general formulas and in the proof of general theorems.5/5(1).

Search within book. Front Matter. Pages i-xv. PDF. Basic Concepts. Karl Blum. Pages General Density Matrix Theory. Karl Blum. Pages Coupled Systems. Karl Blum. Pages Irreducible Components of the Density Matrix. Karl Blum. Pages Radiation from Polarized Atoms. The use of density matrix methods also has the advan.

Get this from a library. Irreducible components of the density matrix: application to optical pumping. [Alain Omont]. General Density Matrix Theory Coupled Systems Irreducible Components of the Density Matrix Radiation from Polarized Atoms.

Quantum Beats Some Applications The Role of Orientation and Alignment in Molecular Processes Quantum Theory of Relaxation. Basic Concepts.- General Density Matrix Theory.- Coupled Systems.- Irreducible Components of the Density Matrix.- Radiation from Polarized Atoms: Quantum Beats.- Some Applications.- The Role of Orientation and Alignment in Molecular Processes.- Quantum Theory of Relaxation.

Series Title: Springer series on atomic, optical, and plasma physics, In Pure and Applied Mathematics, Proof. The semisimplicity of A/R is obvious. Any irreducible representation S of R would extend by to an irreducible representation T of A, and we would have R ⊄ Ker(T), contradicting the definition of R is a radical algebra.

Let J be a two-sided ideal of A and a radical algebra. If T is an irreducible representation of A and J. General Density Matrix Theory Coupled Systems Irreducible Components of the Density Matrix Radiation from Polarized Atoms.

Quantum Beats Some Applications The Role of Orientation and Alignment in Molecular Processes Quantum Theory of Relaxation --Appendixes --References.

Series Title: Physics of atoms and molecules. Density matrix theory and applications. [Karl Blum] Book: All Authors / Contributors: Karl Blum. Find more information about: Contents: 1. Basic Concepts.- 2. General Density Matrix Theory.- 3. Coupled Systems.- 4.

Irreducible Components of the Density Matrix.- 5. Radiation from Polarized Atoms. Quantum Beats.- 6. Some Applications.- 7. Kranendonk for the representation of the density matrix components, the atom-laser interaction and the radiation damping operator [32], where ~ = 1.

The atomic basis operators using the irreducible set e(F) i;k have been presented in [35]. The indices iand knumerate hyperﬁne states from one to four.

In this paper, the bases operators e(F). rithm for density matrix propagation. This issue has been investigated for optimal control prob-lems9, symplectic propagation of large regular spin lattices10 and observable dynamics in spin systems The primary obstacle is that propagation steps under the Liouville - von Neumann equation involve double-sided matrix multiplication.

xiv Contents 3 Coupled Systems. 61 The Nonseparability of Quantum Systems after an Interaction. 61 Interaction with an Unobserved System. The theoretical framework chosen for its formulation is the QED theory of Landi Degl'Innocenti (), which specifies the excitation state of the atoms in terms of the irreducible tensor components of the atomic density matrix.

We can see that the density matrix contains only population and z alignment by decomposing it into its irreducible tensor components using Decomposition.A list containing one rank-0 (one component), one rank-1 (three components), and one rank-2 (five components) irreducible tensor is produced.

1. Introduction. Recently, the irreducible spherical tensor analysis (STA) method has been put forward by Levitt and coworkers for analyzing NMR signals of dipolar coupled spin-1 2 nuclei.

It provides a convenient decomposition of NMR signals into components reflecting the inherent symmetries of the density matrix components and is thus useful to determine the.

We have obtained the irreducible tensorial components of the second‐order density matrix corresponding to a spin‐projected, single‐determinantal function.

The results are applicable to projected‐unrestricted or spin‐extended SCF functions. adshelp[at] The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A.

The density matrix was introduced by J. von Neumann in to describe statistical concepts in quantum mechanics.

The main virtue of the density matrix is its analytical power in the construction of general formulas and in the proof of general theorems. Irreducible Components of the Density Matrix. Book Title Density Matrix Theory and. The conversion for the 2p3P, 3p3P, and 3d3D multiplets of helium have been calculated.

By expanding the density matrix into the irreducible tensor components of orientation and alignment operators, the calculation expresses orientation and alignment as an initial value problem.

For the three multiplets as much as 2% orientation results from initial alignment. We have obtained the irreducible tensorial components of the second‐order density matrix corresponding to a spin‐projected, single‐determinantal function.

The results are applicable to projected‐unrestricted or spin‐extended SCF functions. The natural basis set for the problem is provided by the eigenfunctions of the first‐order charge density matrix. Quantum mechanics has been mostly concerned with those states of systems that are represented by state vectors.

In many cases, however, the system of interest is incompletely determined; for example, it may have no more than a certain probability of being in the precisely defined dynamical state. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): lig pr +a ves rou ear puls tion Published by Elsevier B.V.

larizat rmatio gases state [12–14]. Also, collisional depolarization cross section measured for colliders as rare gas or molecules is very important to the applications of laser induced fluorescence, atmospheric and com-bustion monitoring [15]. case considered in this paper.

The unknowns of these equations are the irreducible ten-sor components of the atomic density matrix whose self-consistent values have ﬁrst to be obtained to be able to calculate the emergent Stokes proﬁles. To solve this non-LTE problem of the 2nd kind we present some iterative methods that are very suitable for.

density matrix formed by the degenerate single particle ground states is irreducible,57 This re-sult also applies to the case of a at band at the top of the spectrum via particle-hole transforma-tion and even extends to the case where the at band lies somewhere in the spectrum using a per-turbative argument The perturbative argument.

The matrix that contains only the basic rows of DM is called basic matrix and is denoted by BM. Let TT(M) be the set of all irreducible testors of the Boolean matrix M, then.

Proposition 1. TT(DM) = TT(BM). This proposition indicates that the set of all irreducible testors calculated using DM or BM is the same (Lazo-Cortés et al., ).

At a later part the writer shows how he derives the spin-1/2 system density matrix from the first equation as follows.

Consider as a first example the decomposition of the density matrix of spin 1/2 particles. According to Eq. We have obtained the irreducible tensorial components of the second-order density matrix corresponding to a spin-projected, single-determinantal function.

The results are applicable to projected-unrestricted or spin-extended SCF functions. The natural basis set for the problem is provided by the eigenfunctions of the first-order charge density matrix.

Throughout, δ ij is the Kronecker delta, the components of the identity matrix. The number in the superscripted brackets denotes the tensor rank. These three terms are irreducible, which means they cannot be decomposed further and still be tensors satisfying the defining transformation laws under which they must be invariant.

The expansions of a spin density matrix describing a statistical ensemble of wavepackets into Poincaré‐ and Lorentz‐irreducible components are derived.

The infinite‐dimensional associative algebra for the Poincaré‐irreducible tensor operators of the second class is constructed. comparing the time evolutions of the density matrix during the quadrupole echo13 and Hahn14 echoes. Sections 4 and 5 describe two different methods to obtain spin-1 preces-sion equations without the need to explicitly evaluate com-mutators.

Section 4 describes how to use the behavior of irreducible tensor operators under rotation to obtain preces. How does one show a matrix is irreducible and reducible. An example would also be great. I know that a matrix is reducible if and only if it can be. Book January The Irreducible Components of the Density Matrix References References Blum, K.: Density Matrix Theory and Applications, 2nd edn.

Plenum Press, New York () Dubbers, D. The expansions of a spin density matrix describing a statistical ensemble of wavepackets into Poincaré- and Lorentz-irreducible components are derived. The infinite-dimensional associative algebra for the Poincaré-irreducible tensor operators of the second class is constructed.

A matrix is irreducible if it is not similar via a permutation to a block upper triangular matrix (that has more than one block of positive size). (Replacing non-zero entries in the matrix by one, and viewing the matrix as the adjacency matrix of a directed graph, the matrix is irreducible if and only if such directed graph is strongly connected.).Density Matrix - Theory and Applications, Plenum, New York ().

Google book, Pages and ; Mitchel Weissbluth Atoms and Molecules, Student edition Academic, New York (). The Wigner passive rotation matrix presented in this book is D (2, passive,W) (α, β, γ). Ulrich Haeberlen High Resolution NMR in Solids, Selective Averaging.The spherical harmonics of a particular rank are covariant components of an irreducible tensor.

This can be used to find the prescription for converting between the spherical and Cartesian bases. This loads the package with coordinate systems. (Quiet suppresses some shadowing warnings that will occur if the ADM package is already loaded.) Here are the spherical .