scholarly journals Reduction Formulae for the Seniority Diagonal Matrix Element of a Two-Body Interaction in a Boson System

1970 ◽  
Vol 43 (1) ◽  
pp. 241-242
Author(s):  
Masao Nomura
Keyword(s):  
Matrix Element ◽  
Diagonal Matrix ◽  
Diagonal Matrix Element ◽  
Body Interaction ◽  
Boson System

Effect of Phase Choices in Rovibrational Wavefunctions on the Labeling of K-and l-Type Doubling in Molecular Energy Levels

1983 ◽  
Vol 38 (8) ◽  
pp. 821-834 ◽  
Author(s):  
Koichi Yamada
Keyword(s):  
Matrix Element ◽  
Energy Levels ◽  
Diagonal Matrix ◽  
Phase Factor ◽  
Diagonal Matrix Element ◽  
Phase Dependence ◽  
The Matrix ◽  
Symmetry Species ◽  
Asymmetric Top ◽  
Symmetric Top Molecules

Abstract The change in phase factor of the wavefunction does not affect the absolute value of the matrix element, but does change the phase factor of the off-diagonal matrix element. This phase dependence causes a serious confusion in the sign of some parameters in the molecular Hamiltonian, which appear only in the off-diagonal matrix element; for example, the sign of the l-type doubling constant q of a linear or a symmetric-top molecule. In the present paper, the energy eigenvalues, symmetry species, and labeling of the eigenfunctions are discussed for the K-type doubling of asymmetric-top molecules and for the l-type doubling of linear or symmetric-top molecules in relation to the choices of phases in the basis wavefunctions.

An expansion method for calculating atomic properties IV. Transition probabilities

1964 ◽  
Vol 280 (1381) ◽  
pp. 258-270 ◽  
Keyword(s):  
Wave Function ◽  
Matrix Element ◽  
Transition Probabilities ◽  
Expansion Method ◽  
The State ◽  
Diagonal Matrix Element ◽  
Expectation Value ◽  
First Order ◽  
Hartree Fock ◽  
Atomic Properties

An earlier expression for the expectation value of a single-electron operator which isstationary with respect to first-order variations of the state wave function has been generalized to the case of an off-diagonal matrix element connecting two different states. Explicit calculations are carried out of the probabilities of dipole transitions between configurations 1 s a 2 s b 2 p c and 1 s a 2 s b–1 2 p c+1 for all members of the isoelectronic sequences from helium to neon and the importance of taking into account the mixing of degenerate configurations is demonstrated. The accuracy is at least comparable to that of the Hartree-Fock approximation and in cases where degeneracy is important it is much superior.

Dipole Moment of CS2 in its ã3A2 State

1975 ◽  
Vol 53 (16) ◽  
pp. 1579-1586 ◽  
Author(s):  
M. Larzillière ◽  
D. A. Ramsay
Keyword(s):  
Dipole Moment ◽  
Matrix Element ◽  
Vibrational State ◽  
Stark Effect ◽  
Ultraviolet Spectrum ◽  
Lower State ◽  
Diagonal Matrix Element ◽  
Near Ultraviolet ◽  
Systematic Discrepancy ◽  
Infrared Data

The Stark effect on the [Formula: see text] system of 12C32S2 has been investigated. The most pronounced effects involve the 270,27 and 261,26 rotational levels of the 140 vibrational state and the 290,29 and 281,28 rotational levels of the 050 vibrational state. These pairs of levels are nearly degenerate and are coupled by an off-diagonal matrix element in the presence of an electric field. An analysis of the Stark shifts and the shapes of the Stark broadened lines yields[Formula: see text]Comparison of these energy separations with values calculated from measurements in the near ultraviolet spectrum and lower state term values based primarily on infrared data reveals a systematic discrepancy of 0.022 cm−1.

scholarly journals High Order Coherence Functions and Spectral Distributions as Given by the Scully-Lamb Quantum Theory of the Laser

2021 ◽  
Vol 9 ◽  
Author(s):  
Tao Peng ◽  
Xingchen Zhao ◽  
Yanhua Shih ◽  
Marlan O. Scully
Keyword(s):  
Quantum Theory ◽  
Matrix Element ◽  
Density Matrix ◽  
Time Evolution ◽  
Decay Rates ◽  
Reduced Density Matrix ◽  
Diagonal Matrix Element ◽  
Spectral Distributions ◽  
Reduced Density ◽  
First Time

We propose and demonstrate a method for measuring the time evolution of the off-diagonal elements ρn,n+k(t) of the reduced density matrix obtained from the quantum theory of the laser. The decay rates of the off-diagonal matrix element ρn,n+k(t) (k = 2,3) are measured for the first time and compared with that of ρn,n+1(t), which corresponds to the linewidth of the laser. The experimental results agree with the Scully-Lamb quantum theory of the laser.

scholarly journals Phase transition in an interacting boson system at finite temperatures

2019 ◽  
Vol 46 (3) ◽  
pp. 035002 ◽  
Author(s):  
D Anchishkin ◽  
I Mishustin ◽  
H Stoecker
Keyword(s):  
Phase Transition ◽  
Boson System

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals The normalized distance Laplacian

2021 ◽  
Vol 9 (1) ◽  
pp. 1-18
Author(s):  
Carolyn Reinhart
Keyword(s):  
Spectral Radius ◽  
Characteristic Polynomial ◽  
Adjacency Matrix ◽  
Connected Graph ◽  
Distance Matrix ◽  
Laplacian Matrix ◽  
Diagonal Matrix ◽  
The Matrix

Abstract The distance matrix 𝒟(G) of a connected graph G is the matrix containing the pairwise distances between vertices. The transmission of a vertex vi in G is the sum of the distances from vi to all other vertices and T(G) is the diagonal matrix of transmissions of the vertices of the graph. The normalized distance Laplacian, 𝒟𝒧(G) = I−T(G)−1/2 𝒟(G)T(G)−1/2, is introduced. This is analogous to the normalized Laplacian matrix, 𝒧(G) = I − D(G)−1/2 A(G)D(G)−1/2, where D(G) is the diagonal matrix of degrees of the vertices of the graph and A(G) is the adjacency matrix. Bounds on the spectral radius of 𝒟 𝒧 and connections with the normalized Laplacian matrix are presented. Twin vertices are used to determine eigenvalues of the normalized distance Laplacian. The distance generalized characteristic polynomial is defined and its properties established. Finally, 𝒟𝒧-cospectrality and lack thereof are determined for all graphs on 10 and fewer vertices, providing evidence that the normalized distance Laplacian has fewer cospectral pairs than other matrices.

scholarly journals K → μ+μ− as a clean probe of short-distance physics

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Avital Dery ◽  
Mitrajyoti Ghosh ◽  
Yuval Grossman ◽  
Stefan Schacht
Keyword(s):  
Matrix Element ◽  
Standard Model ◽  
Short Distance ◽  
Time Dependent ◽  
Final States ◽  
Interference Effects ◽  
Fundamental Theory ◽  
Long Distance ◽  
Ckm Matrix ◽  
The Standard Model

Abstract The K → μ+μ− decay is often considered to be uninformative of fundamental theory parameters since the decay is polluted by long-distance hadronic effects. We demonstrate that, using very mild assumptions and utilizing time-dependent interference effects, ℬ(KS → μ+μ−)ℓ=0 can be experimentally determined without the need to separate the ℓ = 0 and ℓ = 1 final states. This quantity is very clean theoretically and can be used to test the Standard Model. In particular, it can be used to extract the CKM matrix element combination $$ \mid {V}_{ts}{V}_{td}\sin \left(\beta +{\beta}_s\right)\mid \approx \mid {A}^2{\lambda}^5\overline{\eta}\mid $$ ∣ V ts V td sin β + β s ∣ ≈ ∣ A 2 λ 5 η ¯ ∣ with hadronic uncertainties below 1%.

Sign in / Sign up

Export Citation Format

Share Document