Structure of the two-neutrino double-βdecay matrix elements within perturbation theory

2015 ◽  
Vol 91 (6) ◽  
Author(s):  
Dušan Štefánik ◽  
Fedor Šimkovic ◽  
Amand Faessler
Keyword(s):  
Perturbation Theory ◽  
Matrix Elements

scholarly journals One-loop non-planar anomalous dimensions in super Yang-Mills theory

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Tristan McLoughlin ◽  
Raul Pereira ◽  
Anne Spiering
Keyword(s):  
Perturbation Theory ◽  
Integrable Systems ◽  
Chaotic Systems ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Mechanical Perturbation ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Dilatation Operator ◽  
Scalar Products

Abstract We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find compact expressions in terms of off-shell scalar products and hexagon-like functions. We then use non-degenerate quantum-mechanical perturbation theory to compute the leading 1/N2 corrections to operator dimensions and as an example compute the large R-charge limit for two-excitation states through subleading order in the R-charge. Finally, we numerically study the distribution of level spacings for these theories and show that they transition from the Poisson distribution for integrable systems at infinite N to the GOE Wigner-Dyson distribution for quantum chaotic systems at finite N.

Intramolecular Electron Transfer in Nonconjugated Polyenes

1981 ◽  
Vol 36 (8) ◽  
pp. 859-867 ◽  
Author(s):  
Michael C. Böhm
Keyword(s):  
Electron Transfer ◽  
Perturbation Theory ◽  
Unitary Transformation ◽  
Intramolecular Electron Transfer ◽  
Direct Transfer ◽  
Matrix Elements ◽  
Local Perturbations ◽  
Transfer Channel ◽  
Transfer Mechanisms ◽  
Transport Type

AbstractThe probability of hole-propagation of initially prepared vacancies in 1,5-hexadiene (1) and 1,6-heptadiene (2) as well as the transfer mechanisms in 1 and 2 are studied by means of timedependent perturbation theory. Times of equibrilation of about 10-15 sec are calculated. Local perturbations in the π moieties are efficiently transmitted via CH-σ states while CC-σ functions and the direct transfer channel are less important. The theoretical key step consist in an unitary transformation of the canonical molecular orbitals (CMO's) with the diagonal Fock operator into a set of one-electron states forming a transport-type Fockian, FHT, where only a few matrix elements (between the evoluting orbitals and a set of messenger states) differ from zero.

Analytical formulas for the Stark effect on intensity of hydrogen radiation lines

2003 ◽  
Vol 81 (5) ◽  
pp. 755-769 ◽  
Author(s):  
A A Kamenski ◽  
V D Ovsiannikov
Keyword(s):  
Perturbation Theory ◽  
Green Function ◽  
Field Strength ◽  
Stark Effect ◽  
Selection Rule ◽  
Magnetic Quantum Number ◽  
Matrix Elements ◽  
Analytical Formulas ◽  
Degenerate States ◽  
Analytical Expressions

A regular method for deriving the consecutive terms of a series in powers of field strength F for the intensities of hydrogen radiation lines is presented both analytically and numerically. Specific modification of the perturbation theory for degenerate states and the Sturm-series expansion for the completely reduced Coulomb–Green function in parabolic coordinates are used to derive simple analytical formulas for matrix elements and the intensities of the radiation transitions between circular states. Particular cases of transitions between the closest Rydberg levels are presented and discussed in detail. Analytical expressions are also derived for the quadrupole matrix elements, which may contribute to the probability of σ-transitions with the selection rule for the magnetic quantum number Δm = ±1 and determine the probability of the dipole-forbidden radiation transitions between Stark levels with Δm = ±2. PACS Nos.: 32.60.+i, 32.70.–n, 32.70.Fw

On the perturbation theory of small disturbances

1956 ◽  
Vol 238 (1213) ◽  
pp. 269-275 ◽  
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Diagonal Matrix ◽  
Stationary System ◽  
Matrix Elements ◽  
Perturbation Techniques ◽  
Wide Range ◽  
Kinetic And Potential Energies ◽  
Small Disturbances

As a preliminary to a wide range of applications, conventional perturbation theory is re-examined and a number of useful properties emphasized. It is shown in particular that the total, kinetic and potential energies can be obtained to the (2 s + 1)th order from a knowledge of only the s th-order wave function and that similar though less powerful theorems hold for other diagonal matrix elements. A combination of variational and perturbation techniques is suggested as the best method of calculating small disturbances of a stationary system.

scholarly journals A New Family of Interactions between Clothed Particles in QED

2021 ◽  
Vol 66 (10) ◽  
pp. 833
Author(s):  
A. Arslanaliev ◽  
Y. Kostylenko ◽  
O. Shebeko
Keyword(s):  
Perturbation Theory ◽  
Compton Scattering ◽  
Quantum Electrodynamics ◽  
Matrix Elements ◽  
Energy Shell ◽  
New Family ◽  
Shell Matrix ◽  
Electron Positron ◽  
S Matrix ◽  
Novel Interactions

The method of unitary clothing transformations (UCTs) has been applied to the quantum electrodynamics (QED) by using the clothed particle representation (CPR). Within CPR, the Hamiltonian for interacting electromagnetic and electron-positron fields takes the form in which the interaction operators responsible for such two-particle processes as e−e− → e−e−, e+e+ → e+e+, e−e+ → e−e+, e−e+ → yy, yy → e−e+, ye− → ye−, and ye+ → ye+ are obtained on the same physical footing. These novel interactions include the off-energy-shell and recoil effects (the latter without any expansion in (v/c)2-series) and their on-energy shell matrix elements reproduce the well-known results derived within the perturbation theory based on the Dyson expansion for the S-matrix (in particular, the Møller formula for the e−e−-scattering, the Bhabha formula for e−e+-scattering, and the Klein–Nishina one for the Compton scattering).

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