T‐matrix theory for near‐adiabatic processes. I. Generalized coordinate representation for the T matrix and expansion around the potential crossing point

1973 ◽  
Vol 58 (6) ◽  
pp. 2480-2488 ◽  
Author(s):  
T. Matsushita ◽  
R. Paul
Keyword(s):  
Matrix Theory ◽  
Coordinate Representation ◽  
T Matrix ◽  
Adiabatic Processes ◽  
Crossing Point ◽  
Generalized Coordinate

UNIFIED VARIATIONAL PRINCIPLES FOR THE VON NEUMANN, MASTER AND BOLTZMANN-BLOCH EQUATIONS AND THE T-MATRIX

1995 ◽  
Vol 09 (10) ◽  
pp. 1227-1242
Author(s):  
MASUMI HATTORI ◽  
HUZIO NAKANO
Keyword(s):  
Density Matrix ◽  
Variational Principles ◽  
Matrix Theory ◽  
Bloch Equation ◽  
Irreversible Processes ◽  
Collision Term ◽  
Maximum Condition ◽  
Von Neumann ◽  
Maximum Problem ◽  
T Matrix

The variational principle of irreversible processes, which was previously presented for the von Neumann equation as a stationarity problem and then converted into a maximum problem by contracting the density matrix perturbatively, is reinvestigated w.r.t. the contraction of the density matrix. The present contraction relies on the T-matrix theory of scattering, where no perturbational consideration enters. By taking the electron transport in solids as a typical example, the contraction is performed in two steps: the even component of the density matrix as to time reversal is eliminated first and then the off-diagonal elements in the scheme of diagonalizing the unperturbed Hamiltonian. The maximum problem thus obtained is for the diagonal elements of the odd component of the density matrix. The maximum condition gives the master equation, which is reduced to the Boltzmann-Bloch equation in the scheme of one-body picture. It is noticeable in this equation that the collision term is given in terms of the T-matrix in scattering theory.

Light scattering by anisotropic spherical particles: Rayleigh-Gans approximation versus T-matrix theory

2002 ◽  
Author(s):  
Alexei D. Kiselev ◽  
A. A. Panyukov ◽  
Victor Y. Reshetnyak ◽  
Timothy J. Sluckin
Keyword(s):  
Light Scattering ◽  
Matrix Theory ◽  
Spherical Particles ◽  
T Matrix

The elastic shell T‐matrix theory evaluated

2004 ◽  
Vol 115 (5) ◽  
pp. 2538-2538
Author(s):  
Michael Werby ◽  
H. Uberall
Keyword(s):  
Matrix Theory ◽  
Elastic Shell ◽  
T Matrix

scholarly journals Compound Nucleus Formulation of Reaction Matrix Theory

1972 ◽  
Vol 25 (5) ◽  
pp. 479
Author(s):  
JL Cook ◽  
WK Bertram
Keyword(s):  
Cross Section ◽  
Compound Nucleus ◽  
Cross Sections ◽  
Matrix Theory ◽  
Complex Reaction ◽  
Resonance Parameters ◽  
Channel Matrix ◽  
Reaction Matrix ◽  
T Matrix ◽  
Additional Constraints

It is shown that multilevel resonance parameters for each element of the reaction matrix cannot be determined from available data. However, additional constraints may be introduced without affecting agreement with experiment. The Bohr compound nucleus hypothesis, which states that the modes of formation and decay of a compound nucleus are independent, is applied to the T-matrix and it is found, as in Newton's model, that the channel matrix can be inverted analytically to provide simple formulae for cross sections, for both the real Wigner?Eisenbud reaction matrix and Moldauer's complex reaction matrix. Wigner?Eisenbud theory leads directly to Newton's strong correlation model and its unacceptable consequences. Moldauer's theory does not, however, and can explain cross section behaviour adequately while being consistent with Bohr's hypothesis. Cross sections can be written as a sum of single level contributions, as in the Adler?Adler formulation. Finally, Moldauer's statistical theory is shown to be applicable, and expressions are derived for the �averaged cross sections as functions of the complex Moldauer resonance parameters.

Linear master equation in the generalized coordinate representation

1988 ◽  
Vol 37 (12) ◽  
pp. 4785-4791 ◽  
Author(s):  
Wang Kaige
Keyword(s):  
Master Equation ◽  
Coordinate Representation ◽  
Generalized Coordinate

Adiabatic T matrix theory for three dimensional reactive scattering: Application to the (H, H2) system

1983 ◽  
Vol 78 (7) ◽  
pp. 4523-4532 ◽  
Author(s):  
J. C. Sun ◽  
B. H. Choi ◽  
R. T. Poe ◽  
K. T. Tang
Keyword(s):  
Matrix Theory ◽  
Three Dimensional ◽  
Reactive Scattering ◽  
T Matrix
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