Quantum transition probabilities due to overlapping electromagnetic pulses: Persistent differences between Dirac’s form and nonadiabatic perturbation theory

2021 ◽  
Vol 154 (2) ◽  
pp. 024116
Author(s):  
Anirban Mandal ◽  
Katharine L. C. Hunt
Keyword(s):  
Perturbation Theory ◽  
Transition Probabilities ◽  
Quantum Transition ◽  
Electromagnetic Pulses

Perturbation theory and finite Markov chains

1968 ◽  
Vol 5 (2) ◽  
pp. 401-413 ◽  
Author(s):  
Paul J. Schweitzer
Keyword(s):  
Perturbation Theory ◽  
Markov Chain ◽  
Markov Chains ◽  
Stationary Distribution ◽  
Fundamental Matrix ◽  
Transition Probabilities ◽  
Semi Group ◽  
Partial Derivatives ◽  
Finite Markov Chains ◽  
Derivatives Of

A perturbation formalism is presented which shows how the stationary distribution and fundamental matrix of a Markov chain containing a single irreducible set of states change as the transition probabilities vary. Expressions are given for the partial derivatives of the stationary distribution and fundamental matrix with respect to the transition probabilities. Semi-group properties of the generators of transformations from one Markov chain to another are investigated. It is shown that a perturbation formalism exists in the multiple subchain case if and only if the change in the transition probabilities does not alter the number of, or intermix the various subchains. The formalism is presented when this condition is satisfied.

Study of molecular collisions using a new interpolation scheme

1979 ◽  
Vol 57 (1) ◽  
pp. 69-72 ◽  
Author(s):  
G. K. Johri ◽  
Suresh C. Mehrotra
Keyword(s):  
Perturbation Theory ◽  
Line Width ◽  
Transition Probabilities ◽  
Rotational Transition ◽  
Time Dependent ◽  
Interpolation Scheme ◽  
Molecular Collisions ◽  
First Time

An interpolation scheme as suggested, by Mehrotra and Boggs in their time-dependent perturbation theory is applied for the first time to the study of strong collisions and to evaluate the collision induced transition probabilities when their absolute values are more than one. This approximation is used to compute the line width parameter of the rotational transition J = 1 → 2 of the OCS–OCS system.

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