Fermi master equation

Transition between states of probabilities pt and p3 is assumed to obey Fermi s master equation... 

Not only is the master equation more convenient for mathematical operations than the original Chapman-Kolmogorov equation, it also has a more direct physical interpretation. The quantities W(y y ) At or Wnn> At are the probabilities for a transition during a short time At. They can therefore be computed, for a given system, by means of any available approximation method that is valid for short times. The best known one is time-dependent perturbation theory, leading to Fermi s Golden Rule f)... 

The rate constants in the master equation can be derived from Fermi s golden rule, with the result that (14)... 

This case is analyzed using the H -levels and the H-Al interactions given in Fig. 6 and Table 1, respectively. As the H -level is always above the metal Fermi level, we can use semiclassical master equations for solving the Newns-Anderson Hamiltonian of this problem [21,22]. 

Using a master equation to model the VER process as a multistep reaction, the excess energy flow kinetics in FeP was examined, where the third order Fermi resonance parameters served as approximate reaction rate constants [88]. It was found that the subsequent relaxation is slow relative to relaxation of the initially excited system mode, providing an explanation for the observed difference in relaxation timescales. 

The story, or the myth, goes that when somebody asked Enrico Fermi if he knew the thermal conductivity of some metal, or if he could remember the mathematical equation for a given phenomenon, he would say no , and then proceed to derive the requested information from first principles. Now there is no question that Fermi mastered the principles of physics in the same way as that Maurizio Pollini masters the keyboard of his piano, but there is also no question that there must be a certain amount of exaggeration in the story. 

Under the condition that the system is close to equilibrium (i.e., the difference between donor and acceptor quasi Fermi levels jUd—jUa kT), the master equation with Miller-Abrahams transition rates can be linearized to obtain a conductance [26] ... 

The Molecular Theory of Solutions , by Prigogine, includes thermodynamic considerations, and Zemansky s book is a later edition of the book mentioned earlier. Wilson s volume is of a fairly advanced level and requires a fairly high standard of mathematical ability. It is mainly designed for the use of physicists. Chapters include accounts of partial differentiation, and the book approaches entropy through Carnot cycles but also describes Caratheodory s axiomatic approach. Superconductivity and solutions are considered thermodynamically. Caldin s introduction is designed for chemistry undergraduates. A student who has mastered the text should be well prepared to go on to more advanced work. Chisholm and de Borde s book develops the equations for Bose-Einstein, Fermi-Dirac, and classical statistics by unusual routes and then applies the... 

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