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On the kinetics of systems with discrete energy levels
Author(s) -
Aminov L. K.
Publication year - 1972
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220500147
Subject(s) - relaxation (psychology) , master equation , differential equation , perturbation theory (quantum mechanics) , physics , nonlinear system , mathematics , rate equation , phonon , statistical physics , quantum , quantum mechanics , mathematical analysis , mathematical physics , kinetics , psychology , social psychology
The nonlinear generalization of the Konstantinov and Perel diagram method is used for a derivation of the quantum kinetic equation. Under definite conditions this equation may be rewritten as a differential equation analogous to that known from the theory of paramagnetism as the Wangsness‐Bloch equation, but the relaxation term of which is not limited by the second order in a corresponding interaction. This fact allows to investigate the contribution of multiphonon relaxation processes to the rate equations for populations of the energy levels of systems with discrete energy levels. It is made clear that the relaxation parameters of the rate equations in general do not coincide with the total probabilities of transitions between levels calculated by the perturbation theory. It is shown how the procedure of the calculation of two‐phonon (Raman) transitions is modified when an intermediate level occurs inside a frequency spectrum of the lattice vibrations.