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Theory of phonon relaxation due to multilevel impurities
Author(s) -
Joshi Y. P.
Publication year - 1975
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.2220680112
Subject(s) - impurity , phonon , condensed matter physics , hamiltonian (control theory) , degenerate energy levels , relaxation (psychology) , lattice (music) , quadratic equation , physics , scattering , quantum mechanics , mathematics , psychology , mathematical optimization , social psychology , acoustics , geometry
A theory is developed for the calculation of the single‐mode relaxation time of phonons in a crystal containing impurities that have a possibly degenerate spectrum of energy levels. Transitions of the impurities from one level to another under the effect of the lattice waves can result in the scattering of the latter. Following earlier calculations corresponding to the case of nondegenerate two‐level impurities, certain operators are defined to describe these transitions, which allow to describe the phonon‐impurity system with a model Hamiltonian that is suited to the diagrammatic technique of the thermodynamic Green's functions. The relaxation time obtained exhibits resonant behaviour with peaks at frequencies equal to the energy gaps between various pairs of energy levels. The relaxation time is also found to be quadratic in the degeneracy factors of the impurity levels and shows a dependence on temperature through the occupation probability of these levels.