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Phonon—Phonon Interaction in a One‐Dimensional Anharmonic Lattice
Author(s) -
Chatterjee R.
Publication year - 1990
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.2221610118
Subject(s) - anharmonicity , phonon , physics , condensed matter physics , lattice (music) , long wavelength limit , scattering , equations of motion , nonlinear system , quantum mechanics , quantum , acoustics
A higher order partial nonlinear differential equation is obtained when phonon—phonon interaction in a one‐dimensional anharmonic lattice is treated quantum mechanically. Few assumptions are made to derive this equation of motion, such as long‐wavelength approximation, omission of normally ordered terms, continuum limit, and no umklapp scattering. The validity of these assumptions is discussed. The limitation to up to sixth higher order phonon—phonon interaction terms agrees with the earlier conclusion, reached from the stability consideration of the solitonic solution of this equation of motion.