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Derivation of the Self‐Consistent Phonon Theory from Zubarev Type Green's Function
Author(s) -
Shukla R. C.
Publication year - 1998
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/(sici)1521-3951(199802)205:2<481::aid-pssb481>3.0.co;2-q
Subject(s) - hamiltonian (control theory) , physics , anharmonicity , mathematical physics , helmholtz free energy , quantum mechanics , mathematics , mathematical optimization
We have presented a new method for the derivation of the Helmholtz free energy ( F ) of an anharmonic crystal from the Zubarev type Green's function. The Hamiltonian ( H ) employed in the derivation contains the contributions from all the even terms of the Taylor's expansion of the crystal potential energy. In the language of perturbation theory (PT) these are essentially all the first order PT contributions summed to infinity to the free energy, the self‐energy of the Green's function, and the renormalized phonon frequencies. The self‐consistency condition arises because in evaluating the correlation functions from the Zubarev type Green's functions the full Hamiltonian is required instead of the usual harmonic Hamiltonian. The final equations which determine F and the self‐consistent phonon frequencies are shown to be identical to those of the first order self‐consistent phonon (SC1) theory.