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Nonlinear phase excitations in the PPP model of polyacetylene
Author(s) -
Sasai Masaki
Publication year - 1990
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560370424
Subject(s) - hamiltonian (control theory) , bosonization , excited state , physics , polyacetylene , ultra high frequency , quantum mechanics , nonlinear system , magnon , amplitude , condensed matter physics , quantum electrodynamics , mathematics , ferromagnetism , doping , mathematical optimization , telecommunications , fermion , computer science
The Pariser‐Parr‐Pople ( PPP ) method has revealed rich effects of the π electron Coulomb interaction in (CH) x . We discuss results obtained by the PPP model with the unrestricted Hartree‐Fock (UHF) approximation and we show that concepts introduced by the PPP ‐ UHF model give a new insight on Franck‐Condon‐type electronically excited states in (CH) x . In the first part of this paper, a brief review of the PPP ‐ UHF model is given. We introduce phase and amplitude variables and show that solitons in the PPP ‐ UHF model are phase excitations. In the second part of this paper, the effective Hamiltonian describing phase excitations is derived. We show that the phase Hamiltonian derived by the time‐dependent Hartree‐Fock approximation is the classical limit of the Hamiltonian derived by the bosonization method of Tomonaga, Luther, and others. The phase Hamiltonian has a family of new soliton solutions. These solitons are pure electronic excitations and correspond to the exciton and the magnon in (CH) x .