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Nonlinear oscillations in the molecular dimer: Asymptotic solutions
Author(s) -
Maximov S. G.,
Kuzmenkov L. S.,
Guardado Zavala J. L.
Publication year - 2004
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.20181
Subject(s) - hamiltonian (control theory) , nonlinear system , physics , quantum mechanics , quantum , ordinary differential equation , exciton , hamiltonian system , dimer , radius , differential equation , mathematical physics , mathematics , mathematical optimization , computer security , nuclear magnetic resonance , computer science
Nonlinear oscillations in the molecular dimer, composed of two monomers, are investigated, considering an arbitrary number of excitons in the system. The bosonic operators are used to describe the exciton dynamics, that leads to value of the radius of a Bloch sphere that differs from known results. The Hamiltonian of the system is used to reduce the system of equations of motion to a single nonlinear ordinary differential operator equation of the fourth order. Then, the energy of the system is involved in this equation as a parameter. The stability problem is investigated for different energy values. A bifurcation occurs for the energies E > −1/2 p . The asymptotic quasiclassical solution for the case E > −1/2 p is obtained. The solution contains the number of excitons as a parameter. The quantum solutions can be obtained from the classical solutions using the continual integral technique. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004