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The higher time derivatives of the generalized liapunov function
Author(s) -
Schieve W. C.,
Bulsara Adi R.
Publication year - 2009
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.560090857
Subject(s) - anharmonicity , diagonal , liapunov function , sign (mathematics) , lattice (music) , scattering , diagonal matrix , quantum mechanics , mathematical analysis , physics , mathematical physics , mathematics , geometry , nonlinear system , acoustics
Using the generalized N ‐body expression for a Liapunov functional developed by Prigogine and coworkers, a condition is obtained whereby the successive time derivatives of this function alternate in sign for weakly coupled systems. This generalized Liapunov function contains contributions from the diagonal as well as off‐diagonal (correlation) components of the density matrix. The alternating sign condition is applied (and seen to hold true) for the cases of elastic phonon scattering in a lattice, three‐phonon scattering (the anharmonic lattice), and the quantum electron gas. It is also proved simply for the Friedrichs model.