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Classical theory of nonlinear oscillators interacting with a medium
Author(s) -
Dykman M. I.,
Krivoglaz M. A.
Publication year - 1971
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.2220480206
Subject(s) - nonlinear system , physics , vibration , representation (politics) , spectrum (functional analysis) , mathematical analysis , function (biology) , correlation function (quantum field theory) , constant (computer programming) , mathematics , mathematical physics , classical mechanics , statistical physics , quantum mechanics , evolutionary biology , politics , political science , dielectric , law , biology , computer science , programming language
The correlation function Q x ( t ) of the normal coordinates of singled out nonlinear vibrations interacting with the vibrations of the continuous spectrum of a medium (e.g. of local or quasi‐local vibrations in crystals) as well as its spectral representation Q x (ω) were investigated. The calculations have been carried out for the case of high temperatures when the classical approach is applicable. The use of asymptotic methods of nonlinear mechanics and some results of the theory of random processes allowed to consider the case of an arbitrary ratio between the constants characterizing the non‐linearity of singled out oscillators and their energy of interaction with the medium (but with the assumption that both these constants are small). In this general case asymptotic explicit expressions were derived for Q x ( t ) and Q x (ω). Using the Fokker‐Planck equation for this problem we have also derived the difference equations which determine Q x (ω).