Reduced description of nonequilibrium processes and correlation functions. Divergences and non-analyticity
A complete theory for investigation of time correlation functions is developed on the basis of the Bogolyubov reduced description method proceeding from his functional hypothesis. The problem of convergence in the theory of nonequilibrium processes and its relation to the non-analytic dependence o...
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| Дата: | 2006 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2006
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/121366 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Reduced description of nonequilibrium processes and correlation functions. Divergences and non-analyticity / A.I. Sokolovsky // Condensed Matter Physics. — 2006. — Т. 9, № 3(47). — С. 415–430. — Бібліогр.: 17 назв. — англ. |
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irk-123456789-1213662017-06-15T03:03:18Z Reduced description of nonequilibrium processes and correlation functions. Divergences and non-analyticity Sokolovsky, A.I. A complete theory for investigation of time correlation functions is developed on the basis of the Bogolyubov reduced description method proceeding from his functional hypothesis. The problem of convergence in the theory of nonequilibrium processes and its relation to the non-analytic dependence of basic values of the theory on a small parameter of the perturbation theory are discussed. A natural regularization of integral equations of the theory is proposed. In the framework of a model of slow variables (hydrodynamics of a fluid, kinetics of a gas) a generalized perturbation theory without divergencies is constructed corresponding to a partial summation in a usual perturbation theory. Properties of Green functions are discussed on the basis of resolvent formalism for the Liouville operator. A generalized Ernst and Dorfman theory is elaborated allowing to study the peculiarities of correlation and Green functions and to solve the convergence problem in the reduced description method. На основi методу скороченого опису Боголобова, що ґрунтується на функцiональнiй гiпотезi, розвивається повна теорiя для дослiдження часових кореляцiйних функцiй. Обговорюється проблема розбiжностей в теорiї нерiвноважних процесiв та її зв’язок з неаналiтичною залежнiстю основних величин теорiї вiд малого параметра теорiї збурень. Пропонується природна регуляризацiя iнтегральних рiвнянь теорiї. В рамках моделi повiльних змiнних (гiдродинамiка рiдини, кiнетика газу) конструюється узагальнена теорiя збурень, яка вiдповiдає частковому сумуванню у звичайнiй теорiї збурень. Властивостi функцiй Грiна обговорюються на основi формалiзму резольвенти оператора Лiувiлля. Розробляється узагальнена теорiя Ернста та Дорфмана, яка дозволяє вивчати особливостi кореляцiйних функцiй i функцiй Грiна та розв’язувати проблему збiжностi у методi скороченого опису 2006 Article Reduced description of nonequilibrium processes and correlation functions. Divergences and non-analyticity / A.I. Sokolovsky // Condensed Matter Physics. — 2006. — Т. 9, № 3(47). — С. 415–430. — Бібліогр.: 17 назв. — англ. 1607-324X PACS: 05.20.Dd, 05.30-d DOI:10.5488/CMP.9.3.415 http://dspace.nbuv.gov.ua/handle/123456789/121366 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
A complete theory for investigation of time correlation functions is developed on the basis of the Bogolyubov
reduced description method proceeding from his functional hypothesis. The problem of convergence in the
theory of nonequilibrium processes and its relation to the non-analytic dependence of basic values of the
theory on a small parameter of the perturbation theory are discussed. A natural regularization of integral
equations of the theory is proposed. In the framework of a model of slow variables (hydrodynamics of a fluid,
kinetics of a gas) a generalized perturbation theory without divergencies is constructed corresponding to a
partial summation in a usual perturbation theory. Properties of Green functions are discussed on the basis of
resolvent formalism for the Liouville operator. A generalized Ernst and Dorfman theory is elaborated allowing
to study the peculiarities of correlation and Green functions and to solve the convergence problem in the
reduced description method. |
| format |
Article |
| author |
Sokolovsky, A.I. |
| spellingShingle |
Sokolovsky, A.I. Reduced description of nonequilibrium processes and correlation functions. Divergences and non-analyticity Condensed Matter Physics |
| author_facet |
Sokolovsky, A.I. |
| author_sort |
Sokolovsky, A.I. |
| title |
Reduced description of nonequilibrium processes and correlation functions. Divergences and non-analyticity |
| title_short |
Reduced description of nonequilibrium processes and correlation functions. Divergences and non-analyticity |
| title_full |
Reduced description of nonequilibrium processes and correlation functions. Divergences and non-analyticity |
| title_fullStr |
Reduced description of nonequilibrium processes and correlation functions. Divergences and non-analyticity |
| title_full_unstemmed |
Reduced description of nonequilibrium processes and correlation functions. Divergences and non-analyticity |
| title_sort |
reduced description of nonequilibrium processes and correlation functions. divergences and non-analyticity |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/121366 |
| citation_txt |
Reduced description of nonequilibrium processes and correlation functions. Divergences and non-analyticity / A.I. Sokolovsky // Condensed Matter Physics. — 2006. — Т. 9, № 3(47). — С. 415–430. — Бібліогр.: 17 назв. — англ. |
| series |
Condensed Matter Physics |
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2023-10-18T20:39:17Z |
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2023-10-18T20:39:17Z |
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1796150765078708224 |