Geodesic
Asymptotic behavior of Green's functions and correlation functions in the statistical theory of nonequilibrium processes
Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 3, pp. 407-418 
V. G. Morozov. Asymptotic behavior of Green's functions and correlation functions in the statistical theory of nonequilibrium processes. Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 3, pp. 407-418. http://geodesic.mathdoc.fr/item/TMF_1981_47_3_a11/
@article{TMF_1981_47_3_a11,
     author = {V. G. Morozov},
     title = {Asymptotic behavior of {Green's} functions and correlation functions in the statistical theory of nonequilibrium processes},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {407--418},
     year = {1981},
     volume = {47},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1981_47_3_a11/}
}
TY  - JOUR
AU  - V. G. Morozov
TI  - Asymptotic behavior of Green's functions and correlation functions in the statistical theory of nonequilibrium processes
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1981
SP  - 407
EP  - 418
VL  - 47
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1981_47_3_a11/
LA  - ru
ID  - TMF_1981_47_3_a11
ER  - 
%0 Journal Article
%A V. G. Morozov
%T Asymptotic behavior of Green's functions and correlation functions in the statistical theory of nonequilibrium processes
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1981
%P 407-418
%V 47
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1981_47_3_a11/
%G ru
%F TMF_1981_47_3_a11

Voir la notice de l'article provenant de la source Math-Net.Ru

Expressions are obtained for the asymptotic Green's and correlation functions of arbitrary operators which are not integrals of the motion. The derivation of the expressions presupposes only the existence of a set of operators (coarse-grain variables) such that the variation in time of their mean values determines the slow evolution of the system. It is shown that the correlation functions of the coarse-grain variables, the fluxes, and their “random” components can be expressed in terms of the same transport coefficients. The nonequilibrium statistical operator method is used to derive dynamical equations with sources for the asymptotic Green's functions of the coarse-grain variables.

[1] Zubarev D. N., Neravnovesnaya statisticheskaya termodinamika, Nauka, M.

[2] Akhiezer A. I., Peletminskii S. V., Metody statisticheskoi fiziki, Nauka, M., 1977 | MR

[3] Bogolyubov N. N., K voprosu o gidrodinamike sverkhtekuchei zhidkosti, Preprint R-1395, OIYaI, Dubna, 1963

[4] Kadanoff L. P., Martin P. C., “Hydrodynamic equations and correlation functions”, Ann. Phys., 24 (1963), 419 | DOI | MR | Zbl

[5] Galasiewicz Z., Superconductivity and quantum fluids, Polish Scientific Publishers, Warszawa, 1970

[6] Galasiewicz Z., “Hydrodynamical equations for the superfluid Fermi liquid and two particle Green function”, Phys. Lett., 15 (1965), 39 | DOI

[7] Krasnikov V. A., “K voprosu o gidrodinamicheskom priblizhenii funktsii Grina v sverkhtekuchei boze-sisteme”, DAN SSSR, 174 (1967), 1037

[8] Petru Z. K., “Green's functions for the Bose superfluid and the relations between kinetical coefficients”, Acta Phys. Polon., 35 (1969), 49 | Zbl

[9] Dzheparov F. S., Krasnikov V. A., “Uravneniya gidrodinamiki i funktsii Grina”, TMF, 14 (1973), 82

[10] Szprynger A., “Microscopic theory of $\mathrm{He~II}-\mathrm{He}^3$ mixtures including dissipative processes. I: Derivation of hydrodynamic equations”, Z. Phys., B22 (1975), 79

[11] Martin P. S., “Non local transport coefficients and correlation functions in statistical mechanics of equilibrium and nonequilibrium”, Proc. Int. Sympos. Aachen, ed. J. Meixner, 1965, 100 | MR

[12] Hohenberg P. C., Martin P. C., “Microscopic theory of superfluid helium”, Ann. Phys., 34 (1965), 291 | DOI

[13] Halperin B. I., Hohenberg P. C., “Hydrodynamic theory of spin waves”, Phys. Rev., 188 (1969), 898 | DOI

[14] Zubarev D. N., “Granichnye usloviya dlya statisticheskikh operatorov v teorii neravnovesnykh protsessov i kvazisrednie”, TMF, 3 (1970), 276 | MR

[15] Miyake K., Yamada K., “Dynamics of Bose-Einstein condensate and two-fluid hydrodynamics”, Progr. Theor. Phys., 56 (1976), 1689 | DOI

[16] Morozov V. G., “Uravneniya gidrodinamiki i kineticheskie koeffitsienty sverkhtekuchei boze-zhidkosti”, TMF, 28 (1976), 267

[17] Kawasaki K., Gunton J. D., “Theory of nonlinear shear viscosity and normal stress effects”, Phys. Rev., 8A (1973), 2048 | DOI

[18] Mori H., “Transport, collective motion and Brownian motion”, Progr. Theor. Phys., 33 (1965), 423 | DOI | Zbl

[19] Robertson B., “Equation of motion in nonequilibrium statistical mechanics”, Phys. Rev., 144 (1966), 151 | DOI | MR | Zbl

[20] Tischenko S. V., “Postroenie obobschennoi gidrodinamiki metodom neravnovesnogo statisticheskogo operatora”, TMF, 26 (1976), 96 | Zbl

[21] Kalashnikov V. P., “Lineinye relaksatsionnye uravneniya v metode neravnovesnogo statisticheskogo operatora”, TMF, 34 (1978), 412

[22] Kawasaki K., “Dynamical theory of fluctuations near the critical point”, Critical phenomena, Proc. Int. School Phys. “Enrico Fermi”, Course 51, Acad. Press, N. Y.–London, 1971

[23] Zubarev D. N., Khazanov A. M., “Obobschennoe uravnenie Fokkera-Planka i postroenie proektsionnykh operatorov dlya razlichnykh metodov sokraschennogo opisaniya”, TMF, 34 (1978), 69 | MR