Geodesic
Generalized solutions of the Bogolyubov diffusion hierarchy in the thermodynamic limit. Cluster expansions
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 1, pp. 119-137 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Nonstationary diffusion of charged particles interacting through the Yukawa potential is considered. For a finite time interval and for sufficiently high temperatures we prove convergence of the cluster expansions and the existence of nonequilibrium correlation functions in the limit $\Lambda\nearrow\mathbb R^3$. Exponential clustering of the correlation functions is also established. 
@article{TMF_1992_93_1_a9,
     author = {A. I. Pilyavskii and A. L. Rebenko and V. I. Skripnik},
     title = {Generalized solutions of the {Bogolyubov} diffusion hierarchy in the thermodynamic limit. {Cluster} expansions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {119--137},
     year = {1992},
     volume = {93},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a9/}
}
TY  - JOUR
AU  - A. I. Pilyavskii
AU  - A. L. Rebenko
AU  - V. I. Skripnik
TI  - Generalized solutions of the Bogolyubov diffusion hierarchy in the thermodynamic limit. Cluster expansions
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1992
SP  - 119
EP  - 137
VL  - 93
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a9/
LA  - ru
ID  - TMF_1992_93_1_a9
ER  - 
%0 Journal Article
%A A. I. Pilyavskii
%A A. L. Rebenko
%A V. I. Skripnik
%T Generalized solutions of the Bogolyubov diffusion hierarchy in the thermodynamic limit. Cluster expansions
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1992
%P 119-137
%V 93
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a9/
%G ru
%F TMF_1992_93_1_a9
A. I. Pilyavskii; A. L. Rebenko; V. I. Skripnik. Generalized solutions of the Bogolyubov diffusion hierarchy in the thermodynamic limit. Cluster expansions. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 1, pp. 119-137. http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a9/

[1] Chandrasekar S., Stokhasticheskie problemy v fizike i astronomii, IL, M., 1949

[2] Bogolyubov N. N., Problemy dinamicheskoi teorii v statisticheskoi fizike, Gostekhizdat, M.-L., 1946 | MR

[3] Streltsova E. A., UMZh, 11:1 (1959), 83–92 | MR

[4] Skripnik V. I., TMF, 58:3 (1984), 398–420 | MR

[5] Skripnik V. I., Fizika mnogochastichnykh sistem, 1985, no. 7, 96–104 | MR

[6] Ryuel D., Statisticheskaya mekhanika. Strogie rezultaty, Mir, M., 1971

[7] Ginibre I., Some applications of functional integration in statistical mechanics and quantum field theory, Gordon and Breach science publishers, New York-London-Paris, 1970, 327–427

[8] Brydges D., Commun. Math. Phys., 58 (1978), 313–350 | DOI | MR

[9] Brydges D., Federbush P., Commun. Math. Phys., 73 (1980), 197–246 | DOI | MR

[10] Rebenko A. L., TMF, 53:3 (1982), 429–443 | MR

[11] Rebenko A. L., UMN, 43:3 (1988), 55–97 | MR

[12] Pilyavskii A. I., Rebenko A. L., TMF, 69:2 (1986), 245–258 ; 70:2 (1987), 278–288 | MR | MR

[13] Petrina D. Ya., Gerasimenko V. I., Malyshev P. V., Matematicheskie osnovy klassicheskoi statisticheskoi mekhaniki, Naukova dumka, Kiev, 1986 | MR

[14] Minlos R. A., Tr. Mosk. matem. ob-va, 8 (1959), 497–518 | MR

[15] Kac M., “On some connections between probability theory and differential and integral equations”, Proceed, of the 2-nd Berkeley Sympoth. Math. Stat. and Probab., Berkeley, 1951, 189–215 | MR | Zbl

[16] Glimm D., Dzhaffe A., Spenser T., Korpuskulyarnaya struktura $P(\varphi)_2$-modeli so slabym vzaimodeistviem i drugie primeneniya vysokotemperaturnykh razlozhenii. Korpuskulyarnaya teoriya polya, Mir, M., 1977, 169–267

[17] Glimm D., Dzhaffe A., Spenser T., Razlozhenie v ryad, svyazannoe s priblizheniem srednego polya. Evklidova kvantovaya teoriya polya. Markovskii podkhod, Mir, M., 1978, 65–139 | MR

[18] Brydges D., Federbush P., J. Math. Phys., 19 (1978), 2064–2067 | DOI | MR

[19] Rebenko A. L., Reznichenko P. V., Brydges–Federbush–Mayer expansions for many-body potentials, Preprint Inst. of Math. No 90.20, Kiev, 1990 | MR

[20] Battle G. A., Federbush P., Lett. Math. Phys., 8:1 (1984), 55–57 | DOI | MR

[21] Ginibre I., Commun. Math. Phys., 16:3 (1970), 310–328 | DOI | MR