An approximate method is considered for the solution of the Bogolyubov equation, which is characterized from the physical viewpoint by successively taking account of corrections of ever higher order. In the zeroth approximation the known Vlasov equation is obtained, in the first approximation a system of equations for the unary distribution and second-order correlation functions, and in the second approximation, a system of three equations for the appropriate correlation functions. The properties of the first approximation equations are investigated.
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N. N. Bogolyubov, Selected Works [in Russian], Naukova Dumka, Kiev, 2 (1970).
G. I. Nazin, Teor. Mat. Fiz.,21, No. 3, 388 (1974).
G. I. Nazin, Teor. Mat. Fiz.,42, No. 2, 243 (1980).
N. N. Bogolyubov, D. Ya. Petrina, and B. N. Khatset, Teor. Mat. Fiz.,1, No. 2, 251 (1969).
É. A. Arinshtein, Crystallization Phenomenon in Statistical Physics [in Russian], Cand. Dissert. Moscow State Pedag. Inst., Moscow (1958).
D. Ruell, Statistical Mechanics [Russian translation], Mir, Moscow (1971).
É. A. Arinshtein, Dokl. Akad. Nauk SSSR,112, No. 4, 615 (1957).
N. V. Glukhikh and G. I. Nazin, Teor. Mat. Fiz.,38, No. 3, 423 (1979).
M. A. Krasnosel'skii et al., Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).
A. A. Vlasov, Statistical Distribution Functions [in Russian], Nauka, Moscow (1966).
É. A. Arinshtein and B. G. Abrosimov, Zh. Strukt. Khim.,9, No. 6, 1064 (1968).
V. N. Ryzhov and E. E. Tareeva, Dokl. Akad. Nauk SSSR,257, No. 5, 1102 (1981).
C. Crockston, Physics of the Liquid State [Russian translation], Mir, Moscow (1978).
R. C. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics, Wiley (1975).
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 95–99, April, 1984.
The authors are grateful to É. A. Arinshtein and N. M. Placid for useful discussions.
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Kasimov, N.S., Nazin, G.I. Projection method of solving the Bogolyubov equation for the generating functional in classical statistical physics. Soviet Physics Journal 27, 342–346 (1984). https://doi.org/10.1007/BF00893721
- Statistical Physic
- Correlation Function
- Projection Method
- Approximate Method
- Vlasov Equation