59 BOGOLYUBOV 



from a single point of view the theory of and the calculation of 

 kinetic equations for systems of interacting particles, and pro- 

 vided a general procedure for synthesizing them based on the 

 fundamental theorems of statistical mechanics. 



He obtained results of no lesser importance in quantum sta- 

 tistics. Generalizing for the case of quantum systems the 

 method of kinetic distribution functions, he provided a general 

 method of constructing kinetic equations for quantum systems. 

 Interesting results were also obtained by him in questions con- 

 nected with the behavior of electrons in metal. Here he de- 

 veloped a method of approximate second quantization based on 

 the fact that, under certain assumptions, it is possible to repre- 

 sent the energy spectrum of a Fermi system in the form of an 

 aggregate of elementary excitations that are subject to Boze 

 statistics. 



Highly important accomplishments of Bogolyubov are set 

 forth in investigations dealing with superfluidity and super- 

 conductivity. It is well known that quantum systems consisting 

 of a large number of identical particles manifest, at low tem- 

 peratures, the highly unique phenomenon of degeneration. This 

 phenomenon had been studied only for ideal gases. The first 

 results in the theory of the degeneration of non-ideal gases 

 were obtained by him as early as 1947, it being shown that a 

 weakly non-ideal Boze gas can occur in a degenerate state and 

 will then possess the property of superfluidity. In this manner, 

 the first step was made toward the development of the micro- 

 scope theory of the superfluidity of Helium II. 



Development of the ideas and methods which he expressed in 

 his works of 1947 and 1948 made it possible for him to evolve 

 in 1958 a systematic microscopic theory of superconductivity. 

 An important part in understanding the essence of superconduc- 

 tivity was played by Froelich's idea of the decisive role of the 

 interaction of electrons with lattice oscillations, and the pre- 

 diction on that basis of the isotopic .effect. It was, however, 

 impossible to solve the problem on the Hamiltonian basis pro- 

 posed by Froelich on account of the many difficulties of a pure- 

 ly mathematical nature. Bogolyubov was successful in solving 

 this problem and, as a result, not only developed a systematic 

 theory of superfluidity, but also established the fundamental 

 fact that superconductivity may be regarded as the superfluidity 

 of an electron gas, or more generally, as the superfluidity of 

 Fermi systems. Recently these results have found application 

 in nuclear theory. 



