Nikolay Nikolayevich Bogolyubov (21 August 1909 – 13 February 1992) was a Soviet mathematician and theoretical physicist known for his significant contributions to quantum field theory, classical and quantum statistical mechanics, and the theory of dynamical systems; he was the recipient of the 1992 Dirac Medal for his works and studies.
Nikolay Bogolyubov was born on 21 August 1909 in Nizhny Novgorod, Russia. His father, Nikolay Mikhaylovich Bogolyubov, was a Russian Orthodox priest and a teacher of theology, philosophy, and psychology at the Nizhny Novgorod Theological Seminary. His mother, Olga Nikolayevna, née Lyuminarskaya, was a music teacher.
Six months after Nikolay's birth, the family moved to Nezhin (present-day Ukraine), where his father taught him until 1913.
From 1913 to 1918, the family lived in Kiev. Nikolay was innitially homeschooled. His father taught him the basics of arithmetic, as well as German, French, and English. At the age of six, he attended a preparatory class in the Kiev Gymnasium. However, he did not stay in the gymnasium for long, as the family moved to the village of Velyka Krucha. From 1919 to 1921, he studied at the Velykokruchanska seven-year school, whcih was the only educational institution he graduated from.
The family soon moved to Kiev in 1921, where they continued to live in poverty as the elder Nikolay Bogolyubov only found a position as a priest in 1923. After finishing seven years of school, Bogolyubov independently studied physics and mathematics, and by the age of 14, he was already participating in the seminar of the Department of Mathematical Physics at Kiev University under the supervision of academician Dmitry Grave.
In 1924, at the age of 15, Bogolyubov wrote his first published scientific paper On the behavior of solutions of linear differential equations at infinity. In 1925, he entered Ph.D. program at the Academy of Sciences of the Ukrainian SSR under the supervision of the well-known contemporary mathematician Nikolay Krylov and obtained the degree of Candidate of Sciences (equivalent to a Ph.D.) in 1928, at the age of 19, with the doctoral thesis titled On direct methods of variational calculus. In 1930, at the age of 21, he obtained the degree of Doctor of Sciences (equivalent to habilitation), the highest degree in the Soviet Union, which requires the recipient to have made a significant independent contribution to his or her scientific field.
This early period of Bogolyubov's work in science was concerned with such mathematical problems as direct methods of the calculus of variations, the theory of almost periodic functions, methods of approximate solution of differential equations, and dynamical systems. This earlier research had already earned him recognition. One of his essays was awarded the Bologna Academy of Sciences Prize in 1930, and the author was awarded the erudite degree of doctor of mathematics. This was the period when the scientific career of the young Bogolyubov began, later producing new scientific trends in modern mathematics, physics, and mechanics.
Since 1931, Krylov and Bogolyubov worked together on the problems of nonlinear mechanics and nonlinear oscillations. They were the key figures in the Kiev school of nonlinear oscillation research, where their cooperation resulted in the paper "On the quasiperiodic solutions of the equations of nonlinear mechanics" (1934) and the book Introduction to Nonlinear Mechanics (1937; translated to English in 1947), leading to a creation of a large field of non-linear mechanics.
And this can explain, as the authors believe, the need to shape the collection of problems of non-linear perturbation theory into a special science, which could be named NON-LINEAR MECHANICS.
Distinctive features of the Kiev school approach included an emphasis on the computation of solutions (not just a proof of its existence), approximations of periodic solutions, the use of the invariant manifolds in the phase space, and applications of a single unified approach to many different problems. From a control engineering point of view, the key achievement of the Kyiv School was the development by Krylov and Bogolyubov of the describing function method for the analysis of nonlinear control problems.
In 1936, Bogolyubov was awarded the title of professor, and from 1936 to 1940, he chaired the Department of Mathematical Physics at Kiev University. In 1939, he was elected a corresponding member of the Academy of Sciences of the Ukrainian SSR. In 1940, after northern Bukovina was annexed to the Ukrainian SSR, Bogolyubov was sent to Chernivtsi to organize mathematical departments at the Faculty of Physics and Mathematics of Chernivtsi State University.
Following the German invasion of the Soviet Union on 22 June 1941, most institutes and universities from the western part were evacuated into the eastern regions, far from the battle lines. Bogolyubov moved to Ufa, where he became Head of the Departments of Mathematical Analysis at Ufa State Aviation Technical University and at Ufa Pedagogical Institute, remaining in these positions from July 1941 to August 1943.
In the autumn of 1943, Bogolyubov arrived at Moscow, and on 1 November 1943, he accepted a position in the Department of Theoretical Physics at Moscow State University. At that time, the head of the department was Anatoly Vlasov (for a short period in 1944 the head of the department was Vladimir Fock). Theoretical physicists working in the department in that period included Dmitri Ivanenko, Arseny Sokolov, and others.
From 1943 to 1946, Bogolyubov's research was essentially concerned with the theory of stochastic processes and asymptotic methods. A simple example of an anharmonic oscillator driven by a superposition of incoherent sinusoidal oscillations with continuous spectrum was used to show that depending on a specific approximation time scale the evolution of the system can be either deterministic, or a stochastic process satisfying Fokker–Planck equation, or even a process which is neither deterministic nor stochastic. In other words, he showed that depending on the choice of the time scale for the corresponding approximations the same stochastic process can be regarded as both dynamical and Markovian, and in the general case as a non-Markov process. This work was the first to introduce the notion of time hierarchy in non-equilibrium statistical physics which then became the key concept in all further development of the statistical theory of irreversible processes.
In 1945, Bogolyubov proved a fundamental theorem on the existence and basic properties of a one-parameter integral manifold for a system of non-linear differential equations. He investigated periodic and quasi-periodic solutions lying on a one-dimensional manifold, thus forming the foundation for a new method of non-linear mechanics, the method of integral manifolds.
In 1946, he published two works in the Journal of Experimental and Theoretical Physics on equilibrium and non-equilibrium statistical mechanics which became the essence of his fundamental monograph Problems of dynamical theory in statistical physics (Moscow, 1946).
On 26 January 1953, Bogolyubov became the head of the Department of Theoretical Physics at Moscow State University, after Anatoly Vlasov decided to leave the position on January 2, 1953.
In 1947, Bogolyubov organized and became the head of the Department of Theoretical Physics at the Steklov Institute of Mathematics. In 1969, the Department of Theoretical Physics was separated into the Departments of Mathematical Physics (head: Vasily Vladimirov), of Statistical Mechanics, and of Quantum Field Theory (Head Mikhail Polivanov). While working in the Steklov Institute, Bogolyubov and his school contributed to science with many important works including works on renormalization theory, renormalization group, axiomatic S-matrix theory, and works on the theory of dispersion relations.