Nikolay Bogolyubov


Nikolay Nikolayevich Bogolyubov, also transliterated as Bogoliubov and Bogolubov, was a Soviet mathematician and theoretical physicist known for a significant contribution to quantum field theory, classical and quantum statistical mechanics, and the theory of dynamical systems; he was the recipient of the 1992 Dirac Prize.

Biography

Early life (1909–1921)

Nikolay Bogolyubov was born on 21 August 1909 in Nizhny Novgorod, Russian Empire to Russian Orthodox Church priest and seminary teacher of theology, psychology and philosophy Nikolay Mikhaylovich Bogolyubov, and Olga Nikolayevna Bogolyubova, a teacher of music. The Bogolyubovs relocated to the village of Velikaya Krucha in the Poltava Governorate in 1919, where the young Nikolay Bogolyubov began to study physics and mathematics. 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.
He attended research seminars in Kiev University and soon started to work under the supervision of the well-known contemporary mathematician Nikolay Krylov. In 1924, at the age of 15, Nikolay 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 and obtained the degree of Kandidat Nauk 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 Doktor nauk, 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 Nikolai 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" and the book Introduction to Nonlinear Mechanics leading to a creation of a large field of non-linear mechanics.
Distinctive features of the Kiev School approach included an emphasis on the computation of solutions, approximations of periodic solutions, 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 Kiev School was the development by Krylov and Bogolyubov of the describing function method for the analysis of nonlinear control problems.
In the period 1928—1973, Nikolay Bogolyubov worked in the of the Academy of Sciences of the Ukrainian SSR holding the position of the Director of the institute since 1965. He lectured at Kiev University in the period 1936—1959.

In evacuation (1941–1943)

After the German attack against the Soviet Union on 22 June 1941, most institutes and universities from the western part of Russia were evacuated into the eastern regions, far from the battle lines. Nikolay 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 on these positions during the period of July 1941 – August 1943.

Moscow (1943–?)

In autumn 1943, Bogolyubov came from evacuation to Moscow and on 1 November 1943 he accepted a position in the Department of Theoretical Physics at the Moscow State University. At that time the Head of the Department was Anatoly Vlasov. Theoretical physicists working in the department in that period included Dmitry Ivanenko, Arsenij Sokolov, and other physicists.
In the period 1943–1946, Bogolyubov's research was essentially concerned with the theory of stochastic processes and asymptotic methods. In his work 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 in JETP two works on equilibrium and non-equilibrium statistical mechanics which became the essence of his fundamental monograph Problems of dynamical theory in statistical physics.
On 26 January 1953, Nikolay Bogolyubov became the Head of the Department of Theoretical Physics at MSU, after Anatoly Vlasov decided to leave the position on January 2, 1953.

Steklov Institute (1947–?)

In 1947, Nikolay Bogolyubov organized and became the Head of the Department of Theoretical Physics at the Steklov Mathematical Institute. In 1969, the Department of Theoretical Physics was separated into the Departments of Mathematical Physics, of Statistical Mechanics, and of Quantum Field Theory. While working in the Steklov Institute, Nikolay 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.
In the late 1940s and 1950s, Bogoliubov worked on the theory of superfluidity and superconductivity, where he developed the method of BBGKY hierarchy for a derivation of kinetic equations, formulated microscopic theory of superfluidity, and made other essential contributions. Later he worked on quantum field theory, where introduced the Bogoliubov transformation, formulated and proved the Bogoliubov's edge-of-the-wedge theorem and Bogoliubov–Parasyuk theorem, and obtained other significant results. In the 1960s his attention turned to the quark model of hadrons; in 1965 he was among the first scientists to study the new quantum number color charge.
In 1946, Nikolay Bogoliubow was elected as a Corresponding Member of the Academy of Sciences of the USSR. He was elected a full member of the Academy of Sciences of the Ukrainian SSR and in full member of the Academy of Sciences of the USSR in 1953.

Dubna (1956–1992)

Since 1956, he worked in the Joint Institute for Nuclear Research, Dubna, Russia, where he was a founder and the first director of the . This laboratory, where Nikolay Bogolyubov worked for a long time, has traditionally been the home of the prominent Russian schools in quantum field theory, theoretical nuclear physics, statistical physics, and nonlinear mechanics. Nikolay Bogolyubov was Director of the JINR in the period 1966—1988.

Family

His son Nikolay Boglyubov is a theoretical physicist working in the fields of mathematical physics and statistical mechanics.

Students

Nikolay Bogoliubov was a scientific supervisor of Yurii Mitropolskiy, Dmitry Shirkov, Selim Krein, Iosif Gihman, Tofik Mamedov, Kirill Gurov, Mikhail Polivanov, Naftul Polsky, Galina Biryuk, Sergei Tyablikov, Dmitry Zubarev, Vladimir Kadyshevsky, and many other students. His method of teaching, based on creation of a warm atmosphere, politeness and kindness, is famous in Russia and is known as the "Bogoliubov approach".

Awards

Nikolay Bogolyubov received various high USSR honors and international awards.
;Soviet
;Foreign awards
;Academic awards
;Academic recognition
;Memory
Institutions, awards and locations have been named in Bogolyubov's memory:
In 2009, the centenary of Nikolay Bogolyubov's birth was celebrated with two conferences in Russia and Ukraine:
Fundamental works of Nikolay Bogoliubov were devoted to asymptotic methods of nonlinear mechanics, quantum field theory, statistical field theory, variational calculus, approximation methods in mathematical analysis, equations of mathematical physics, theory of stability, theory of dynamical systems, and to many other areas.
He built a new theory of scattering matrices, formulated the concept of microscopical causality, obtained important results in quantum electrodynamics, and investigated on the basis of the edge-of-the-wedge theorem the dispersion relations in elementary particle physics. He suggested a new synthesis of the Bohr theory of quasiperiodic functions and developed methods for asymptotic integration of nonlinear differential equations which describe oscillating processes.

Mathematics and non-linear mechanics

Books

Mathematics and Non-linear Mechanics:
  1. N. M. Krylov and N. N. Bogoliubov : On various formal expansions of non-linear mechanics. Kiev, Izdat. Zagal'noukr. Akad. Nauk.
  2. N. M. Krylov and N. N. Bogoliubov : Introduction to Nonlinear Mechanics. Princeton, Princeton University Press.
  3. N. N. Bogoliubov, Y. A. Mitropolsky : Asymptotic Methods in the Theory of Non-Linear Oscillations. New York, Gordon and Breach.
Statistical Mechanics:
  1. N. N. Bogoliubov : On Some Statistical Methods in Mathematical Physics. Kyiv.
  2. N. N. Bogoliubov, V. V. Tolmachev, D. V. Shirkov : A New Method in the Theory of Superconductivity. New York, Consultants Bureau.
  3. N. N. Bogoliubov : Problems of Dynamic Theory in Statistical Physics. Oak Ridge, Tenn., Technical Information Service.
  4. N. N. Bogoliubov : Lectures on Quantum Statistics. Problems of Statistical Mechanics of Quantum Systems. New York, Gordon and Breach.
  5. N. N. Bogolubov and N. N. Bogolubov, Jnr. : Introduction to Quantum Statistical Mechanics. Gordon and Breach..
Quantum Field Theory:
  1. N. N. Bogoliubov, B. V. Medvedev, M. K. Polivanov : Problems in the Theory of Dispersion Relations. Institute for Advanced Study, Princeton.
  2. N. N. Bogoliubov, D. V. Shirkov : The Theory of Quantized Fields. New York, Interscience. The first text-book on the renormalization group theory.
  3. N. N. Bogoliubov, A. A. Logunov and I. T. Todorov : Introduction to Axiomatic Quantum Field Theory. Reading, Mass.: W. A. Benjamin, Advanced Book Program...
  4. N. N. Bogoliubov, D. V. Shirkov : Introduction to the Theory of Quantized Field. John Wiley & Sons Inc; 3rd edition...
  5. N. N. Bogoliubov, D. V. Shirkov : Quantum Fields. Benjamin-Cummings Pub. Co.,.
  6. N. N. Bogoliubov, A. A. Logunov, A. I. Oksak, I. T. Todorov : General Principles of Quantum Field Theory. Dordrecht ; Boston, Kluwer Academic Publishers...
;Selected works
  1. N. N. Bogoliubov, Selected Works. Part I. Dynamical Theory. Gordon and Breach, New York, 1990.,.
  2. N. N. Bogoliubov, Selected Works. Part II. Quantum and Classical Statistical Mechanics. Gordon and Breach, New York, 1991..
  3. N. N. Bogoliubov, Selected Works. Part III. Nonlinear Mechanics and Pure Mathematics. Gordon and Breach, Amsterdam, 1995..
  4. N. N. Bogoliubov, Selected Works. Part IV. Quantum Field Theory. Gordon and Breach, Amsterdam, 1995.,.

    Selected papers