Nikolay Bogolyubov
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Nikolay Nikolayevich (Mykola Mykolayovych) Bogolyubov (; ; 21 August 1909 – 13 February 1992) was a
Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...
, Ukrainian and Russian
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
and
theoretical physicist Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict natural phenomena. This is in contrast to experimental physics, which uses experi ...
known for a significant contribution to
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
, classical and quantum
statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...
, and the theory of dynamical systems; he was the recipient of the 1992 Dirac Medal for his works and studies.


Biography


Early life (1909–1921)

Nikolay Bogolyubov was born on 21 August 1909 in
Nizhny Novgorod Nizhny Novgorod ( ; rus, links=no, Нижний Новгород, a=Ru-Nizhny Novgorod.ogg, p=ˈnʲiʐnʲɪj ˈnovɡərət, t=Lower Newtown; colloquially shortened to Nizhny) is a city and the administrative centre of Nizhny Novgorod Oblast an ...
,
Russian Empire The Russian Empire was an empire that spanned most of northern Eurasia from its establishment in November 1721 until the proclamation of the Russian Republic in September 1917. At its height in the late 19th century, it covered about , roughl ...
to
Russian Orthodox Church The Russian Orthodox Church (ROC; ;), also officially known as the Moscow Patriarchate (), is an autocephaly, autocephalous Eastern Orthodox Church, Eastern Orthodox Christian church. It has 194 dioceses inside Russia. The Primate (bishop), p ...
priest A priest is a religious leader authorized to perform the sacred rituals of a religion, especially as a mediatory agent between humans and one or more deity, deities. They also have the authority or power to administer religious rites; in parti ...
and
seminary A seminary, school of theology, theological college, or divinity school is an educational institution for educating students (sometimes called seminarians) in scripture and theology, generally to prepare them for ordination to serve as cle ...
teacher of
theology Theology is the study of religious belief from a Religion, religious perspective, with a focus on the nature of divinity. It is taught as an Discipline (academia), academic discipline, typically in universities and seminaries. It occupies itse ...
,
psychology Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feel ...
and
philosophy Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
Nikolay Mikhaylovich Bogolyubov, and Olga Nikolayevna Bogolyubova, a teacher of music. Six months after Nicolay's birth, the family moved to
Nizhyn Nizhyn (, ; ) is a city located in Chernihiv Oblast of northern Ukraine along the Oster River. The city is located north-east of the national capital Kyiv. Nizhyn serves as the capital city, administrative center of Nizhyn Raion. It hosts the ...
, city of
Chernihiv Oblast Chernihiv Oblast (), also referred to as Chernihivshchyna (), is an administrative divisions of Ukraine, oblast (province) in northern Ukraine. The capital city, administrative center of the oblast is the city of Chernihiv. There are 1,511 sett ...
, where his father taught until 1913. From 1913 to 1918, the family lived in
Kyiv Kyiv, also Kiev, is the capital and most populous List of cities in Ukraine, city of Ukraine. Located in the north-central part of the country, it straddles both sides of the Dnieper, Dnieper River. As of 1 January 2022, its population was 2, ...
. Nikolay received his initial education at home. His father taught him the basics of arithmetic, as well as German, French, and English. At the age of six, he attended the preparatory class of the Kyiv Gymnasium. However, he did not stay long in the gymnasium, the family moved to the village of Velyka Krucha. From 1919 to 1921, he studied at the Velykokruchanska seven-year school – the only educational institution he graduated from.


Kyiv period (1921-1940)

The family soon moved to
Kyiv Kyiv, also Kiev, is the capital and most populous List of cities in Ukraine, city of Ukraine. Located in the north-central part of the country, it straddles both sides of the Dnieper, Dnieper River. As of 1 January 2022, its population was 2, ...
in 1921, where they continued to live in poverty as the elder Nikolay Bogolyubov only found a position as a priest in 1923.Bogolyubov, A. N. (2009).
"Nikolay Nikolayevich Bogolyubov".
' ''N. N. Bogolyubov: K 100-letiyu so dnya rozhdeniya'' (Joint Institute for Nuclear Research). Retrieved 8 January 2012.
After finishing the seven-year 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 Kyiv University under the supervision of Academician Dmitry Grave. 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 The Ukrainian Soviet Socialist Republic, abbreviated as the Ukrainian SSR, UkrSSR, and also known as Soviet Ukraine or just Ukraine, was one of the Republics of the Soviet Union, constituent republics of the Soviet Union from 1922 until 1991. ...
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 Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...
), 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 calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of f ...
, the theory of almost periodic functions, methods of approximate solution of differential equations, and
dynamical systems In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...
. 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 Nikolay 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 "Kyiv 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. Distinctive features of the Kyiv School approach included an emphasis on the computation of solutions (not just a proof of its existence), 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 Control engineering, also known as control systems engineering and, in some European countries, automation engineering, is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with d ...
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, M. M. Bogolyubov was awarded the title of professor, and from 1936 to 1940, he chaired the Department of Mathematical Physics at Kyiv University In 1939, he was elected a corresponding member of the Academy of Sciences of the Ukrainian SSR (since 1994 – National Academy of Sciences of Ukraine). In 1940, after the reunification of Northern Bukovyna with Ukraine, Nikolay Bogolyubov was sent to
Chernivtsi Chernivtsi (, ; , ;, , see also #Names, other names) is a city in southwestern Ukraine on the upper course of the Prut River. Formerly the capital of the historic region of Bukovina, which is now divided between Romania and Ukraine, Chernivt ...
to organize mathematical departments at the Faculty of Physics and Mathematics of Chernivtsi State University.


In evacuation (1941–1943)

After the German attack against the
Soviet Union The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...
on 22 June 1941 (beginning of the Eastern front of World War II), most institutes and universities from the western part 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 Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...
(MSU). 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 other physicists. In the period 1943–1946, Bogolyubov's research was essentially concerned with the theory of
stochastic process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Sto ...
es and asymptotic methods. In his work a simple example of an anharmonic oscillator driven by a superposition of incoherent
sinusoidal A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine function. In mechanics, as a linear motion over time, this is '' simple harmonic motion''; as rotation, it correspond ...
oscillations with
continuous spectrum In the physical sciences, the term ''spectrum'' was introduced first into optics by Isaac Newton in the 17th century, referring to the range of colors observed when white light was dispersion (optics), dispersed through a prism (optics), prism. ...
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 In statistical mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of the velocity of a particle under the influence of drag (physi ...
, 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 Non-equilibrium may refer to: * generally the absence of an equilibrium * Non-equilibrium economics * Non-equilibrium statistical mechanics * Non-equilibrium thermodynamics {{disambiguation ...
statistical physics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...
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'' (Moscow, 1946). 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 Institute of Mathematics Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Stek ...
. 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, Nikolay Bogolyubov and his school contributed to science with many important works including works on renormalization theory,
renormalization group In theoretical physics, the renormalization group (RG) is a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying p ...
, axiomatic
S-matrix In physics, the ''S''-matrix or scattering matrix is a Matrix (mathematics), matrix that relates the initial state and the final state of a physical system undergoing a scattering, scattering process. It is used in quantum mechanics, scattering ...
theory, and works on the theory of dispersion relations. In the late 1940s and 1950s, Bogolyubov worked on the theory of
superfluid Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortex, vortices that continue to rotate indefinitely. Superfluidity occurs ...
ity and
superconductivity Superconductivity is a set of physical properties observed in superconductors: materials where Electrical resistance and conductance, electrical resistance vanishes and Magnetic field, magnetic fields are expelled from the material. Unlike an ord ...
, 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 In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
, where introduced the Bogoliubov transformation, formulated and proved the Bogoliubov's edge-of-the-wedge theorem and Bogoliubov–Parasyuk theorem (with Ostap Parasyuk), and obtained other significant results. In the 1960s his attention turned to the
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...
model of
hadrons In particle physics, a hadron is a composite subatomic particle made of two or more quarks held together by the strong nuclear force. Pronounced , the name is derived . They are analogous to molecules, which are held together by the electric ...
; in 1965 he was among the first scientists to study the new
quantum number In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system. To fully specify the state of the electron in a hydrogen atom, four quantum numbers are needed. The traditional set of quantu ...
color charge. In 1946, Nikolay Bogolyubov was elected as a Corresponding Member of the Academy of Sciences of the Soviet Union. He was elected a full member ( academician) 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 (JINR), Dubna, Russia, where he was a founder (together with Dmitry Blokhintsev) and the first director of th
Laboratory of Theoretical Physics
This laboratory, where Nikolay Bogolyubov worked for a long time, has traditionally been the home of the prominent Russian schools in
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
, theoretical
nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies th ...
,
statistical physics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...
, and nonlinear mechanics. Nikolay Bogolyubov was Director of the JINR in the period 1966–1988.


Work in Ukraine after the WWII

In the post-war years, M. M. Bogolyubov worked as the dean of the Faculty of Mechanics and Mathematics at Kyiv University and headed the Department of Probability Theory at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR (now – NASU Institute of Mathematics). His first students in nonlinear mechanics were Yurii Mitropolskyi and Yu. V. Blagoveshchensky, and in probability theory and mathematical statistics, I. I. Gikhman. In the first half of the 1960s, Bogolyubov worked on organizing th
Institute for Theoretical Physics
of the Academy of Sciences of the Ukrainian SSR (now – Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine) and from 1966 to 1973, he served as its director. When the institute was established in 1966, it consisted of three departments: Mathematical Methods in Theoretical Physics (Head: Academician Ostap Parasyuk), Theory of the Nucleus (Head: Oleksandr Davydov), and Theory of Elementary Particles (Albert Tavkhelidze). In 1968, the institute organized the Department of Nuclear Reaction Theory (Head: Oleksiy Sytenko).


Family

Nikolay Bogolyubov was married (since 1937) to Evgenia Pirashkova. They had two sons – Pavel and Nikolay (jr). Nikolay Boglyubov (jr) is a theoretical physicist working in the fields of mathematical physics and statistical mechanics. Pavel was a theoretical physicist, Doctor of Physical and Mathematical Sciences, senior researcher, and head of the sector at the Laboratory of Theoretical Physics of the Joint Institute for Nuclear Research.


Students

Nikolay Bogolyubov 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 "Bogolyubov approach".


Awards

Nikolay Bogolyubov received various high USSR honors and international awards. ;Soviet * Two Stalin Prizes (1947, 1953) * USSR State Prize (1984) * Lenin Prize (1958) *
Hero of Socialist Labour The Hero of Socialist Labour () was an Title of honor, honorific title in the Soviet Union and other Warsaw Pact countries from 1938 to 1991. It represented the highest degree of distinction in the USSR and was awarded for exceptional achievem ...
, twice (1969, 1979) * Six Orders of Lenin (1953, 1959, 1967, 1969, 1975, 1979) *
Order of the October Revolution The Order of the October Revolution (, ''Orden Oktyabr'skoy Revolyutsii'') was instituted on 31 October 1967, in time for the 50th anniversary of the October Revolution. It was conferred upon individuals or groups for services furthering communis ...
(1984) * Order of the Red Banner of Labour, twice (1948, 1954) * Order of the Badge of Honour, twice (1944, 1944) ;Foreign awards * Order of Cyril and Methodius, 1st class (Bulgaria, 1969) * Order "For merits", 2nd class (Poland, 1977) ;Academic awards * Award of the Bologna Academy of Sciences (1930) * Heineman Prize for Mathematical Physics (
American Physical Society The American Physical Society (APS) is a not-for-profit membership organization of professionals in physics and related disciplines, comprising nearly fifty divisions, sections, and other units. Its mission is the advancement and diffusion of ...
, 1966) * Gold Medal Helmholtz ( Academy of Sciences of the German Democratic Republic, 1969) *
Max Planck Medal The Max Planck Medal is the highest award of the German Physical Society , the world's largest organization of physicists, for extraordinary achievements in theoretical physics. The prize has been awarded annually since 1929, with few exceptions ...
(1973) * Franklin Medal (1974) *
Gold Medal A gold medal is a medal awarded for highest achievement in a non-military field. Its name derives from the use of at least a fraction of gold in form of plating or alloying in its manufacture. Since the eighteenth century, gold medals have b ...
"For service to science and humanity" ( Slovak Academy of Sciences, 1975) * Karpinski Prize (Germany, 1981) * Gold Medal Lavrent'ev (1983) – for his work "On stochastic processes in dynamical systems" * Lomonosov Gold Medal (1985) – for outstanding achievement in mathematics and theoretical physics * Gold Medal of Lyapunov (1989) – for his work on sustainability, critical phenomena and phase transitions in the theory of many interacting particles * Dirac Medal (1992,
posthumously Posthumous may refer to: * Posthumous award, an award, prize or medal granted after the recipient's death * Posthumous publication, publishing of creative work after the author's death * Posthumous (album), ''Posthumous'' (album), by Warne Marsh, 1 ...
) ;Academic recognition * Foreign Honorary Member of the
National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...
(United States, 1959),
American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...
(1960), Bulgarian Academy of Sciences (1961); a foreign member of the
Polish Academy of Sciences The Polish Academy of Sciences (, PAN) is a Polish state-sponsored institution of higher learning. Headquartered in Warsaw, it is responsible for spearheading the development of science across the country by a society of distinguished scholars a ...
(1962), GDR Academy of Sciences (1966), Hungarian Academy of Sciences (1970), Academy of Sciences in Heidelberg (1968), Czechoslovak Academy of Sciences (1980), Indian Academy of Sciences (1983), Mongolian Academy of Sciences (1983) * Honorary Doctor of the University of Allahabad, India (1958),
Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...
(East Germany, 1960),
Chicago Chicago is the List of municipalities in Illinois, most populous city in the U.S. state of Illinois and in the Midwestern United States. With a population of 2,746,388, as of the 2020 United States census, 2020 census, it is the List of Unite ...
(USA, 1967),
Turin Turin ( , ; ; , then ) is a city and an important business and cultural centre in northern Italy. It is the capital city of Piedmont and of the Metropolitan City of Turin, and was the first Italian capital from 1861 to 1865. The city is main ...
(Italy, 1969), Wroclaw (Poland, 1970),
Bucharest Bucharest ( , ; ) is the capital and largest city of Romania. The metropolis stands on the River Dâmbovița (river), Dâmbovița in south-eastern Romania. Its population is officially estimated at 1.76 million residents within a greater Buc ...
(Romania, 1971),
Helsinki Helsinki () is the Capital city, capital and most populous List of cities and towns in Finland, city in Finland. It is on the shore of the Gulf of Finland and is the seat of southern Finland's Uusimaa region. About people live in the municipali ...
(Finland, 1973), Ulan Bator (Mongolia, 1977),
Warsaw Warsaw, officially the Capital City of Warsaw, is the capital and List of cities and towns in Poland, largest city of Poland. The metropolis stands on the Vistula, River Vistula in east-central Poland. Its population is officially estimated at ...
(Poland, 1977) ;Memory Institutions, awards and locations have been named in Bogolyubov's memory: * N.N. Bogolyubov Institute for Theoretical Problems of Microphysics (
Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...
) * Bogoliubov Institute of Theoretical Physics National Academy of Sciences of Ukraine (Kyiv, Ukraine) * Bogoliubov Laboratory of Theoretical Physics ( Joint Institute for Nuclear Research, Dubna) * Bogolyubov Prize ( Joint Institute for Nuclear Research) for scientists with outstanding contribution to theoretical physics and applied mathematics * Bogolyubov Prize for young scientists (Joint Institute for Nuclear Research) * Bogolyubov Prize ( National Academy of Sciences of Ukraine) for scientists with outstanding contribution to theoretical physics and applied mathematics * Bogolyubov Gold Medal (
Russian Academy of Sciences The Russian Academy of Sciences (RAS; ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such ...
) * Bust of Academician NN Bogolyubov (Nizhny Novgorod) * Bust of Academician NN Bogolyubov (Dubna) * ''Bogolyubov prospect'' () (Dubna's central street) * Commemorative plaque at the entrance of the Physics Department of Moscow State University In 2009, the
centenary A centennial, or centenary in British English, is a 100th anniversary or otherwise relates to a century. Notable events Notable centennial events at a national or world-level include: * Centennial Exhibition, 1876, Philadelphia, Pennsylvania. ...
of Nikolay Bogolyubov's birth was celebrated with two conferences in Russia and Ukraine:
International Bogolyubov Conference: Problems of Theoretical and Mathematical Physics
21–27 August, Moscow-Dubna, Russia.
Bogolyubov Kyiv Conference: Modern Problems of Theoretical and Mathematical Physics
15–18 September,
Kyiv Kyiv, also Kiev, is the capital and most populous List of cities in Ukraine, city of Ukraine. Located in the north-central part of the country, it straddles both sides of the Dnieper, Dnieper River. As of 1 January 2022, its population was 2, ...
, Ukraine.


Research

Fundamental works of Nikolay Bogolyubov 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

*In 1932–1943, in the early stage of his career, he worked in collaboration with Nikolay Krylov on mathematical problems of nonlinear mechanics and developed mathematical methods for asymptotic integration of non-linear differential equations. He also applied these methods to problems of statistical mechanics. *In 1937, jointly with Nikolay Krylov he proved the Krylov–Bogolyubov theorems. *In 1956, at the International Conference on Theoretical Physics in Seattle, USA (September, 1956), he presented the formulation and the first proof of the edge-of-the-wedge theorem. This theorem in the theory of functions of several complex variables has important implications to the dispersion relations in elementary particle physics.


Statistical mechanics

*1939 Jointly with Nikolay Krylov gave the first consistent microscopic derivation of the
Fokker–Planck equation In statistical mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of the velocity of a particle under the influence of drag (physi ...
in the single scheme of classical and quantum mechanics. *1945 Suggested the idea of hierarchy of relaxation times, which is significant for statistical theory of
irreversible process In thermodynamics, an irreversible process is a thermodynamic processes, process that cannot be undone. All complex natural processes are irreversible, although a phase transition at the coexistence temperature (e.g. melting of ice cubes in wate ...
es. *1946 Developed a general method for a microscopic derivation of kinetic equations for classical systems. The method was based on the hierarchy of equations for multi-particle distribution functions known now as Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy. *1947 Jointly with K. P. Gurov extended this method to the derivation of kinetic equations for quantum systems on the basis of the quantum BBGKY hierarchy. *1947—1948 Introduced kinetic equations in the theory of
superfluidity Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortices that continue to rotate indefinitely. Superfluidity occurs in two ...
, computed the excitation spectrum for a weakly imperfect Bose gas, showed that this spectrum has the same properties as spectrum of Helium II, and used this analogy for a theoretical description of superfluidity of Helium II. *1958 Formulated a microscopic theory of
superconductivity Superconductivity is a set of physical properties observed in superconductors: materials where Electrical resistance and conductance, electrical resistance vanishes and Magnetic field, magnetic fields are expelled from the material. Unlike an ord ...
and established an analogy between superconductivity and superfluidity phenomena; this contribution was discussed in details in the book ''A New Method in the Theory of Superconductivity'' (co-authors V. V. Tolmachev and D. V. Shirkov, Moscow, Academy of Sciences Press, 1958).


Quantum theory

*1955 Developed an axiomatic theory for the scattering matrix (''S''-matrix) in quantum field theory and introduced the causality condition for ''S''-matrix in terms of variational derivatives. *1955 Jointly with Dmitry Shirkov developed the
renormalization group In theoretical physics, the renormalization group (RG) is a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying p ...
method. *1955 Jointly with Ostap Parasyuk proved the theorem on the finiteness and uniqueness (for renormalizable theories) of the scattering matrix in any order of perturbation theory ( Bogoliubov-Parasyuk theorem) and developed a procedure ( R-operation) for a practical subtraction of singularities in quantum field theory. *1965 Jointly with Boris Struminsky and Albert Tavkhelidze and independently of Moo-Young Han, Yoichiro Nambu and Oscar W. Greenberg suggested a triplet
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...
model and introduced a new quantum degree of freedom (later called as color charge) for quarks. *Suggested a first proof of dispersion relations in quantum field theory.


Publications


Books

Mathematics and Non-linear Mechanics: # N. M. Krylov and N. N. Bogoliubov (1934): ''On various formal expansions of non-linear mechanics''. Kyiv, Izdat. Zagal'noukr. Akad. Nauk. # N. M. Krylov and N. N. Bogoliubov (1947): ''Introduction to Nonlinear Mechanics.'' Princeton, Princeton University Press. #N. N. Bogoliubov, Y. A. Mitropolsky (1961): ''Asymptotic Methods in the Theory of Non-Linear Oscillations''. New York, Gordon and Breach. Statistical Mechanics: #N. N. Bogoliubov (1945): ''On Some Statistical Methods in Mathematical Physics''. Kyiv . #N. N. Bogoliubov, V. V. Tolmachev, D. V. Shirkov (1959): ''A New Method in the Theory of Superconductivity''. New York, Consultants Bureau. #N. N. Bogoliubov (1960): ''Problems of Dynamic Theory in Statistical Physics''. Oak Ridge, Tenn., Technical Information Service. #N. N. Bogoliubov (1967—1970): ''Lectures on Quantum Statistics. Problems of Statistical Mechanics of Quantum Systems''. New York, Gordon and Breach. #N. N. Bogolubov and N. N. Bogolubov, Jnr. (1992): ''Introduction to Quantum Statistical Mechanics''. Gordon and Breach. . Quantum Field Theory: #N. N. Bogoliubov, B. V. Medvedev, M. K. Polivanov (1958): ''Problems in the Theory of Dispersion Relations''. Institute for Advanced Study, Princeton. #N. N. Bogoliubov, D. V. Shirkov (1959): ''The Theory of Quantized Fields''. New York, Interscience. The first text-book on the
renormalization group In theoretical physics, the renormalization group (RG) is a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying p ...
theory. #N. N. Bogoliubov, A. A. Logunov and I. T. Todorov (1975): ''Introduction to Axiomatic Quantum Field Theory''. Reading, Mass.: W. A. Benjamin, Advanced Book Program. . . #N. N. Bogoliubov, D. V. Shirkov (1980): ''Introduction to the Theory of Quantized Field''. John Wiley & Sons Inc; 3rd edition. . . #N. N. Bogoliubov, D. V. Shirkov (1982): ''Quantum Fields''. Benjamin-Cummings Pub. Co., . #N. N. Bogoliubov, A. A. Logunov, A. I. Oksak, I. T. Todorov (1990): ''General Principles of Quantum Field Theory''. Dordrecht olland Boston, Kluwer Academic Publishers. . . ;Selected works #N. N. Bogoliubov, ''Selected Works. Part I. Dynamical Theory.'' Gordon and Breach, New York, 1990. , . #N. N. Bogoliubov, ''Selected Works. Part II. Quantum and Classical Statistical Mechanics.'' Gordon and Breach, New York, 1991. . #N. N. Bogoliubov, ''Selected Works. Part III. Nonlinear Mechanics and Pure Mathematics.'' Gordon and Breach, Amsterdam, 1995. . #N. N. Bogoliubov, ''Selected Works. Part IV. Quantum Field Theory.'' Gordon and Breach, Amsterdam, 1995. , .


Selected papers

* *"On Question about Superfluidity Condition in the Nuclear Matter Theory" (in Russian), Doklady Akademii Nauk USSR, 119, 52, 1958. * "On One Variational Principle in Many Body Problem" (in Russian), Doklady Akademii Nauk USSR, 119, N2, 244, 1959. *"On Compensation Principle in the Method of Self conformed Field" (in Russian), Uspekhi Fizicheskhih Nauk, 67, N4, 549, 1959. *"The Quasi-averages in Problems of Statistical Mechanics" (in Russian), Preprint D-781, JINR, Dubna, 1961. *"On the Hydrodynamics of a Superfluiding" (in Russian), Preprint P-1395, JINR, Dubna, 1963.


See also

* Bogoliubov approximation * Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy * Bogoliubov causality condition * Bogolyubov's edge-of-the-wedge theorem * Bogolyubov inequality * Bogoliubov inner product * Bogolyubov's lemma * Bogoliubov-Parasyuk theorem * Bogoliubov quasiparticle * Bogoliubov transformation * Describing function method * Goldstone boson * Krylov-Bogoliubov averaging method * Krylov-Bogolyubov theorem * Landau pole * Peierls–Bogoliubov inequality * Quantum triviality


Notes


References


Further reading

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External links


Bogolyubov Institute for Theoretical Physics
of the National Academy of Sciences of Ukraine.
Bogolyubov Institute for Theoretical Problems of Microphysics
at the Lomonosov Moscow State University, Russia.
Bogolyubov Laboratory of Theoretical Physics
at the Joint Institute for Nuclear Research, Dubna, Russia.
Department of Theoretical Physics
in the Steklov Mathematical Institute, Moscow, Russia (created by Nikolay Bogolyubov).

(in Russian). *
Author profile
in the database zbMATH {{DEFAULTSORT:Bogolyubov, Nikolay 1909 births 1992 deaths Fellows of the American Academy of Arts and Sciences Foreign associates of the National Academy of Sciences Foreign fellows of the Indian National Science Academy Foreign members of the Bulgarian Academy of Sciences Full Members of the Russian Academy of Sciences Full Members of the USSR Academy of Sciences Members of the German Academy of Sciences at Berlin Members of the National Academy of Sciences of Ukraine Academic staff of Moscow State University Taras Shevchenko National University of Kyiv alumni Academic staff of the Taras Shevchenko National University of Kyiv Seventh convocation members of the Soviet of the Union Eighth convocation members of the Soviet of the Union Ninth convocation members of the Soviet of the Union Tenth convocation members of the Soviet of the Union Eleventh convocation members of the Soviet of the Union Heroes of Socialist Labour Recipients of the Stalin Prize Recipients of the Lenin Prize Recipients of the Lomonosov Gold Medal Recipients of the Order of Lenin Recipients of the Order of the Red Banner of Labour Recipients of the USSR State Prize Winners of the Max Planck Medal Control theorists Mathematical physicists Quantum physicists Soviet physicists Soviet mathematicians Soviet inventors Theoretical physicists Superfluidity Burials at Novodevichy Cemetery Recipients of Franklin Medal Russian scientists