Nikolay Nikolaevich Bogolyubov (another spelling
Bogoliubov, , ; 21 August 1909,
Nizhny NovgorodNizhny Novgorod , colloquially shortened as Nizhny, is the fourth largest city in Russia, ranking after Moscow, St. Petersburg, and Novosibirsk...
— 13 February 1992,
MoscowMoscow is the capital and the largest city of Russia. It is also the largest metropolitan area in Europe, and ranks among the largest urban areas in the world. Moscow is a major political, economic, cultural, religious, financial, educational, and transportation centre of Russia and the world, a...
) was a
RussianThe Russian people are an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries....
and
UkrainianUkraine is a country in Eastern Europe. It is bordered by Russia to the east; Belarus to the north; Poland, Slovakia, and Hungary to the west; Romania and Moldova to the southwest; and the Black Sea and Sea of Azov to the south. The city of Kiev is both the capital and the largest city of...
Soviet
mathematicianA mathematician is a person whose primary area of study and/or research is the field of mathematics. Mathematicians are concerned with particular problems related to logic, space, transformations, numbers and more general ideas which encompass these concepts...
and
theoretical physicistTheoretical physics is a branch of physics which employs mathematical models and abstractions of physics in an attempt to explain natural phenomena. Its central core is mathematical physics,[Sometimes mathematical physics and theoretical physics are used synonymously to refer to the...]
known for a significant contribution to
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically described by fields or of many-body systems. It is widely used in particle physics and condensed matter physics...
, classical and quantum
statistical mechanicsStatistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force...
, and to the theory of dynamical systems; a recipient of the
Dirac PrizeThe Dirac Prize is the name of three prominent awards in the field of theoretical physics, computational chemistry, and mathematics, awarded by different organizations.- Dirac Medal of the ICTP :...
(1992).
Early life (1909-1921)
Nikolay Bogolyubov was born on 21 August 1909 in
Nizhny NovgorodNizhny Novgorod , colloquially shortened as Nizhny, is the fourth largest city in Russia, ranking after Moscow, St. Petersburg, and Novosibirsk...
,
RussiaRussia , officially known as both Russia and the Russian Federation , is a country in northern Eurasia . It is a semi-presidential republic, comprising 83 federal subjects...
, in the family of a priest of
Russian Orthodox ChurchThe Russian Orthodox Church ; or The Moscow Patriarchate , also known...
, teacher of
theologyThe term "theology" literally means the study of God, deriving from the Greek word theos, meaning 'God', and the suffix -ology from the Greek word logos meaning "discourse", "theory", or "reasoning"...
,
psychologyPsychology is an academic and applied discipline involving the systematic, and sometimes scientific, study of human or animal mental functions and behavior...
and
philosophyPhilosophy is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing these questions by its critical, generally systematic approach and its reliance on reasoned...
Nikolay Mikhailovich Bogolyubov and Ol'ga Nikolaevna, teacher of musics. The
Soviet UnionThe Union of Soviet Socialist Republics was a constitutionally socialist state that existed in Eurasia from 1922 to 1991. The name is a translation of the , tr. Soyuz Sovetskikh Sotsialisticheskikh Respublik, abbreviated СССР, SSSR. The common short name is Soviet Union, from , Sovetskiy Soyuz...
regulations issued soon after the
October RevolutionTheOctober Revolution , also known as the Soviet Revolution or Bolshevik Revolution, was a political revolution and a part of the Russian Revolution. It began with an armed insurrection in Petrograd traditionally dated to 25 October 1917 Julian calendar...
in 1917 did not allow for children of priests to obtain a good education, and in 1921 the family of Nikolay Bogolyubov moved to
KievKiev or Kyiv , is the capital and the largest city of Ukraine, located in the north central part of the country on the Dnieper River. The population as of the 2001 census was 2,611,300...
, where these regulations did not work.
Kiev (1921-?)
In Kiev Nikolay Bogolyubov began to actively study physics and mathematics. He attended research seminars in
Kiev UniversityKiev University or officially the National Taras Shevchenko University of Kyiv is the university located in Kiev, the capital of Ukraine. It was founded in 1834 as the University of Saint Vladimir, and since then it has changed its name several times...
and soon started to work under the supervision of a famous mathematician
Nikolay KrylovNikolay Mitrofanovich Krylov was a Russian mathematician known for works on interpolation, non-linear mechanics, and numerical methods for solving equations of mathematical physics.-Biography:...
. In 1924, at the age of 13, 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
Ukrainian SSRThe Ukrainian Soviet Socialist Republic or the Ukrainian SSR was one of the founders of the Soviet Union constituent republic that made up the former Soviet Union from its formation in 1922 to its abolition in 1991.-Name:...
and obtained the degree of Kandidat Nauk (
Candidat of Sciences, equivalent to Ph.D.) in 1928, at the age of 19, with the Ph.D. thesis
On direct methods of variational calculus. In 1930, at the age of 21, he obtained the degree of
Doktor naukDoktor nauk is a higher doctoral degree, the second and the highest post-graduate academic degree in the Soviet Union, Russia and in many post-Soviet states. The prerequisite is the first degree, Kandidat nauk which is informally regarded equivalent to Ph.D. degree...
(
Doctor of Sciences, equivalent to
HabilitationHabilitation is the highest academic qualification a person can achieve by their own pursuit in certain European and Asian countries. Earned after obtaining a research doctorate Habilitation is the highest academic qualification a person can achieve by their own pursuit in certain European and...
), the highest degree in the Soviet Union, which requires to make a significant independent contribution to the science after Ph.D.
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 wide 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 great scientific rise of the young Nikolai Bogolyubov began, later producing new multiple 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.
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, use of the invariant manifolds in the phase space, and applications of a single unified approach to many different problems. From a
control engineeringControl engineering or Control systems engineering is the engineering discipline that applies control theory to design systems with predictable behaviors...
point of view, the key achievement of the Kiev School was the development by Krylov and Bogolyubov of the
describing functionThe Describing function method of Krylov and Bogolyubov is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, which is the approximation of the non-linear system under investigation by a linear system that depends on the amplitude of the...
method for the analysis of nonlinear control problems.
In the period 1928—1973, Nikolay Bogolyubov worked in the
Institute for Theoretical Physics of the National Academy of Sciences of Ukraine holding the position of the Director of the institute since 1965. He lectured in the Kiev University in the period 1936—1959.
In evacuation (1941-1943)
After the
German attackOperation Barbarossa was the code name for Nazi Germany's invasion of the Soviet Union during World War II that began on 22 June 1941. Over 4.5 million troops of the Axis powers invaded the USSR along a 2,900 km front...
against the
Soviet UnionThe Union of Soviet Socialist Republics was a constitutionally socialist state that existed in Eurasia from 1922 to 1991. The name is a translation of the , tr. Soyuz Sovetskikh Sotsialisticheskikh Respublik, abbreviated СССР, SSSR. The common short name is Soviet Union, from , Sovetskiy Soyuz...
on 22 June, 1941 (beginning of the
Great Patriotic WarThe term Great Patriotic War is used in Russia and some other states of the former Soviet Union to describe their portion of the Second World War from June 22, 1941, to May 9, 1945, against Nazi Germany and its allies...
), most institutes and universities from west part of Russia were evacuated into east regions far from the battle lines. Nikolay Bogolyubov moved to
UfaUfa is the capital of the Republic of Bashkortostan, Russia Ufa is the one of the largest cities of Russia, administrative, political, economic, scientific and cultural center of the republic. Population: 1,021,500 ; 1,042,437...
, where he became Head of the Departments of Mathematical Analysis at
Ufa State Aviation Technical UniversityUfa State Aviation Technical University is a state higher school, located in Ufa, Bashkortostan, Russia. Ufa State Aviation Technical University was founded in 1932 in Rybinsk, USSR. Nowadays, Ufa State Aviation Technical University has become the one of leading higher educational institutions of...
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 November 1, 1943 he accepted a position in the Department of Theoretical Physics at the
Moscow State UniversityM. V. Lomonosov Moscow State University , for a time the Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be the oldest university in Russia and the tallest educational building in the world...
(MSU). At that time the Head of the Department was
Anatoly VlasovAnatoly Alexandrovich Vlasov was a Russian theoretical physicist prominent in the fields of statistical mechanics, kinetics, and especially in plasma physics.-Biography:...
(for a short period in 1944 the Head of the Department was
Vladimir FockVladimir Aleksandrovich Fock was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics....
). Theoretical physicists working in the department in that period included Dmitry Ivanenko,
Arsenij SokolovArsenij Alexandrovich Sokolov was a Russian theoretical physicist known for the development of synchrotron radiation theory.-Biography:...
, and other famous physicists.
In the period 1943-1946, Bogolyubov's resesarch was essentially concerned with the theory of
stochastic processIn probability theory, a stochastic process, or sometimes random process, is the counterpart to a deterministic process...
es and asymptotic methods. In his work "?" a simple example of an anharmonic oscillator evolving under the force of the form as 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 equationThe Fokker–Planck equation describes the time evolution of the probability density function of the position of a particle, and can be generalized to other observables as well....
, 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
MarkovianA Markov process, named after the Russian mathematician Andrey Markov, is a mathematical model for the random evolution of a memoryless system, that is, one for which the likelihood of a given future state, at any given moment, depends only on its present state, and not on any past states.In a...
, 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 (Moscow, 1946).
On January 26, 1953 Nikolay Bogolyubov became the Head of the Department of Theoretical Physics at MSU, after Anatoly Vlasov decided to left 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 (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 groupIn theoretical physics, renormalization group refers to a mathematical apparatus that allows one to investigate the changes of a physical system as one views it at different distance scales. In particle physics it reflects the changes in the underlying force laws as one varies the energy scale at...
, axiomatic S-matrix theory, and works on the theory of dispersion relations.
In the late 1940s and 1950s, Bogoliubov worked on the theory of
superfluidSuperfluidity is a phase of matter or description of heat capacity in which unusual effects are observed when liquids, typically of helium-4 or helium-3, overcome friction by surface interaction when at a stage at which the liquid's viscosity becomes zero...
ity and
superconductivitySuperconductivity is a phenomenon occurring in certain materials generally at very low temperatures, characterized by exactly zero electrical resistance and the exclusion of the interior magnetic field . It was discovered by Heike Kamerlingh Onnes in 1911. Like ferromagnetism and atomic spectral...
, where he developed the method of
BBGKY hierarchyIn statistical physics, the BBGKY hierarchy is a set of equations describing the dynamics of a system of a large number of interacting particles...
for a derivation of kinetic equations, formulated microscopic theory of superfluidity, and made other essential contributions. Later he worked on
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically described by fields or of many-body systems. It is widely used in particle physics and condensed matter physics...
, where introduced the
Bogoliubov transformationIn theoretical physics, the Bogoliubov transformation, named after Nikolay Bogolyubov, is a unitary transformation from a unitary representation of some canonical commutation relation algebra or canonical anticommutation relation algebra into another unitary representation, induced by an...
, formulated and proved the
Bogoliubov's edge-of-the-wedge theoremIn mathematics, Bogoliubov's edge-of-the-wedge theorem implies that holomorphic functions on two "wedges" with an "edge" in common are analytic continuations of each other provided they both give the same continuous function on the edge. It is used in quantum field theory to construct the...
and
Bogoliubov-Parasyuk theoremThe Bogoliubov-Parasyuk theorem in quantum field theory states that renormalized Green's functions and matrix elements of the scattering matrix are free of ultraviolet divergencies. Green's functions and scattering matrix are the fundamental objects in quantum field theory which determine basic...
(with Ostap Parasyuk), and obtained other significant results. In the 1960s his attention turned to the
quarkA quark is an 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 nuclei. Due to a phenomenon known as color confinement, quarks are never found in...
model of hadrons; in 1965 he was among the first scientists to study the new
quantum numberQuantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...
color chargeIn particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,...
.
In 1946, Nikolay Bogoliubow was elected as a Corresponding Member of the
USSR Academy of SciencesThe Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals.Headquartered in Moscow, the Academy is...
. In 1948, he became
AcademicianThe title Academician denotes a Full Member of an art, literary, or scientific academy.In many countries it is a honorary title."Academician" may also be a functional title and denote a full member of the National Academy of Sciences in those countries where the academy has a strong influence on...
of the National Academy of Sciences of Ukraine and in 1953 Academician of the USSR Academy of Sciences.
Dubna (1956-1992)
Since 1956, he worked in the
Joint Institute for Nuclear ResearchThe Joint Institute for Nuclear Research, JINR in Dubna, Moscow Oblast , Russia is an international research centre for nuclear sciences, involving around 5500 staff members, 1200 researchers including 1000 Ph.D.s from eighteen member states The Joint Institute for Nuclear Research, JINR in...
(JINR),
DubnaDubna is a town in Moscow Oblast, Russia, under immediate jurisdiction of Moscow Oblast. It has a status of naukograd, housing an international nuclear physics research centre , one of the largest scientific foundations in the country. It is home to MKB Raduga, a defence aerospace company...
, Russia, where he was a founder (together with Dmitry Blokhintsev) and the first director of the
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 theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically described by fields or of many-body systems. It is widely used in particle physics and condensed matter physics...
, theoretical
nuclear physicsNuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei.The most commonly known applications of nuclear physics are nuclear power and nuclear weapons, but the research has provided wider applications, including those in medicine , materials...
,
statistical physicsStatistical physics is the area of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature...
, and nonlinear mechanics. Nikolay Bogolyubov was Director of the JINR in the period 1966—1988.
Family
His son Nikolay Boglyubov (jr) is a famous theoretical physicist working in the fields of mathematical physics and statistical mechanics.
Students
Nikolay Bogoliubov was a scientific supervisor of
Yurii MitropolskiyYurii Alekseevich Mitropolskiy was a renowned Soviet, Ukrainian mathematician known for his contributions to the fields of dynamical systems and nonlinear oscillations. Yurii Mitropolskiy was a student of a theoretical physicist and mathematician Nikolay Bogolyubov.-Books:#N. N. Bogoliubov and Y....
,
Dmitry ShirkovDmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
, Selim Krein, Iosif Gihman, Tofik Mamedov,
Kirill GurovKirill Gurov was a Russian theoretical physicist working in the field of physical kinetics.-Biography:Kirill Gurov was born in Moscow, Russia, in the family of a military officer...
, Mikhail Polivanov, Naftul Polsky, Galina Biryuk,
Sergei TyablikovSergei Vladimirovich Tyablikov was a Russian theoretical physicist known for his significant contributions to statistical mechanics, solid-state physics, and for the development of the double-time Green function's formalism....
,
Dmitry ZubarevDmitry Nikolaevich Zubarev was a Russian theoretical physicist known for his contributions to statistical mechanics, non-equilibrium thermodynamics, plasma physics, theory of turbulence, and to the development of the double-time Green function's formalism.-Biography:Dmitry Zubarev was born in...
, Vladimir Kadyshevsky, and many other students. His method of teaching, based on creation of a warmth atmosphere, politeness and kindness, is famous in Russia and is known as the "Bogoliubov approach".
Awards
Nikolay Bogolyubov was a recipient of various USSR highest honors and international awards, including
- USSR State Prize
The USSR State Prize was the Soviet Union's state honour. It was established on September 9 1966. After the breakup of the Soviet Union the prize was followed up by the State Prize of the Russian Federation....
(1947, 1953, 1984)
- Lenin Prize
The Lenin Prize was one of the most prestigious awards of the USSR, presented to individuals for accomplishments relating to science, literature, arts, architecture, and technology. It was created on June 23 1925 and was awarded until 1934. During the period from 1935 to 1956, the Lenin Prize was...
(1958)
- Heineman Prize for Mathematical Physics
Dannie Heineman Prize for Mathematical Physics is an award given each year since 1959 jointly by the American Physical Society and American Institute of Physics. It is established by the Heineman Foundation in honour of Dannie Heineman...
(1966)
- Hero of Socialist Labor
Hero of Socialist Labor was an honorary title in the Soviet Union and other Warsaw Pact countries. It was the highest degree of distinction for exceptional achievements in national economy and culture...
(1969, 1979)
- Max Planck medal
The Max Planck medal is an award for extraordinary achievements in theoretical physics. It is awarded annually by the Deutsche Physikalische Gesellschaft , the world's largest organization of physicists.- List of recipients :...
(1973)
- The Lomonosov Gold Medal (1985)
- Dirac Prize
The Dirac Prize is the name of three prominent awards in the field of theoretical physics, computational chemistry, and mathematics, awarded by different organizations.- Dirac Medal of the ICTP :...
(1992)
Joint Institute for Nuclear Research awards two prizes in memory of Nikolay Bogolyubov: The Bogolyubov Prize for scientists with outstanding contribution to theoretical physics and applied mathematics and the Bogolyubov Prize for young scientists. National Academy of Sciences of Ukraine awards the Bogolyubov Prize for scientists with outstanding contribution to theoretical physics and applied mathematics.
The central street of
DubnaDubna is a town in Moscow Oblast, Russia, under immediate jurisdiction of Moscow Oblast. It has a status of naukograd, housing an international nuclear physics research centre , one of the largest scientific foundations in the country. It is home to MKB Raduga, a defence aerospace company...
is named in the memory of Nikolay Bogolyubov as
Bogolyubov prospect .
Bogolyubov year
In 2009, the 100th anniversary of the birth of Nikolay Bogolyubov will be selebrated with two conferences organized in the memory of Nikolay Bogolyubov in Russia and Ukraine:
- International Bogolyubov Conference: Problems of Theoretical and Mathematical Physics August 21-27, Moscow-Dubna, Russia.
- Bogolyubov Kyiv Conference: Modern Problems of Theoretical and Mathematical Physics September 15-18, Kiev
Kiev or Kyiv , is the capital and the largest city of Ukraine, located in the north central part of the country on the Dnieper River. The population as of the 2001 census was 2,611,300...
, Ukraine.
Research
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 causalityBogoliubov causality condition is a causality condition for scattering matrix in axiomatic quantum field theory. The condition was introduced in axiomatic quantum field theory by Nikolay Bogolyubov in 1955.-Formulation:...
, obtained important results in quantum electrodynamics, and investigated on the basis of the
edge-of-the-wedge theoremIn mathematics, Bogoliubov's edge-of-the-wedge theorem implies that holomorphic functions on two "wedges" with an "edge" in common are analytic continuations of each other provided they both give the same continuous function on the edge. It is used in quantum field theory to construct the...
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
Nikolay Mitrofanovich Krylov was a Russian mathematician known for works on interpolation, non-linear mechanics, and numerical methods for solving equations of mathematical physics.-Biography:...
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-Bogoliubov 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
Nikolay Mitrofanovich Krylov was a Russian mathematician known for works on interpolation, non-linear mechanics, and numerical methods for solving equations of mathematical physics.-Biography:...
gave the first consistent microscopic derivation of the Fokker-Planck equationThe Fokker–Planck equation describes the time evolution of the probability density function of the position of a particle, and can be generalized to other observables as well....
in the single scheme of classical and quantum mechanics.
- 1945 Suggested the idea of hierarchy of relaxation time
Relaxation time is a general concept in physics for the characteristic time in which a system changes to an equilibrium condition from a non-equilibrium condition...
s, which is significant for statistical theory of irreversible processes.
- 1946 Developed a general method for a microscopic derivation of kinetic equations for classical systems. The method was based on the hierarhy of equations for multi-particle distribution functions known now as Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy
In statistical physics, the BBGKY hierarchy is a set of equations describing the dynamics of a system of a large number of interacting particles...
.
- 1947 Jointly with K. P. Gurov
Kirill Gurov was a Russian theoretical physicist working in the field of physical kinetics.-Biography:Kirill Gurov was born in Moscow, Russia, in the family of a military officer...
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., computed the excitation spectrum for a weakly imperfect Bose gas
An ideal Bose gas is a quantum-mechanical version of a classical ideal gas. It is composed of bosons, which have an integer value of spin, and obey Bose-Einstein statistics...
, 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 phenomenon occurring in certain materials generally at very low temperatures, characterized by exactly zero electrical resistance and the exclusion of the interior magnetic field . It was discovered by Heike Kamerlingh Onnes in 1911. Like ferromagnetism and atomic spectral...
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. ShirkovDmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
, Moscow, Academy of Sciences Press, 1958).
Quantum theory
- 1955 Developed an axiomatic theory for scattering matrix (S—matrix) in quantum field theory and introduced the causality condition
Bogoliubov causality condition is a causality condition for scattering matrix in axiomatic quantum field theory. The condition was introduced in axiomatic quantum field theory by Nikolay Bogolyubov in 1955.-Formulation:...
for S—matrix in terms of variational derivatives.
- 1955 Jointly with Dmitry Shirkov
Dmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
developed the renormalization groupIn theoretical physics, renormalization group refers to a mathematical apparatus that allows one to investigate the changes of a physical system as one views it at different distance scales. In particle physics it reflects the changes in the underlying force laws as one varies the energy scale at...
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
The Bogoliubov-Parasyuk theorem in quantum field theory states that renormalized Green's functions and matrix elements of the scattering matrix are free of ultraviolet divergencies. Green's functions and scattering matrix are the fundamental objects in quantum field theory which determine basic...
) and developed a procedure (R-operation) for a practical subtraction of singularities in quantum field theory.
- 1965 Jointly with Boris Struminsky and Albert Tavchelidze and independently of Moo-Young Han
Dr. Moo-Young Han is a professor of physics at Duke University. Along with Dr. Yoichiro Nambu of the University of Chicago, Dr. Han is credited with introducing the SU symmetry of quarks, today known as the color charge...
, Yoichiro Nambuis a Japanese-born American physicist, currently a professor at the University of Chicago. Known for his contributions to the field of theoretical physics, he was awarded the Nobel Prize in Physics in 2008 for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics.-Early...
and Oscar W. GreenbergOscar Wallace Greenberg is an American physicist and professor at University of Maryland, College Park. He is famous for positing the existence of a property of subatomic particles called color charge.-Educational background:...
suggested a triplet quarkA quark is an 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 nuclei. Due to a phenomenon known as color confinement, quarks are never found in...
model and introduced a new quantum degree of freedom (later called as color chargeIn particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,...
) for quarks.[N. Bogolubov, B. Struminsky, A. Tavkhelidze. On composite models in the theory of elementary particles. JINR Preprint D-1968, Dubna]Dubna is a town in Moscow Oblast, Russia, under immediate jurisdiction of Moscow Oblast. It has a status of naukograd, housing an international nuclear physics research centre , one of the largest scientific foundations in the country. It is home to MKB Raduga, a defence aerospace company...
1965.
- Suggested a first proof of dispersion relations in quantum field theory.
See also
- Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy
In statistical physics, the BBGKY hierarchy is a set of equations describing the dynamics of a system of a large number of interacting particles...
- Bogoliubov causality condition
Bogoliubov causality condition is a causality condition for scattering matrix in axiomatic quantum field theory. The condition was introduced in axiomatic quantum field theory by Nikolay Bogolyubov in 1955.-Formulation:...
- Bogolyubov's edge-of-the-wedge theorem
- Bogoliubov inner product
The Bogoliubov inner product is a special inner product in the space of operators...
- Bogoliubov-Parasyuk theorem
The Bogoliubov-Parasyuk theorem in quantum field theory states that renormalized Green's functions and matrix elements of the scattering matrix are free of ultraviolet divergencies. Green's functions and scattering matrix are the fundamental objects in quantum field theory which determine basic...
- Bogoliubov transformation
In theoretical physics, the Bogoliubov transformation, named after Nikolay Bogolyubov, is a unitary transformation from a unitary representation of some canonical commutation relation algebra or canonical anticommutation relation algebra into another unitary representation, induced by an...
- Describing function method
The Describing function method of Krylov and Bogolyubov is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, which is the approximation of the non-linear system under investigation by a linear system that depends on the amplitude of the...
- Krylov-Bogoliubov averaging method
The Krylov–Bogolyubov averaging method is a mathematical method for approximate analysis of oscillating processes in non-linear mechanics. The method is based on the averaging principle when the exact differential equation of the motion is replaced by its averaged version...
- Krylov-Bogolyubov theorem
In mathematics, the Krylov–Bogolyubov theorem may refer to any of the two related fundamental theorems within the theory of dynamical systems...
Books
Mathematics and Non-linear Mechanics:
- N. M. Krylov
Nikolay Mitrofanovich Krylov was a Russian mathematician known for works on interpolation, non-linear mechanics, and numerical methods for solving equations of mathematical physics.-Biography:...
and N. N. Bogoliubov (1934): On various formal expansions of non-linear mechanics. Kiev, Izdat. Zagal'noukr. Akad. Nauk.
- N. M. Krylov
Nikolay Mitrofanovich Krylov was a Russian mathematician known for works on interpolation, non-linear mechanics, and numerical methods for solving equations of mathematical physics.-Biography:...
and N. N. Bogoliubov (1947): Introduction to Nonlinear Mechanics. Princeton, Princeton University Press.
- N. N. Bogoliubov, Y. A. Mitropolsky
Yurii Alekseevich Mitropolskiy was a renowned Soviet, Ukrainian mathematician known for his contributions to the fields of dynamical systems and nonlinear oscillations. Yurii Mitropolskiy was a student of a theoretical physicist and mathematician Nikolay Bogolyubov.-Books:#N. N. Bogoliubov and Y....
(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
Dmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
(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. ISBN 2881248799.
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
Dmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
(1959): The Theory of Quantized Fields. New York, Interscience. The first text-book on the renormalization groupIn theoretical physics, renormalization group refers to a mathematical apparatus that allows one to investigate the changes of a physical system as one views it at different distance scales. In particle physics it reflects the changes in the underlying force laws as one varies the energy scale at...
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. ISBN 9780805309829. ISBN 0805309829.
- N. N. Bogoliubov, D. V. Shirkov
Dmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
(1980): Introduction to the Theory of Quantized Field. John Wiley & Sons Inc; 3rd edition. ISBN 0471042234. ISBN 9780471042235.
- N. N. Bogoliubov, D. V. Shirkov
Dmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
(1982): Quantum Fields. Benjamin-Cummings Pub. Co., ISBN 0805309837.
- N. N. Bogoliubov, A. A. Logunov, A. I. Oksak, I. T. Todorov (1990): General Principles of Quantum Field Theory. Dordrecht [Holland]; Boston, Kluwer Academic Publishers. ISBN 079230540X. ISBN 978-0792305408.
Selected works
- N. N. Bogoliubov, Selected Works. Part I. Dynamical Theory. Gordon and Breach, New York, 1990. ISBN 2881247520, ISBN 9782881247521.
- N. N. Bogoliubov, Selected Works. Part II. Quantum and Classical Statistical Mechanics. Gordon and Breach, New York, 1991. ISBN 2881247687.
- N. N. Bogoliubov, Selected Works. Part III. Nonlinear Mechanics and Pure Mathematics. Gordon and Breach, Amsterdam, 1995. ISBN 2881249183.
- N. N. Bogoliubov, Selected Works. Part IV. Quantum Field Theory. Gordon and Breach, Amsterdam, 1995. ISBN 2881249264, ISBN 978-2881249266.
Selected papers
- N. N. Bogoliubov (1948). "Equations of Hydrodynamics in Statistical Mechanics" (in Ukrainian). Sbornik Trudov Instituta Matematiki AN USSR 10: 41—59.
- "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 Selfconformed 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.
Further reading
- Yu. A. Mitropolskiy
Yurii Alekseevich Mitropolskiy was a renowned Soviet, Ukrainian mathematician known for his contributions to the fields of dynamical systems and nonlinear oscillations. Yurii Mitropolskiy was a student of a theoretical physicist and mathematician Nikolay Bogolyubov.-Books:#N. N. Bogoliubov and Y....
and S. V. TyablikovSergei Vladimirovich Tyablikov was a Russian theoretical physicist known for his significant contributions to statistical mechanics, solid-state physics, and for the development of the double-time Green function's formalism....
(1959). "Nikolai Nikolaevich Bogolyubov (on the occasion of his fiftieth birthday)". Soviet Physics Uspekhi, 2(5): 765—770.
- D. N. Zubarev
Dmitry Nikolaevich Zubarev was a Russian theoretical physicist known for his contributions to statistical mechanics, non-equilibrium thermodynamics, plasma physics, theory of turbulence, and to the development of the double-time Green function's formalism.-Biography:Dmitry Zubarev was born in...
et al. (1970). "Nikolai Nikolaevich Bogolyubov (On his 60th birthday)", Soviet Physics Uspekhi, 12(4): 590—593.
- V. S. Vladimirov et al. (1969). "Nikolai Nikolaevich Bogolyubov (on the occasion of his sixtieth birthday)", Russian Math. Surveys, 24(4): 167—175.
- V. A. Ambartsumyan et al. (1979). "Nikolai Nikolaevich Bogolyubov (on his seventieth birthday)", Soviet Physics Uspekhi, 22(8): 672—676.
- P. S. Aleksandrov et al. (1979). "Nikolai Nikolaevich Bogolyubov (on his seventieth birthday)", Russian Math. Surveys, 34(5): 1—10.
- A. A. Logunov, S. P. Novikov
Sergei Petrovich Novikov is a Russian mathematician, noted for work in both algebraic topology and soliton theory.-Early life:...
, V. S. Vladimirov (1989). "Nikolai Nikolaevich Bogolyubov (on his 80th birthday)", Russian Math. Surveys, 44(5): 1—10.
- A. A. Abrikosov
Alexei Alexeyevich Abrikosov is a Russian theoretical physicist whose main contributions are in the field of condensed matter physics. He was awarded the Nobel Prize in Physics in 2003.-Biography :...
et al. (1989). "Nikolai Nikolaevich Bogolyubov (on his eightieth birthday)", Soviet Physics Uspekhi, 32(12): 1111—1112.
- L. D. Faddeev
Ludvig Dmitrievich Faddeev , also Ludwig Dmitriyevich is a Russian theoretical physicist and mathematician. He is famous for the discovery of Faddeev-Popov ghosts and Faddeev equations....
et al. (1992). "Nikolai Nikolaevich Bogolyubov (obituary)". Russian Math. Surveys 47(3): 1—3 (in English).
- D. V. Anosov (1994). "On the contribution of N.N. Bogolyubov to the theory of dynamical systems", Russian Math. Surveys, 49(5): 1—18.
- N. N. Bogolyubov (jr) and D. P. Sankovich (1994). "N. N. Bogolyubov and statistical mechanics". Russian Math. Surveys 49(5): 19—49.
- V. S. Vladimirov, V. V. Zharinov, A. G. Sergeev (1994). "Bogolyubov's “edge of the wedge” theorem, its development and applications", Russian Math. Surveys, 49(5): 51—65.
- O. I. Zav'yalov (1994). "Bogolyubov's R-operation and the Bogolyubov-Parasyuk theorem", Russian Math. Surveys, 49(5): 67—76.
- B. M. Levitan (1994). "On the work of Nikolai Nikolaevich Bogolyubov in the theory of almost periodic functions", Russian Math. Surveys, 49(5): 77—88.
- B. V. Medvedev (1994). "N.N. Bogolyubov and the scattering matrix", Russian Math. Surveys, 49(5): 89—108.
- A. M. Samoilenko (1994). "N.N. Bogolyubov and non-linear mechanics", Russian Math. Surveys, 49(5): 109—154.
- D. V. Shirkov
Dmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
(1994). "The Bogoliubov renormalization group". Russian Math. Surveys 49(5): 155—176.
- V. S. Vladimirov (2001). "N. N. Bogoliubov and mathematics". Russian Math. Surveys 56(3): 607—613.
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
M. V. Lomonosov Moscow State University , for a time the Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be the oldest university in Russia and the tallest educational building in the world...
, Russia.
- Bogolyubov Laboratory of Theoretical Physics at the Joint Institute for Nuclear Research
The Joint Institute for Nuclear Research, JINR in Dubna, Moscow Oblast , Russia is an international research centre for nuclear sciences, involving around 5500 staff members, 1200 researchers including 1000 Ph.D.s from eighteen member states The Joint Institute for Nuclear Research, JINR in...
, Dubna, Russia.
- Department of Theoretical Physics in the Steklov Mathematical Institute, Moscow, Russia (created by Nikolay Bogolyubov).
- The role of Nikolay Bogoliubov in Dubna's Russian Orthodox Christian church (in Russian).