Nikolai Nikolayevich Bogolyubov (Jr.)
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Інститут фізики конденсованих систем НАН України
2010
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| Назва видання: | Condensed Matter Physics |
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| Цитувати: | Nikolai Nikolayevich Bogolyubov (Jr.) / A. Prykarpatsky, D. Sankovich // Condensed Matter Physics. — 2010. — Т. 13, № 4. — С. 40101:1-4. — Бібліогр.: 21 назв. — англ. |
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irk-123456789-321162012-04-10T12:09:22Z Nikolai Nikolayevich Bogolyubov (Jr.) Prykarpatsky, A. Sankovich, D. Foreword 2010 Article Nikolai Nikolayevich Bogolyubov (Jr.) / A. Prykarpatsky, D. Sankovich // Condensed Matter Physics. — 2010. — Т. 13, № 4. — С. 40101:1-4. — Бібліогр.: 21 назв. — англ. 1607-324X http://dspace.nbuv.gov.ua/handle/123456789/32116 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Foreword Foreword |
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Foreword Foreword Prykarpatsky, A. Sankovich, D. Nikolai Nikolayevich Bogolyubov (Jr.) Condensed Matter Physics |
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Prykarpatsky, A. Sankovich, D. |
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Prykarpatsky, A. Sankovich, D. |
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Prykarpatsky, A. |
| title |
Nikolai Nikolayevich Bogolyubov (Jr.) |
| title_short |
Nikolai Nikolayevich Bogolyubov (Jr.) |
| title_full |
Nikolai Nikolayevich Bogolyubov (Jr.) |
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Nikolai Nikolayevich Bogolyubov (Jr.) |
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Nikolai Nikolayevich Bogolyubov (Jr.) |
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nikolai nikolayevich bogolyubov (jr.) |
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Інститут фізики конденсованих систем НАН України |
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2010 |
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Foreword |
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http://dspace.nbuv.gov.ua/handle/123456789/32116 |
| citation_txt |
Nikolai Nikolayevich Bogolyubov (Jr.) / A. Prykarpatsky, D. Sankovich // Condensed Matter Physics. — 2010. — Т. 13, № 4. — С. 40101:1-4. — Бібліогр.: 21 назв. — англ. |
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Condensed Matter Physics |
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Condensed Matter Physics 2010, Vol. 13, No 4, 40101: 1–4
http://www.icmp.lviv.ua/journal
Foreword
Nikolai Nikolayevich Bogolubov (Jr.)
Dedicated to 70-th Birthday Jubilee of
prominent Russian mathematician and theoret-
ical physicist Nikolai N. Bogolubov (Jr.)
Nikolai N. Bogolubov (Jr.) was born on
March 7, 1940 in Kyiv, Ukraine, and moved
to Moscow jointly with his parents in 1952. In
1963 he graduated from the Physics Depart-
ment of M. Lomonosov Moscow State Univer-
sity with major in theoretical physics.
N. Bogolubov (Jr.) began his scientific ac-
tivities in 1962. The direction of scientific in-
terests of a young scientist was certainly de-
fined and strongly influenced by the well-known
school in theoretical and mathematical physics
of academician N. N. Bogolubov (Sr.). From
the very first steps in science N. Bogolubov
(Jr.) showed unusual analytical abilities, dili-
gence and such an important quality for scien-
tist as aspiration to create an independent way
in his studies. N. Bogolubov (Jr.) was able to
find and form his own scientific style in modern theoretical and mathematical physics, to unite
around himself and to involve into active scientific work many friends and pupils, amongst whom
first of all it is necessary to mention B. Sadovnikov, A. Kurbatov, A. Shumovsky, J. Brankov,
D. Sankovich, A. Prykarpatsky, A. Kireev, V. Plechko, A. Soldatov, A. Kazaryan. Being initially
interested in mathematical properties of nonlinear dynamical systems, N. Bogolubov (Jr.) de-
fended his Ph.D. devoted to some mathematical problems of weakly perturbed evolution equations
of mathematical physics and their applications. The obtained experience in mathematical studies
was very beneficial for N. Bogolubov (Jr.) since soon he started to study very interesting math-
ematical problems of quantum statistical mechanics related with rigorous proofs of the results
obtained by means of the well known N. Bogolubov’s (Sr.) method of approximating Hamilto-
nian for models of BCS-types. These results were accumulated in the first N. Bogolubov’s (Jr.)
monograph [1] “Method of studying model Hamiltonians” published in 1974, and which were also
successfully defended as his Doctor of Mathematical and Physical Sciences thesis in 1971. In the
meanwhile N. Bogolubov (Jr.) was nominated the head of Statistical Mechanics division at the
Laboratory of Theoretical Physics of Joint Institute for Nuclear Research, Dubna, and became a
leading researcher at the V. A. Steklov Mathematical Institute of the Russian Academy of Sciences,
where he is working permanently up to the present.
Actively working at modern problems of quantum statistical physics N. Bogolubov (Jr.) jointly
with his colleagues and disciples published new scientific monographs [2, 3]. In the collective mono-
graph [3], the method of approximating Hamiltonian obtained a new trend of development to which
strong proofs were constructed for a wide class of model systems. N. Bogolubov’s (Jr.) works on
the approximating Hamiltonian method have greatly contributed to the development of rigorous
methods of statistical mechanics. The developed technique of majorizing estimates of differences
subject to the corresponding thermodynamic quantities for the model and the approximating sys-
tem makes it possible to get rid of many difficulties which, as was first noted by Bogolubov (Sr.),
c© A. Prykarpatsky, D. Sankovich 40101-1
http://www.icmp.lviv.ua/journal
had been severely bounding the applications of statistical mechanics.
The work of N. Bogolubov (Jr.) [1] stimulated a further development of the approximating
Hamiltonian method in the modern quantum theory of many-particle systems. Originally devised
for solving statistical physics model problems connected with fermion operators, owing to the
results of Bogolubov (Jr.), this method has naturally found many applications for a wider range
of problems. So, in the well-known work by Ginibre [4], an essential part of his results is based on
the N. Bogolubov’s (Jr.) remarkable work [5]. Recently the approximating Hamiltonian method
has been also applied to the rigorous research of some bose-systems [6, 7].
An important contribution to the development of foundations of modern mathematical physics
was made by monograph [8] written jointly with with N. Bogolubov (Sr.). In this work the Au-
thors managed to unveil a deep physical meaning underlying the second quantization method,
owing to which a so important notion as “quasi-particle” acquired its modern status and physical
argumentation. For the first time in the world literature there was shown a way of formulating a
classical analogue of the second quantization method. As concerns the uniform study of quantum
and classical problems, the potential underlying this method is far from being exhausted.
N. Bogolubov’s (Jr.) scientific works on the polaron theory are extremely valuable [9, 10]. In
1954 N. Bogolubov (Sr.) [11] developed an approach that makes it possible to express some physical
observables as continual path integrals. This approach was based on the representation of suitable
Green functions in terms of vacuum expectations of chronological products. The corresponding
operation of averaging over the boson vacuum was interpreted as a functional integral. In 1981
N. Bogolubov (Sr.) and N. Bogolubov (Jr.) [9] developed this construction within the framework
of quantum statistical mechanics. A measure that arises in this approach is the Gaussian measure
defined in an appropriate space of continuous functions. The Gibbs equilibrium averages of the
operator chronological products are, respectively, expressed as functional integrals with respect
to this measure. Subsequently, some important mathematical problems of functional integration
with respect to this Bogolubov’s measure were considered in detail in [12]. It was found that the
Bogolubov-Bogolubov (Jr.) approach is highly beneficial in quantum statistical mechanics side
by side with the Feynman functional integration. Unlike the Feynman approach, the Bogolubov-
Bogolubov (Jr.) approach is based on the well defined Gaussian measure. (It is worth mentioning
that the natural analogue of the Wiener measure with complex variance parameter is not a count-
ably additive complex measure).
The next topic of studies related with the integrability of nonlinear quantum and classical
dynamical systems by means of the new and very powerful inverse spectral transform method
[13], was initiated by N. Bogolubov (Jr.) in 1977 jointly with his collaborators from Lviv and
Kyiv, A. Prykarpatsky and V. Samoylenko. These investigations were first started in Moscow and
Leningrad by prominent Soviet scientists academicians V. Zakharov, S. Novikov and L. Faddeev
jointly with their collaborators, and in Kharkiv and Kyiv by academicians V. Marchenko and
O. Parasyuk with his very talented disciple P. Holod. Very soon their results were profoundly
substantiated by members of this N. Bogolubov’s (Jr.) Ukrainian group and applied to many
other important problems of mathematical and quantum statistical physics. In particular, there
was devised a very powerful direct gradient-holonomic algorithm [13–15] for an analytical study
of the so-called Lax type integrability of a wide class of nonlinear differential and differential-
difference dynamical systems on functional and operator manifolds. As concerns the Lax type
integrable nonlinear quantum mechanical models, N. Bogolubov (Jr.) jointly with his disciple
A. Prykarpatsky proposed a new quantum many-particle Schrödinger type dynamical system on
the real axis with a combined (δ + iδ′)-interparticle potential. They also proved its both classical
and quantum Lax type integrability and analyzed its quantum statistical mechanical properties by
means of the Quantum Inverse Scattering Transform [14], devised by the Leningrad research group
of L. Faddeev. A part of these results was published by N. Bogolubov (Jr.) in 1987 in monograph
[16], written jointly with his Ukrainian collaborators. Developing his former research on operator
approaches to the study of quantum statistical many-body problems, N. Bogolubov (Jr.) jointly
with his disciple A. Prykarpatsky started the investigation of the old problem, posed many years
ago by N. Bogolubov (Sr.), and consisting in constructing a rigorous mathematical theory of the
40101-2
Nikolai Nikolayevich Bogolubov (Jr.)
Bogolubov’s generating functional for many-particle distribution functions both in classical and
quantum cases. This problem was very uniquely and completely solved [17] by introducing into
the field such mathematical tools as quantum Lie algebras of currents and their representations in
the generalized Hilbert-Fock type spaces. Moreover, making use of some results from the spectral
theory of operators, N. Bogolubov (Jr.) jointly with A. Prykarpatsky studied special solutions to
the Bogolubov’s generating functional equation and found new and very compact proofs of the
statistical sum expansions related with the well-known Bogolubov-Zubarev-Yukhnovsky collective
variable method. Later these results were further developed and extended in N. Bogolubov’s (Jr.)
work [18] which founded a new field in modern mathematical physics and is referred to as “quantum
mathematics”.
Here it is also worth mentioning a cycle of investigations initiated by N. Bogolubov (Jr.) jointly
with his colleagues and disciples in such fields as quantum model systems of statistical physics and
quantum optics. Part of these studies was later published both in the Lecture Notes [19], written
jointly with his collaborators A. Prykarpatsky and U. Taneri, and in books [2, 20, 21], written
jointly with A. Shumovsky, B. Sadovnikov and V. Yukalov.
One can say with satisfaction that the hard and intensive work of N. Bogolubov (Jr.) was highly
estimated by the scientific community in 1984, having elected him a corresponding member of the
USSR Academy of Sciences.
For many years the Ukrainian scientific community has been maintaining a fruitful cooperation
with N. Bogolubov (Jr.). In 1989 he was awarded the M. Krylov prize and in 2000 he got the
N. Bogolubov (Sr.) prize of the Ukrainian Academy of Sciences for his works in statistical and
mathematical physics fulfilled jointly with Ukrainian scientists.
Nikolai Bogolubov (Jr.) is worldwide recognized as a leading figure and contributor to siz-
able communities within modern mathematical and theoretical physics, in particular, in nonlinear
dynamical systems of quantum many-body theory and condensed matter physics. He has played
indispensable roles in the promotion, organization, and guidance of many prominent conferences
in these subfields. As a major voice in statistical mechanics community, N. Bogolubov (Jr.) has
gained respect from his colleagues for his integrity and wisdom, his dedication, and his clear-headed
approach to problems.
One of the characteristics which features N. Bogolubov’s (Jr.) activities is an extremely close tie
between his research work and his teaching. For many years N. Bogolubov (Jr.) keeps a professor
position at the M. Lomonosov State University in Moscow, being a Mr. and Ph.D. adviser for many
gifted students and graduates, respectively. His monograph on quantum statistical physics [8], being
translated and published abroad, is one of the best manuals on the second quantization method
in quantum statistical physics used by students worldwide. The formulation of new problems and
unexpected questions, a tendency to look at seemingly well-known things from a novel view-point
characterizes N. Bogolubov (Jr.) as a teacher, regardless of whether at the present moment he
is holding a conversation with students or with his own colleagues or disciples. He is not only a
teacher to the young. We continue to learn from him, year by year.
N. Bogolubov (Jr.) is a very open minded, good willing and extremely polite man, he knows
and likes talking of diverse scientific histories he had heard or had been himself a witness. Having
a spare time, he enjoys much to converse, to discuss, to argue with friends and colleagues. He also
likes to travel visiting historical cities and villages in Europe, Asia and other countries worldwide.
Celebrating this year his 70-th Birthday Jubilee, Nikolai N. Bogolubov (Jr.) intensively contin-
ues his scientific research in most urgent and hot fields of modern mathematical and theoretical
physics including quantum statistical mechanics and field theory, hydrodynamics, classical and
quantum electrodynamics. He remains to be full of new ideas and challenging scientific plans.
From the bottom of our hearts we congratulate Professor Nikolai N. Bogolubov (Jr.) with his
Jubilee, wishing him to stay in robust health, enjoy simple human pleasures and further success in
his scientific life for many years.
A. Prykarpatsky, D. Sankovich
40101-3
References
1. Bogolubov N.N. (Jr.), Method of Studying Model Hamiltonians. Nauka, Moscow, 1974.
2. Bogolubov N.N. (Jr.), Sadovnikov B.J., Selected Problems of Statistical Mechanics. Vysshaya Shkola,
Moscow, 1975.
3. Boglolubov N.N. (Jr.), Brankov J.G., Zagrebnov V.A., Kurbatov A.M., Tonchev N.S., Approximating
Hamiltonian Method in Statistical Physics. Bulgarian Academy of Sciences Publ., Sophia, 1981.
4. Ginibre J., Commun. Math. Phys., 1968, 8, 26–51.
5. Bogolubov N.N. (Jr.), Physica, 1966, 32, 933.
6. Pulé J.V., Zagrebnov V.A., J. Phys. A: Math. Gen., 2004, 37, 8929.
7. Bogolyubov N.N. (Jr.), Sankovich D.P., Ukr. J. Phys., 2010, 55, 104–108.
8. Bogolubov N.N., Bogolubov N.N. (Jr.), Introduction to Quantum Statistical Mechanics. Gordon and
Breach, New York, London, 1992.
9. Bogolubov N.N., Bogolubov N.N. (Jr.), Aspects of polaron theory, Report No. R17–81–65, JINR,
Dubna, 1981.
10. Bogolubov N.N., Bogolubov N.N. (Jr.), Polaron Theory. Model Problems. Gordon and Breach, New
York, London, 2000.
11. Bogolubov N.N., Dokl. Akad. Nauk SSSR, 1954, 99, 225.
12. Sankovich D.P., Bogolubov’s Functional Integral. Proc. Steklov Inst. of Math., 2005, 251, 1.
13. Prykarpatsky A.K., Mykytyuk I.V. Algebraic Integrability of Nonlinear Dynamical Systems on Mani-
folds. Classical and Quantum Aspects. Kluwer, Dordrecht, 1998.
14. Hentosh O.Ye., Prytula M.M., Prykarpatsky A.K., Differential-geometric integrability fundamentals
of nonlinear dynamical systems on functional manifolds. (The second revised edition). Lviv University
Publisher, Lviv, 2006.
15. Blackmore D., Prykarpatsky A.K., Samoylenko V.H., Nonlinear Dynamical Systems of Mathematical
Physics: Spectral and Differential-Geometric Integrability Analysis. World Scientific, N.Y., 2010.
16. Mitropolsky Yu.A., Bogolyubov N.N. (Jr.), Prikarpatskii A.K., Samoylenko V.G., Integrable Dynam-
ical Systems: Spectral and Differential-Geometric Aspects. Naukova Dumka, Kyiv, 1987.
17. Bogoliubov N.N. (Jr.), Prykarpatsky A.K. Physics of Elementary Particles and Atomique Nucleus,
1986, 17, 4, 791–827 (in Russian)
18. Bogolyubov N. (Jr.), Prykarpatsky A.K., Golenia J., Taneri U., Int. J. Theor. Phys., 2008, 47, 2882–
2897.
19. Prykarpatsky A.K., Taneri U., Bogolubov N.N. (Jr.), Quantum Field Theory with Applications to
Quantum Nonlinear Optics. World Scientific, New York, 2002.
20. Bogolubov N.N. (Jr.), Sadovnikov B.J., Shumovsky A.S., Mathematical Methods of Statistical Me-
chanical Model Systems. CRC, 1984.
21. Bogolyubov N.N. (Jr.), Shumovsky A.S., Yukalov V.I., Interaction of Electromagnetic Field with Con-
densed Matter. World Scientific, N.Y., 1990.
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