Столетие концепции конденсата Бозе-Эйнштейна и полвека экспериментов ОИЯИ по наблюдению конденсата в сверхтекучем <sup>4</sup>Не (He II)

Дополнительно

Прислана: 02.10.2025; Принята: 13.10.2025; Опубликовано 07.11.2025; Обновлена 26.11.2025;
Просмотры: 302; Загружено: 62

Как цитировать

В. А. Загребнов. "A century of the Bose–Einstein condensation concept and half a century of the JINR experiments for observation of condensate in superfluid 4He (He II)" Natural Sci. Rev. 2 100504 (2025)
https://doi.org/10.54546/NaturalSciRev.100504
В. А. Загребнов1,a
  • 1Математический институт Марселя – Национальный Центр Научных Исследований, Университет Экс-Марсель, кампус Сен–Шарль, 3, площадь Виктора Гюго, корпус 19, 13331, Марсель – 3, Франция
  • aValentin.Zagrebnov@univ-amu.fr
DOI: 10.54546/NaturalSciRev.100504
Ключевые слова: статистика и конденсат Бозе-Эйнштейна, обычные и необычные конденсации, обобщённые конденсации, теория сверхтекучести Боголюбова, глубоко-неупругое рассеяние нейтронов, конденсат Бозе-Эйнштейна в жидком гелии-4, ОИЯИ (Дубна)
Категории: Физика , Физика конденсированного состояния (теория) , Физика конденсированного состояния (эксперимент) , Исторические / юбилейные обзоры
PDF (Английский)

Аннотация

Данный краткий обзор посвящён празднованию двух важнейших событий в квантовой физике: появлению концепции о конденсации Бозе-Эйнштейна (1925) и её экспериментальному подтверждению, которое установило, что конденсация действительно существует и возникает в жидком 4Не одновременно с появлением сверхтекучести ниже температуры λ-точки (1975).

Оба эти события тесно связаны с теорией сверхтекучести Н. Н. Боголюбова (1947), поскольку ключевой гипотезой этой теории является наличие конденсата в системе взаимодействующих бозонов. Таким образом, эксперименты, начатые в ОИЯИ (Дубна), подтвердили в 1975 году предсказание теории Боголюбова о том, что сверхтекучесть жидкого 4Не (He II) должна возникать одновременно с конденсатом Бозе-Эйнштейна.

Исправлено:
13 ноября 2025 (подписи к рисункам 1 и 2 были изменены)
26 ноября 2025 (были внесены изменения в формулы (53) и (55))

Поддерживающие организации

First of all I am thankful to Irina Aref’eva and Igor Volovich for discussions of the topics aswell as opportuneness and relavence of this article. They convinced me that thisanniversaryrecallabout jubilee of the Bose–Einstein condensation (1925), as well as about its observationin deep-inelastic neutron scattering experiments involving superfluid4He (JINR-Dubna, 1975),may be of interest to readers.During my recent visit to JINR’s BLTP (May–July 2025), I had useful discussions on dif-ferent aspects of the Bose–Einstein condensation with Alexander Povolotsky. My gratitude isowed to him for his attention and generous hospitality.I am also indebted to Viktor Aksenov, Zbigniew Strycharski and Efim Dynin for usefuldiscussions, suggestions and for help with references, as well as with collection of some rarepublications.Finally, I am very thankful to Joseph Pul ́e, one of the authors of the concept ofgeneralisedBose–Einstein condensation, for his useful remarks and a number of important suggestions.

Библиографические ссылки

[1] A. Einstein, Quantentheorie des einatomigen idealen Gases, Sitzungsberichte der PreussischenAkademie der Wissenschaften I (1925) 3–14.

[2] F. London, On the Bose–Einstein condensation, Physical Review 54 (1938) 947–954.

[3] E. Schrödinger, Quantisierung als Eigenwertproblem — Erste Mitteilung, Annalen der Physik 79(1926) 361–376.

[4] M. Planck, Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum, Verhandlungender Deutschen Physikalischen Gesellschaft 2 (1900) 237–246.

[5] A. Einstein, ̈Uber einen die Erzeugung und Verwandlung des Lichts betreffenden heuristischen Gesichtspunkt, Annalen der Physik 322 (1905) 132–148.

[6] I. A. Kvasnikov, Thermodynamics and Statistical Physics: Theory of Equilibrium Systems, Izdatelstvo MGU, Moscow, 1991.

[7] A. Einstein, Strahlungs-emission und -absorption nach der Quantentheorie, Verhandlungen der Deutschen Physikalischen Gesellschaft 18 (1916) 318–323.

[8] A. H. Compton, A Quantum Theory of the Scattering of X-Rays by Light Elements, The Physical Review (Second Series) 25 (5) (1923) 483–502.

[9] Gilbert N. Lewis, The conservation of photons, Nature 118 (2981) (1926) 874–875.

[10] S. N. Bose, Planck’s Gesetz und Lichtquantenhypothese, Zeitschrift für Physik 26 (1924) 168–171.S. N. Bose, The Man and His Work, Part 1: Collected Scientific Papers / Eds. C. K. Majumdar et al., S. N. Bose National Centre for Basic Science, Calcutta, 1994; Part II: Life, Lectures and Addresses, Miscellaneous Pieces, https://newweb.bose.res.in/Prof.S.N.Bose-Archive/BoseCentenaryPublications.

[11] M. Planck, The Theory of Heat Radiation, P. Blakiston’s Son and Co., Philadelphia, PA, 1914.

[12] A. Einstein, Quantentheorie des einatomigen idealen Gases, Sitzungsberichte der Preussischen Akademie der Wissenschaften XXII (1924) 261–267.

[13] I. A. Kvasnikov, Thermodynamics and Statistical Physics, Vol. 4: Quantum Statistics, IzdatelstvoURSS, Moscow, 2010.

[14] G. E. Uhlenbeck and L. Gropper, The equation of state of a non-ideal Einstein–Bose or Fermi–Dirac gas, Physical Review 41 (1932) 79–90.

[15] G. E. Uhlenbeck, Over statistische methoden in de theorie der quanta, Dissertation, Leiden,1927.

[16] B. Kahn and G. E. Uhlenbeck, On the theory of condensation, Physica 5 (1938) 399–415.

[17] P. Kapitza, Viscosity of liquid helium below theλ-point, Nature 141 (1938) 74.

[18] J. F. Allen and A. D. Misener, Flow of liquid helium II, Nature 141 (1938) 75.

[19] M. van den Berg, On boson condensation into an infinite number of low-lying levels, J. Math.Phys. 23 (1982) 1159–1161.

[20] M. van den Berg and J. T. Lewis, On generalized condensation in the free boson gas, Physica A110 (1982) 550–564.

[21] M. van den Berg, On condensation in the free-bosons gas and the spectrum of the Laplacian, J.Stat. Phys. 31 (1983) 623–637.[22] M. van den Berg, J. T. Lewis and J. V. Pul`e, A general theory of Bose–Einstein condensation,Helv. Phys. Acta 59 (1986) 1271–1288.

[23] M. van den Berg, J. T. Lewis and J. V. Pul`e, The large deviation principle and some models ofan interacting boson gas, Communications in Mathematical Physics 118 (1988) 61–85.

[24] M. van den Berg, T. C. Dorlas, J. T. Lewis and J. V. Pul`e, The pressure in the Huang–Yang–Luttinger model of an interacting boson gas, Communications in Mathematical Physics 128(1990) 231–245.[25] V. A. Zagrebnov and J.-B. Bru, The Bogoliubov model of weakly imperfect Bose gas, PhysicsReports 350 (2001) 291–434.

[26] R. M. Ziff, G. E. Uhlenbeck and M. Kac, The ideal Bose–Einstein gas, revisited, Physics ReportsC 32 (1977) 169–248.

[27] A. F. Verbeure, Many-Body Boson Systems: Half a Century Later, Springer-Verlag, Heidelberg,2011.

[28] K. Huang, C. N. Yang and J. M. Luttinger, Imperfect Bose gas with hard-sphere interactions,Physical Review 105 (1957) 776–784.

[29] J.-B. Bru and V. A. Zagrebnov, Exact phase diagram of the Bogoliubov weakly imperfect Bosegas, Physics Letters A 244 (1998) 371–376.

[30] M. Beau and V. A. Zagrebnov, The second critical density and anisotropic generalised conden-sation, Condensed Matter Physics 13 (2) (2010) 23003: 1–10.

[31] R. Seiringer and D. Ueltschi, Rigorous upper bound on the critical temperature of dilute Bosegases, Physical Review B 80 (2009) 014502.

[32] V. Betz and D. Ueltschi, Critical temperature of dilute Bose gases, Physical Review A 81 (2010)023611

[33] J.-B. Bru and V. A. Zagrebnov, Quantum interpretation of thermodynamic behaviour of theBogoliubov weakly imperfect Bose gas, Physics Letters A 247 (1998) 37–41.

[34] V. A. Zagrebnov, Non-conventional dynamical Bose condensation, Physics of Particles and Nu-clei, 52 (2) (2021) 202–238.

[35] D. J. Thouless, The Quantum Mechanics of Many Body Systems, Academic Press, New York,1961.

[36] T. C. Dorlas, J. T. Lewis and J. V. Pul`e, The full diagonal model of a Bose gas, Communicationsin Mathematical Physics 156 (1993) 37–65.

[37] J.-B. Bru and V. A. Zagrebnov, Exact solution of the Bogoliubov Hamiltonian for weakly im-perfect Bose gas, Journal of Physics A: Mathematical and General 31 (1998) 9377–9404.

[38] J.-B. Bru and V. A. Zagrebnov, On condensations in the Bogoliubov weakly imperfect Bose gas,Journal of Statistical Physics 99 (2000) 1297–1338.

[39] M. van den Berg, J. T. Lewis and Ph. de Smedt, Condensation in the imperfect boson gas,Journal of Statistical Physics 37 (1984) 697–707.

[40] J. Lauwers, A. Verbeure and V. A. Zagrebnov, Bose–Einstein condensation for homogeneousinteracting systems with a one-particle spectral gap, Journal of Statistical Physics 112 (2003)397–420.

[41] V. B. Priezzhev, Quasicristal model of liquid helium I (ground state), Acta Physica Polonica A45 (1974) 343–358.

[42] V. B. Priezzhev, Quasicristal model of liquid helium I (collective excitations), Acta PhysicaPolonica A 45 (1974) 359–369.

[43] N. N. Bogoliubov, About the theory of superfluidity, Izvestiya Akademii Nauk SSSR 11 (1947)77–90.

[44] N. N. Bogoliubov, On the theory of superfluidity, Journal of Physics USSR 11 (1947) 23–32.

[45] N. N. Bogoliubov, Energy levels of the imperfect Bose–Einstein gas, Bulletin of Moscow StateUniversity 7 (1947) 43–56.

[46] V. A. Zagrebnov, Phonon–phonon interaction in liquid helium, Moscow University Physics Bul-letin 26 (1) (1971) 54–58; Vestnik MGU, Seriya 3 Fizika, Astronomiya 1 (1971) 75–81 (in Rus-sian).

[47] V. A. Zagrebnov, Phonon interaction in quantum liquid (4He), Vestnik MGU, Seriya 3 Fizika,Astronomiya 5 (1971) 568–578 (in Russian).

[48] Zh. A. Kozlov, V. A. Parfenov and B. Sidzhimov, JINR Communication P3-7519, Dubna 1973.

[49] Zh. A. Kozlov, The spectrum of excitation and Bose condensate phenomena in liquid4He, Physicsof Elementary Particles and Atomic Nuclei 27 (1996) 1705–1751.

[50] P. C. Hohenberg and P. M. Platzman, High-energy neutron scattering from liquid4He, PhysicalReview 152 (1966) 198–200.

[51] R. A. Cowley and A. D. B. Woods, Neutron scattering from liquid helium at high energies,Physical Review Letters 21 (1968) 787–789.

[52] O. Harling, High-momentum-transfer neutron-liquid-helium scattering Bose condensation, Phys-ical Review Letters 24 (1970) 1046–1048.

[53] H. A. Mook, R. Sherm, and M. K. Wilkinson, Search for Bose–Einstein condensation in superfluid4He, Physical Review A 6 (1972) 2268–2271.

[54] H. W. Jackson, Reexamination of evidence for a Bose–Einstein condensate in superfluid4He,Physical Review A 10 (1974) 278–294.

[55] O. Penrose, On the quantum mechanics of helium II, Philosophical Magazine 42 (1951) 1373–1377.

[56] O. Penrose and L. Onsager, Bose–Einstein condensation and liquid helium, Physical Review 104(1956) 576–584.

[57] Zh. A. Kozlov, L. Aleksandrov, V. A. Zagrebnov, V. A. Parfenov and V. B. Priezzhev, Searchingof the Bose condesate in He II, JINR Preprint P4-7895, Dubna, 1974.

[58] L. Aleksandrov, V. A. Zagrebnov, Zh. A. Kozlov, V. A. Parfenov and V. B. Priezzhev, Highenergy neutron scattering and the Bose condensate in He II, Soviet Physics JETP 41 (1975)915–918.

[59] E. V. Dokukin, Zh. K. Kozlov, V. A. Parfenov and A. V. Puchkov, Investigation of the tem-perature dependence of the density of the Bose condensate in helium-4 in connection with thesuperfluidity phenomenon, Soviet Physics JETP 48 (1978) 1146–1149.

[60] L. van Hove, Correlations in space and time and Born approximation scattering in systems ofinteracting particles, Physical Review 95 (1954) 249–262.

[61] V. L. Aksenov and A. M. Balagurov, Principles of the Neutron Crystallography, LomonosovMSU, Moscow, 2023; the second edition, Fizmatlit, Moscow, 2025.

[62] L. Aleksandrov, JINR Preprint P5-6821, Dubna, 1972.

[63] L. Aleksandrov, JINR Preprints P5-7258 and P5-7259, Dubna, 1973.

[64] E. L. Andronikashvili, Soviet Physics JETP 16 (1946) 780, 18 (1948) 424.

[65] I. M. Khalatnikov, Theory of Superfluidity, Nauka, Moscow, 1971; An Introduction to the Theoryof Superfluidity, W. A. Benjamin, New York, 1965.

[66] K. Huang, Statistical Mechanics, John Wiley & Sons, New York, 1987.

[67] V. A. Zagrebnov and V. B. Priezzhev, About problem of Bose-condensate in He II, JINR PreprintP17-9634, Dubna, 1976.

[68] B. N. Esel’son et al., Quantum3He/4He Mixtures, Nauka, Moscow, 1973.

[69] D. S. Betts, An Introduction to Millikelvin Technology, Cambridge University Press, 1989, Ch. 2:Properties of fluid3He/4He mixtures.

[70] H. R. Glyde, Excitations in the quantum liquid4He: A review, Reports on Progress in Physics81 (2018) 014501 (43 pp).

[71] L. D. Landau, The theory of superfluidity of Helium II, Journal of Physics USSR 5 (1941) 71–100.

[72] L. D. Landau, On the theory of superfluidity of Helium II, Journal of Physics USSR 11 (1947)91–92.

[73] J.-B. Bru and V. A. Zagrebnov, Quantum interpretation of thermodynamic behaviour of theBogoliubov weakly imperfect Bose gas, Physics Letters A 247 (1998) 37–41.

[74] S. I. Vilchynskyy, A. I. Yakimenko, K. O. Isaieva and A. V. Chumachenko, The nature ofsuperfluidity and Bose–Einstein condensation: From liquid4He to dilute ultracold atomic gases(Review Article), Low Temperature Physics 39 (2013) 724–740.

[75] E. H. Lieb, R. Seiringer, J. P. Solovej, J. Yngvason, The Mathematics of the Bose Gas and ItsCondensation, Birkh ̈aser Verlag, Basel, 2005.

[76] J. T. Lewis and J. V. Pul`e, The equilibrium states of the free boson gas, Communications inMathematical Physics 36 (1974) 1–18.

[77] O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics, 2ndedition, Vol. 2: Equilibrium States, Models in Quantum Statistical Mechanics, Springer, NewYork–London–Paris, 1996.