Advertisement

Theoretical and Mathematical Physics

, Volume 194, Issue 3, pp 404–414 | Cite as

Bose–Einstein Condensate and Singularities of the Frequency Dispersion of the Permittivity in a Disordered Coulomb System

  • V. V. Bobrov
  • S. A. Trigger
Article
  • 16 Downloads

Abstract

In the framework of linear response theory, we consider the frequency dispersion of the permittivity of a disordered Coulomb system in the presence of the one-particle Bose–Einstein condensate for nuclei. We show that the superconductivity of nuclei exists in such a system and is manifested in the Meissner effect for a weakly nonuniform low-frequency electromagnetic field. The obtained result offers an opportunity to solve the problem of the presence of the one-particle Bose–Einstein condensate in superfluid He-II based on direct experiments.

Keywords

Bose–Einstein condensate Coulomb system permittivity frequency dispersion 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. M. Lifshitz and L. P. Pitaevskii, Statistical Physics: Part 2. Theory of the Condensed State [in Russian], Nauka, Moscow (1978); English transl., Pergamon, Oxford (1980).Google Scholar
  2. 2.
    B. V. Svistunov, E. S. Babaev, and N. V. Prokof’ev, Superfluid States of Matter, CRC Press, Boca Raton, Fla. (2015).CrossRefzbMATHGoogle Scholar
  3. 3.
    E. A. Pashitskii, S. V. Mashkevich, and S. I. Vilchynskyy, “Superfluid Bose liquid with a suppressed BEC and an intensive pair coherent condensate as a model of 4He,” Phys. Rev. Lett., 89, 075301 (2002).CrossRefADSGoogle Scholar
  4. 4.
    A. S. Rybalko, “Observation of the electric induction due to a second-sound wave in He II,” Low Temp. Phys., 30, 994 (2004).CrossRefADSGoogle Scholar
  5. 5.
    A. Rybalko, S. Rubets, E. Rudavskii, V. Tikhly, and S. Tarapov, R. Golovashchenko, and V. Derkach, “Resonance absorption of microwaves in He II: Evidence for roton emission,” Phys. Rev. B, 76, 140503 (2007).CrossRefADSGoogle Scholar
  6. 6.
    E. A. Pashitskii and S. M. Ryabchenko, “On the cause of the electrical activity of superfluid helium upon excitation of a second sound wave and normal-component velocity oscillations in it,” Low Temp. Phys., 33, 8 (2007).CrossRefADSGoogle Scholar
  7. 7.
    S. I. Shevchenko and A. S. Rukin, “On the electric activity of superfluid systems,” JETP Lett., 90, 42–46 (2009).CrossRefADSGoogle Scholar
  8. 8.
    W.-D. Kraeft, D. Kremp, W. Ebeling, and G. Röpke, Quantum Statistics of Charged Particle Systems, Akademie-Verlag, Berlin (1986).CrossRefGoogle Scholar
  9. 9.
    J. M. McMahon, M. A. Morales, C. Pierleoni, and D. M. Ceperley, “The properties of hydrogen and helium under extreme conditions,” Rev. Modern Phys., 84, 1607–1653 (2012).CrossRefADSGoogle Scholar
  10. 10.
    A. V. Burenin, “On the importance of the Born–Oppenheimer approximation in intramolecular dynamics,” Phys. Usp., 53, 713–724 (2010).CrossRefADSGoogle Scholar
  11. 11.
    V. B. Bobrov, “Statistical theory of rarified gases in the Coulomb model of substance: Adiabatic approximation and initial atoms,” Theor. Math. Phys., 178, 374–386 (2014).MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    V. B. Bobrov and S. A. Trigger, “On the properties of systems with Bose–Einstein condensate in the Coulomb model of matter,” Bull. Lebedev Phys. Inst., 42, 13–16 (2015).CrossRefADSGoogle Scholar
  13. 13.
    O. Penrose and L. Onsager, “Bose–Einstein condensation and liquid helium,” Phys. Rev., 104, 576–584 (1956).CrossRefzbMATHADSGoogle Scholar
  14. 14.
    C. N. Yang, “Concept of off-diagonal long-range order and the quantum phases of liquid He and of superconductors,” Rev. Modern Phys., 34, 694–704 (1962).MathSciNetCrossRefADSGoogle Scholar
  15. 15.
    N. N. Bogolubov and N. N. Bogolubov Jr., Introduction to Quantum Statistical Mechanics, World Scientific, Singapore (1982).CrossRefzbMATHGoogle Scholar
  16. 16.
    V. B. Bobrov, S. A. Trigger, and A. G. Zagorodny, “Off-diagonal long-range order and an inhomogeneous Bose–Einstein condensate,” Dokl. Phys., 60, 147–149 (2015).CrossRefADSGoogle Scholar
  17. 17.
    V. P. Silin and A. A. Rukhadze, Electromagnetic Properties of Plasma and Plasma-Like Media [in Russian], Gosatomizdat, Moscow (1961).Google Scholar
  18. 18.
    H. Reinholz, R. Redmer, G. Röpke, and A. Wierling, “Long-wavelength limit of the dynamical local-field factor and dynamical conductivity of a two-component plasma,” Phys. Rev. E, 62, 5648–5666 (2000).CrossRefADSGoogle Scholar
  19. 19.
    H. Reinholz, Yu. Zaporoghets, V. Mintsev, V. Fortov, I. Morozov, and G. Röpke, “Frequency-dependent reflectivity of shock-compressed xenon plasmas,” Phys. Rev. E, 68, 036403 (2003).CrossRefADSGoogle Scholar
  20. 20.
    P. C. Martin, “Sum rules, Kramers–Kronig relations, and transport coefficients in charged systems,” Phys. Rev., 161, 143–155 (1967).CrossRefADSGoogle Scholar
  21. 21.
    D. N. Zubarev, Nonequilibrium Statistical Thermodynamics [in Russian], Nauka, Moscow (1971); English transl., Consultants Bureau, New York (1974).Google Scholar
  22. 22.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics [in Russian], Vol. 5, Statistical Physics: Part 1, Nauka, Moscow (1976); English transl., Pergamon, Oxford (1980).Google Scholar
  23. 23.
    A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloschinskii, Methods of Quantum Field Theory in Statistical Physics [in Russian], Fizmatlit, Moscow (1962); English transl.: Quantum Field Theory in Statistical Physics, Pergamon, New York (1965).Google Scholar
  24. 24.
    V. B. Bobrov, V. D. Ozrin, and S. A. Trigger, “Some peculiarities of the long-wavelength conductivity limit in a charged particle system,” Phys. A, 164, 453–468 (1990).CrossRefGoogle Scholar
  25. 25.
    V. B. Bobrov, N. I. Klyuchnikov, and S. A. Triger, “Exact relations for structure factor of a Coulomb system,” Theor. Math. Phys., 89, 1198–1208 (1991).CrossRefGoogle Scholar
  26. 26.
    E. M. Lifshitz and L. P. Pitaevskii, Course of Theoretical Physics [in Russian], Vol. 10, Physical Kinetics, Nauka, Moscow (1979); English transl., Pergamon, New York (1981).Google Scholar
  27. 27.
    V. B. Bobrov, S. A. Trigger, and A. G. Zagorodny, “Kubo formula for frequency dispersion of dielectric permittivity and static conductivity of the Coulomb system,” Phys. Lett. A, 375, 84–87 (2010).CrossRefzbMATHADSGoogle Scholar
  28. 28.
    R. Kubo, “Statistical-mechanical theory of irreversible processes: I. General theory and simple applications to magnetic and conduction problems,” J. Phys. Soc. Japan, 12, 570–586 (1957).MathSciNetCrossRefADSGoogle Scholar
  29. 29.
    V. Ambegoaker and W. Kohn, “Electromagnetic properties of insulators: I,” Phys. Rev., 117, 423–431 (1960).MathSciNetCrossRefzbMATHADSGoogle Scholar
  30. 30.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics [in Russian], Vol. 8, Electrodynamics of Continuous Matter, Nauka, Moscow (1982); English transl. prev. ed., Pergamon, New York (1979).Google Scholar
  31. 31.
    V. B. Bobrov and S. A. Trigger, “The true dielectric and ideal conductor in the theory of the dielectric function of the Coulomb system,” J. Phys. A: Math. Theor., 43, 365002 (2010).MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    V. B. Bobrov, “Features of the dielectric permittivity of the Coulomb system and the true dielectric state,” Phys. Rev. E, 86, 026401 (2012).CrossRefADSGoogle Scholar
  33. 33.
    V. B. Bobrov, S. A. Trigger, G. J. F. van Heijst, and P. P. J. M. Schram, “Kramers–Kronig relations for the dielectric function and the static conductivity of Coulomb systems,” Europhys. Lett., 90, 10003 (2010).CrossRefADSGoogle Scholar
  34. 34.
    L. D. Landau, “The theory of superfluidity of helium II [in Russian],” Zh. Eksp. Teor. Fiz., 11, 592–624 (1941).ADSGoogle Scholar
  35. 35.
    L. D. Landau, “The theory of superfluidity of helium II,” J. Phys. (USSR), 5, 71–90 (1948).Google Scholar
  36. 36.
    D. V. Shirkov, “Imagery of symmetry in current physics,” Theor. Math. Phys., 170, 239–248 (2012).MathSciNetCrossRefGoogle Scholar
  37. 37.
    A. S. Rybalko, S. P. Rubets, E. Ya. Rudavskii, V. A. Tikhiy, Yu. M. Poluectov, R. V. Golovachenko, V. N. Derkach, S. I. Tarapov, and O. V. Usatenko, “Resonance excitation of single rotons in He II by an electromagnetic wave: Spectral line shape,” Low Temp. Phys., 35, 837–842 (2009).CrossRefADSGoogle Scholar
  38. 38.
    Yu. M. Poluektov, “Absorption of electromagnetic field energy by the superfluid system of atoms with a dipole moment,” Low Temp. Phys., 40, 389–396 (2014).CrossRefADSGoogle Scholar
  39. 39.
    V. B. Bobrov, A. G. Zagorodny, and S. A. Trigger, “Coulomb interaction potential and Bose–Einstein condensate,” Low Temp. Phys., 41, 901–908 (2015).CrossRefADSGoogle Scholar
  40. 40.
    M. Wolfke and W. H. Keesom, “On the electrical resistance of liquid helium,” Phys., 3, 823–824 (1936).ADSGoogle Scholar
  41. 41.
    J. R. Schrieffer, Theory of Superconductivity, Perseus Books, Reading, Mass. (1999).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Joint Institute for High TemperaturesRASMoscowRussia
  2. 2.National Research Institute “Moscow Power Engineering Institute”MoscowRussia

Personalised recommendations