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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Change history
06 June 2018
The first author should be V. B. Bobrov.
References
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).
B. V. Svistunov, E. S. Babaev, and N. V. Prokof’ev, Superfluid States of Matter, CRC Press, Boca Raton, Fla. (2015).
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).
A. S. Rybalko, “Observation of the electric induction due to a second-sound wave in He II,” Low Temp. Phys., 30, 994 (2004).
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).
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).
S. I. Shevchenko and A. S. Rukin, “On the electric activity of superfluid systems,” JETP Lett., 90, 42–46 (2009).
W.-D. Kraeft, D. Kremp, W. Ebeling, and G. Röpke, Quantum Statistics of Charged Particle Systems, Akademie-Verlag, Berlin (1986).
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).
A. V. Burenin, “On the importance of the Born–Oppenheimer approximation in intramolecular dynamics,” Phys. Usp., 53, 713–724 (2010).
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).
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).
O. Penrose and L. Onsager, “Bose–Einstein condensation and liquid helium,” Phys. Rev., 104, 576–584 (1956).
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).
N. N. Bogolubov and N. N. Bogolubov Jr., Introduction to Quantum Statistical Mechanics, World Scientific, Singapore (1982).
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).
V. P. Silin and A. A. Rukhadze, Electromagnetic Properties of Plasma and Plasma-Like Media [in Russian], Gosatomizdat, Moscow (1961).
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).
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).
P. C. Martin, “Sum rules, Kramers–Kronig relations, and transport coefficients in charged systems,” Phys. Rev., 161, 143–155 (1967).
D. N. Zubarev, Nonequilibrium Statistical Thermodynamics [in Russian], Nauka, Moscow (1971); English transl., Consultants Bureau, New York (1974).
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).
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).
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).
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).
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).
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).
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).
V. Ambegoaker and W. Kohn, “Electromagnetic properties of insulators: I,” Phys. Rev., 117, 423–431 (1960).
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).
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).
V. B. Bobrov, “Features of the dielectric permittivity of the Coulomb system and the true dielectric state,” Phys. Rev. E, 86, 026401 (2012).
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).
L. D. Landau, “The theory of superfluidity of helium II [in Russian],” Zh. Eksp. Teor. Fiz., 11, 592–624 (1941).
L. D. Landau, “The theory of superfluidity of helium II,” J. Phys. (USSR), 5, 71–90 (1948).
D. V. Shirkov, “Imagery of symmetry in current physics,” Theor. Math. Phys., 170, 239–248 (2012).
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).
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).
V. B. Bobrov, A. G. Zagorodny, and S. A. Trigger, “Coulomb interaction potential and Bose–Einstein condensate,” Low Temp. Phys., 41, 901–908 (2015).
M. Wolfke and W. H. Keesom, “On the electrical resistance of liquid helium,” Phys., 3, 823–824 (1936).
J. R. Schrieffer, Theory of Superconductivity, Perseus Books, Reading, Mass. (1999).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bobrov, V.V., Trigger, S.A. Bose–Einstein Condensate and Singularities of the Frequency Dispersion of the Permittivity in a Disordered Coulomb System. Theor Math Phys 194, 404–414 (2018). https://doi.org/10.1134/S004057791803008X
Published:
Issue Date:
DOI: https://doi.org/10.1134/S004057791803008X