Bose–Einstein condensate and singularities of the frequency dispersion of the permittivity in a disordered Coulomb system

V. B. Bobrov   ; S. A. Triger

Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 3, pp. 468-480

Résumé

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.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.

Détail

Keywords: Bose–Einstein condensate, permittivity, frequency dispersion.
Mots-clés : Coulomb system

Bibliographie

[1] E. M. Lifshits, L. P. Pitaevskii, Statisticheskaya fizika. Ch. 2. Teoriya kondensirovannogo sostoyaniya, Nauka, M., 1978 | MR | MR

[2] B. V. Svistunov, E. S. Babaev, N. V. Prokof'ev, Superfluid States of Matter, CRC Press, Boca Raton, 2015 | Zbl

[3] E. A. Pashitskii, S. V. Mashkevich, S. I. Vilchynskyy, “Superfluid Bose liquid with a suppressed BEC and an intensive pair coherent condensate as a model of $^4$He”, Phys. Rev. Lett., 89:7 (2002), 075301, 4 pp. | DOI

[4] A. S. Rybalko, “Nablyudenie elektricheskoi induktsii, obuslovlennoi volnoi vtorogo zvuka v He II”, FNT, 30:12 (2004), 1321–1325 | DOI

[5] A. Rybalko, S. Rubets, E. Rudavskii, V. Tikhly, S. Tarapov, R. Golovashchenko, V. Derkach, “Resonance absorption of microwaves in He II: evidence for roton emission”, Phys. Rev. B, 76:14 (2007), 140503, 4 pp. | DOI

[6] E. A. Pashitskii, S. M. Ryabchenko, “O prichine elektricheskoi aktivnosti sverkhtekuchego geliya pri vozbuzhdenii v nem voln vtorogo zvuka i kolebanii skorosti normalnoi komponenty”, FNT, 33:12 (2007), 12–21 | DOI

[7] S. I. Shevchenko, A. S. Rukin, “Ob elektricheskoi aktivnosti sverkhtekuchikh sistem”, Pisma v ZhETF, 90:1 (2009), 46–50 | DOI

[8] V.-D. Kreft, D. Kremp, V. Ebeling, G. Repke, Kvantovaya statistika sistem zaryazhennykh chastits, Mir, M., 1988

[9] J. M. McMahon, M. A. Morales, C. Pierleoni, D. M. Ceperley, “The properties of hydrogen and helium under extreme conditions”, Rev. Modern Phys., 84:4 (2012), 1607–1653 | DOI

[10] A. V. Burenin, “O znachenii priblizheniya Borna-Oppengeimera vo vnutrimolekulyarnoi dinamike”, UFN, 180:7 (2010), 745–757 | DOI

[11] V. B. Bobrov, “O statisticheskoi teorii razrezhennogo gaza v kulonovskoi modeli veschestva. Adiabaticheskoe priblizhenie i iskhodnye atomy”, TMF, 178:3 (2014), 433–448 | DOI | DOI | MR | Zbl

[12] V. B. Bobrov, S. A. Triger, “On the properties of systems with Bose–Einstein condensate in the Coulomb model of matter”, Kratkie soobscheniya po fizike FIAN, 42:1 (2015), 58–64

[13] O. Penrose, L. Onsager, “Bose–Einstein condensation and liquid helium”, Phys. Rev., 104:3 (1956), 576–584 | DOI | Zbl

[14] C. N. Yang, “Concept of off-diagonal long-range order and the quantum phases of liquid He and of superconductors”, Rev. Modern Phys., 34:4 (1962), 694–704 | DOI | MR

[15] N. N. Bogolyubov, N. N. Bogolyubov (ml.), Vvedenie v kvantovuyu statisticheskuyu mekhaniku, Nauka, M., 1984 | MR | MR

[16] V. B. Bobrov, A. G. Zagorodnii, S. A. Triger, “Nediagonalnyi dalnii poryadok i neodnorodnyi kondensat Boze–Einshteina”, Dokl. RAN, 461:4 (2015), 400–402 | DOI | DOI

[17] V. P. Silin, A. A. Rukhadze, Elektromagnitnye svoistva plazmy i plazmopodobnykh sred, Gosatomizdat, M., 1961

[18] H. Reinholz, R. Redmer, G. Röpke, A. Wierling, “Long-wavelength limit of the dynamical local-field factor and dynamical conductivity of a two-component plasma”, Phys. Rev. E, 62:4 (2000), 5648–5666 | DOI

[19] H. Reinholz, Yu. Zaporoghets, V. Mintsev, V. Fortov, I. Morozov, G. Röpke, “Frequency-dependent reflectivity of shock-compressed xenon plasmas”, Phys. Rev. E, 68:3 (2003), 036403, 10 pp. | DOI

[20] P. C. Martin, “Sum rules, Kramers–Kronig relations, and transport coefficients in charged systems”, Phys. Rev., 161:1 (1967), 143–155 | DOI

[21] D. N. Zubarev, Neravnovesnaya statisticheskaya termodinamika, Nauka, M., 1971 | MR

[22] L. D. Landau, E. M. Lifshits, Kurs teoreticheskoi fiziki, v. 5, Statisticheskaya fizika. Chast 1, Nauka, M., 1976 | MR | Zbl

[23] A. A. Abrikosov, L. P. Gorkov, I. E. Dzyaloshinskii, Metody kvantovoi teorii polya v statisticheskoi fizike, Fizmatgiz, M., 1962 | MR | Zbl

[24] V. B. Bobrov, V. D. Ozrin, S. A. Trigger, “Some peculiarities of the long-wavelength conductivity limit in a charged particle system”, Phys. A, 164:2 (1990), 453–468 | DOI

[25] V. B. Bobrov, N. I. Klyuchnikov, S. A. Triger, “Tochnye sootnosheniya dlya strukturnogo faktora kulonovskoi sistemy”, TMF, 89:2 (1991), 263–277 | DOI

[26] E. M. Lifshits, L. P. Pitaevskii, Kurs teoreticheskoi fiziki, v. 10, Fizicheskaya kinetika, Nauka, M., 1979 | MR

[27] V. B. Bobrov, S. A. Trigger, A. G. Zagorodny, “Kubo formula for frequency dispersion of dielectric permittivity and static conductivity of the Coulomb system”, Phys. Lett. A, 375:2 (2010), 84–87 | DOI | Zbl

[28] R. Kubo, “Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems”, J. Phys. Soc. Japan, 12:6 (1957), 570–586 | DOI | MR

[29] V. Ambegoaker, W. Kohn, “Electromagnetic properties of insulators. I.”, Phys. Rev., 117:2 (1960), 423–431 | DOI | MR

[30] L. D. Landau, E. M. Lifshits, Kurs teoreticheskoi fiziki, v. 8, Elektrodinamika sploshnykh sred, Nauka, M., 1982 | MR

[31] V. B. Bobrov, 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., 43:36 (2010), 365002, 11 pp. | DOI | MR | Zbl

[32] V. B. Bobrov, “Features of the dielectric permittivity of the Coulomb system and the true dielectric state”, Phys. Rev. E, 86:2 (2012), 026401, 4 pp. | DOI

[33] V. B. Bobrov, S. A. Trigger, G. J. F. van Heijst, P. P. J. M. Schram, “Kramers–Kronig relations for the dielectric function and the static conductivity of Coulomb systems”, Europhys. Lett., 90:1 (2010), 10003, 4 pp. | DOI

[34] L. D. Landau, “Teoriya sverkhtekuchesti geliya II”, ZhETF, 11:6 (1941), 592–624

[35] E. M. Lifshits, “Teoriya sverkhtekuchesti geliya II”, UFN, 34:4 (1948), 512–559 | DOI

[36] D. V. Shirkov, “Obliki simmetrii v sovremennoi fizike”, TMF, 170:2 (2012), 292–303 | DOI | DOI | MR

[37] A. S. Rybalko, S. P. Rubets, E. Ya. Rudavskii, V. A. Tikhii, Yu. M. Poluektov, R. V. Golovaschenko, V. N. Derkach, S. I. Tarapov, O. V. Usatenko, “Rezonansnoe vozbuzhdenie edinichnykh rotonov v Ne II elektromagnitnoi volnoi. Kontur spektralnoi linii”, FNT, 35:11 (2009), 1073–1080 | DOI

[38] Yu. M. Poluektov, “Pogloschenie energii elektromagnitnogo polya sverkhtekuchei sistemoi atomov s dipolnym momentom”, FNT, 40:5 (2014), 503–512 | DOI

[39] V. B. Bobrov, A. G. Zagorodnii, S. A. Triger, “Kulonovskii potentsial vzaimodeistviya i kondensat Boze–Einshteina”, FNT, 41:11 (2015), 1154–1163 | DOI

[40] M. Wolfke, W. H. Keesom, “On the electrical resistance of liquid helium”, Physica, 3:8 (1936), 823–824 | DOI

[41] J. R. Schrieffer, Theory of Superconductivity, Perseus Books, Reading, MA, 1999 | MR