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Critical opalescence and the true dielectric state in a Coulomb system

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Abstract

To study the critical opalescence effect in a two-component Coulomb system consisting of single-type electrons and nuclei, we consider the limit relations for static structure factors and analyze the singularities of the dielectric permittivity. We show that the critical opalescence effect can be observed not only at the critical point corresponding to the gas-liquid phase transition but also near the true dielectric state with zero static conductivity. With the available experimental data taken into account, we assume that the true dielectric state is the limit state of the liquid-liquid phase transition accompanied by sharp variations in the electrical conduction of the substances. We find that if the thermodynamic parameters correspond to the true dielectric state, then the critical opalescence effect can arise in the case where the squared fluctuation in the total number of electrons and nuclei in a two-component Coulomb system becomes infinite, as this occurs at the critical point corresponding to the gas-liquid phase transition.

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References

  1. B. Chu, Laser Light Scattering, Acad. Press, New York (1991).

    Google Scholar 

  2. D. I. Ivanov, Critical Behavior of Non-Ideal Systems, Wiley-VHC, Vienheim (2008).

    Book  MATH  Google Scholar 

  3. M. V. Smoluchowski, Ann. Phys., 330, 205–226 (1908).

    Article  Google Scholar 

  4. A. Einstein, Ann. Phys., 338, 1275–1298 (1910).

    Article  Google Scholar 

  5. P. Resibois and M. De Lener, Classical Kinetic Theory of Fluids, Wiley, New York (1977).

    Google Scholar 

  6. L. S. Ornstein and F. Zernike, Proc. Acad. Sci. Amsterdam, 17, 793–806 (1914).

    Google Scholar 

  7. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics, Wiley, New York (1975).

    MATH  Google Scholar 

  8. J. E. Thomas and P. W. Schmidt, J. Chem. Phys., 39, 2506–2515 (1963).

    Article  ADS  Google Scholar 

  9. M. A. Anisimov, Critical Phenomena in Liquids and Liquid Crystals, Gordon and Breach, Philadelphia (1991).

    Google Scholar 

  10. G. A. Martynov, Fundamental Theory of Liquids: Method of Distribution Functions, Adam Hilger, Bristol (1992).

    Google Scholar 

  11. G. A. Martynov, Phys.-Usp., 42, 517 (1999).

    Article  ADS  Google Scholar 

  12. L. D. Landau, Phys. Z. Sowjetunion, 11, 26–35 (1937).

    MATH  Google Scholar 

  13. E. A. Guggenheim, J. Chem. Phys., 13, 253–261 (1945).

    Article  ADS  Google Scholar 

  14. X.-G. Wen, Phys. Rev. B, 40, 7387–7390 (1989).

    Article  ADS  Google Scholar 

  15. S. S. Jahromi, S. F. Masoudi, M. Kargarian, and K. P. Schmidt, Phys. Rev. B, 88, 214411 (2013); arXiv:1308.1407v2 [cond-mat.str-el] (2013).

    Article  ADS  Google Scholar 

  16. L. Onsager, Phys. Rev., 65, 117–149 (1944).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  17. E. Ising, Z. Phys., 31, 253–258 (1925).

    Article  ADS  Google Scholar 

  18. B. Widom, J. Chem. Phys., 41, 1633–1634 (1964); 43, 3892–3897, 3898–3904 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  19. L. P. Kadanoff, Physics, 2, 263–272 (1966); Nuovo Cimento B Ser. 10, 44, 276–305 (1966).

    Google Scholar 

  20. K. G. Wilson, Phys. Rev. B, 4, 3174–3183, 3184–3205 (1971).

    Article  ADS  MATH  Google Scholar 

  21. M. E. Fisher, Rev. Modern Phys., 70, 653–681 (1998).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  22. H. E. Stanley, Rev. Modern Phys., 71, S358–S366 (1999).

    Article  Google Scholar 

  23. M. Barmatz, I. Hahn, J. A. Lipa, and R. V. Duncan, Rev. Modern Phys., 79, 1–52 (2007).

    Article  ADS  Google Scholar 

  24. A. Parola and L. Reatto, Adv. Phys., 44, 211–298 (1995).

    Article  ADS  Google Scholar 

  25. G. A. Martynov, Theor. Math. Phys., 119, 796–810 (1999); 156, 1356–1364 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  26. G. A. Martynov, J. Chem. Phys., 129, 244509 (2008); Phys. Rev. E, 79, 031119 (2009).

    Article  ADS  Google Scholar 

  27. R. Evans and J. R. Henderson, J. Phys.: Cond. Matt., 21, 474220 (2009).

    ADS  Google Scholar 

  28. M. E. Fisher, J. Phys.: Cond. Matt., 8, 9103–9110 (1996).

    ADS  Google Scholar 

  29. A. A. Likal’ter, Phys. Usp., 43, 777–797 (2000).

    Article  Google Scholar 

  30. W.-D. Kraeft, D. Kremp, W. Ebeling, and G. Ropke, Quantum Statistics of Charged Particle Systems, Plenum, New York (1986).

    Book  Google Scholar 

  31. D. Pines and P. Noziéres, The Theory of Quantum Liquids, Benjamin, New York (1966).

    Google Scholar 

  32. V. B. Bobrov and S. A. Trigger, Phys. Lett. A, 375, 1716–1719 (2011).

    Article  ADS  MATH  Google Scholar 

  33. V. B. Bobrov, J. Phys.: Cond. Matt., 2, 3115–3118 (1990).

    ADS  Google Scholar 

  34. V. B. Bobrov, N. I. Klyuchnikov, and S. A. Triger, Theor. Math. Phys., 89, 1198–1208 (1991).

    Article  Google Scholar 

  35. V. B. Bobrov, N. I. Klyuchnikov, and S. A. Trigger, Phys. A, 181, 156–172 (1992).

    Article  Google Scholar 

  36. V. B. Bobrov, I. M. Sokolov, and S. A. Trigger, Phys. Plasmas, 19, 062101 (2012).

    Article  ADS  Google Scholar 

  37. L. D. Landau and E. M. Lifshitz, Course in Theoretical Physics [in Russian], Vol. 3, Quantum Mechanics: Nonrelativistic Theory, Nauka, Moscow (1974); English transl., Pergamon, New York (1977).

    Google Scholar 

  38. V. B. Bobrov, Theor. Math. Phys., 178, 374–386 (2014).

    Article  MATH  Google Scholar 

  39. S. Dietrich and A. Haase, Phys. Rep., 260, 1–138 (1995).

    Article  ADS  Google Scholar 

  40. J. Chihara, J. Phys.: Cond. Matt., 12, 231–248 (2000).

    ADS  Google Scholar 

  41. V. B. Bobrov, S. A. Trigger, and S. N. Skovorod’ko, Europhys. Lett., 92, 13001 (2010).

    Article  ADS  Google Scholar 

  42. F. Evers and A. D. Mirlin, Rev. Modern Phys., 80, 1355–1417 (2008).

    Article  ADS  Google Scholar 

  43. V. F. Gantmakher and V. T. Dolgopolov, Phys. Usp., 51, 3–22 (2008).

    Article  Google Scholar 

  44. V. B. Bobrov, V. Ya. Mendeleyev, S. A. Trigger, G. J. F. van Heijst, and P. P. J. M. Schram, High Temperature, 51, 457–464 (2013).

    Article  Google Scholar 

  45. R. Redmer, B. Holst, and F. Hensel, eds., Metal-to-Nonmetal Transitions, Springer, Berlin (2010).

    MATH  Google Scholar 

  46. N. Subramanian, A. F. Goncharov, V. V. Struzhkin, M. Somayazulu, and R. J. Hemley, Proc. Natl. Acad. Sci. USA, 108, 6014–6019 (2011).

    Article  ADS  Google Scholar 

  47. V. Dzyabura, M. Zaghoo, and I. F. Silvera, Proc. Natl. Acad. Sci. USA, 110, 8040–8044 (2013).

    Article  ADS  Google Scholar 

  48. V. B. Bobrov and S. A. Trigger, J. Phys. A: Math. Theor., 43, 365002 (2010).

    Article  MathSciNet  Google Scholar 

  49. V. B. Bobrov, High Temperature, 49, 495–505 (2011).

    Article  Google Scholar 

  50. V. B. Bobrov, Phys. Rev. E, 86, 026401 (2012).

    Article  ADS  Google Scholar 

  51. V. B. Bobrov, S. A. Trigger, and A. G. Zagorodny, Europhys. Lett., 101, 16002 (2013).

    Article  ADS  Google Scholar 

  52. A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics [in Russian], Fizmatlit, Moscow (1962); English transl.: Methods of Quantum Field Theory in Statistical Mechanics (Intl. Ser. Monogr. Nat. Philos., Vol. 4), Pergamon, Oxford (1963).

    Google Scholar 

  53. V. P. Silin and A. A. Rukhadze, Electromagnetic Properties of Plasma and Plasmalike Media [in Russian], Gosatomizdat, Moscow (1961).

    Google Scholar 

  54. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics [in Russian], Vol. 5, Statistical Physics, Nauka, Moscow (1976); English transl. prev. ed., Pergamon, Oxford (1968).

    Google Scholar 

  55. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics [in Russian], Vol. 10, Physical Kinetics, Nauka, Moscow (1979); English transl., Pergamon, Oxford (1981).

    Google Scholar 

  56. D. N. Zubarev, Nonequilibrium Statistical Thermodynamics [in Russian], Nauka, Moscow (1971); English transl., Plenum Consultants Bureau, New York (1974).

    Google Scholar 

  57. V. B. Bobrov, S. A. Trigger, and A. G. Zagorodny, Phys. Lett. A, 375, 84–87 (2010).

    Article  ADS  MATH  Google Scholar 

  58. V. B. Bobrov, S. A. Trigger, G. J. F. van Heijst, and P. P. J. M. Schram, Europhys. Lett., 90, 10003 (2010).

    Article  ADS  Google Scholar 

  59. O. V. Dolgov, D. A. Kirzhnitz, and E. G. Maksimov, Rev. Modern Phys., 53, 81–93 (1981).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Joint Institute for High Temperatures, RAS, Moscow, Russia

    V. B. Bobrov & S. A. Trigger

  2. National Research University “Moscow Power Engineering Institute (MPEI)”, Moscow, Russia

    V. B. Bobrov

  3. Eindhoven University of Technology, Eindhoven, The Netherlands

    S. A. Trigger

Authors
  1. V. B. Bobrov
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  2. S. A. Trigger
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Correspondence to V. B. Bobrov.

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__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 183, No. 1, pp. 120–137, April, 2015.

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Bobrov, V.B., Trigger, S.A. Critical opalescence and the true dielectric state in a Coulomb system. Theor Math Phys 183, 553–566 (2015). https://doi.org/10.1007/s11232-015-0281-3

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