The loss function of dense plasmas and sum rules
DOI:
https://doi.org/10.26577/2218-7987-2014-5-1-53-59Keywords:
coupled plasmas, dielectric function, loss function, sum rules, method of moments.Abstract
Mathematical, particularly, asymptotic properties of the RPA and RPA with dynamic local field corrections of the coupled plasma dielectric function are analyzed within the method of moments which satisfies some exact relations. Particularly f-sum rule,higher-order sum rules and other conservation laws. Thehigher-order sum rules take into account the correlations in the system under scrutiny, so if the system dynamic characteristics, e.g., the dielectric function, do not satisfy these rules which are effectively additional conservation laws, it is difficultto expect the corresponding model to be adequate in the strong-coupling domain.Some other drawbacks and advantages of the above models are pointed out.References
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2. Krein M.G. and Nudel’man A.A. The Markov moment problem and extremal problems.– Providence, R.I.: Trans. of Math. Monographs
(Amer. Math. Soc), 1977. – Vol. 50. – 552 p.
3. Akhiezer N. I. The Classical Moment Problem. – N.Y.: Hafner Publishing Company, 1965. – 253 p.
4. Adamyan V.M., Meyer T. and Tkachenko I.M. RF dielectric constant of a collisuional plasma // Sov. J. Plasma Phys. – 1985. – Vol. 1..481-486.
5. Adamyan V.M. and Tkachenko I.M. Sum rules and exact relations for quantal Coulomb systems // Contrib. Plasma Phys. – 2003. Vol. 43. –
P. 252-257.
6. Arkhipov Y. V., Askaruly A., Ballester D., Davletov A., Meirkanova G. M., and Tkachenko I.
M. Collective and static properties of model twocomponent plasmas // Phys. Rev. E.– 2007. – Vol. 76. –P. 026403.
7. Arkhipov Y. V., Askaruly A., Ballester D., Davletov A., Tkachenko I. M. and Zwicknagel G. Dynamic properties of one-component strongly
coupled plasmas: The sum-rule approach // Phys. Rev. E. – 2010. – Vol.1. – P. 026402.
8. Tkachenko I.M., Arkhipov Y.V. and Askaruly A. The Method of moments and its Applications in Plasma Physics. – SaarbrЁucken,
Germany: LAMBERT Academic Publishing, 2012.– 125 p.
9. Vorberger J., Donko Z., Tkachenko I.M. and Gericke D.O. Dynamic Ion Structure Factor of Warm Dense Matter // Phys. Rev. Lett. – 2012. –
Vol. 109. – P. 225001.
10. Golden K.I. and Kalman G.J. Sum rules for electron-hole bilayer and two-dimensional point dipole systems // Phys. Rev. E. – 2013. –
Vol. 88. – P. 033107.
11. Arkhipov Y.V., Ashikbayeva A.B., Askaruly A., Davletov A.E., and Tkachenko I.M. Optical properties of kelbg-pseudopotentialmodelled
plasmas // Contrib. Plasma Phys. – 2013. –Vol. 53. – P.375-384.
12. Mermin N. D.Lindhard Dielectric Function in the Relaxation-Time Approximation// Phys.
Rev. B. – 1970. – Vol. 1. – P. 2362.
13. Lindhard J. On the properties of a gas of charged particles // K. Dan. Vidensk. Selsk. Mat. Fys. Medd. – 1954. – Vol. 28. –Р. 8.
14. Dolgov O.V., Kirzhnits D.A. and Maksimov E.G.On an admissible sign of the staticdielectric function of matter // Rev. Mod. Phys. –
1981. – Vol. 53. – P. 81.
15. Maksimov E. and Dolgov O.. About possible mechanisms of high emperature superconductors // Phys.-Uspekhi. – 2007. – Vol.
50. P. 933-938.
16. Ichimaru S. Statistical Plasma Physics. – New York:Addison-Wesley, 1991. – Vol. 1.
17. Ichimaru S. Statistical Plasma Physics: Condensed Plasmas. – New York: Addison- Wesley, 1991. – Vol. 2.
18. Perel’ V.I. and Eliashberg G.M.Absorbtion of electromagnetic waves in a plasma // Sov. Phys. JETP. – 1962. – Vol.14(3). – P. 633-637.
19. (a) Reinholz H., Redmer R., Roepke G. and Wierling A. Long-wavelength limit of the dynamical local-field factor and dynamical
conductivity of a two-component plasma // Phys. Rev. E. – 2000. – Vol. 62. – P. 5648; (b) Selchow
A., Roepke G., Wierling A., Reinholz H., Pschiwul T. and Zwicknagel G. Dynamic structure factor for a two-component model plasma // Phys. Rev. E. – 2001. – Vol. 64. – P. 056410.
20. (a) Tkachenko I. M. in 33rd International Workshop on Physics of HED in Matter – Hirschegg, Austria, 2013; (b) Adamyan V.M. and
Tkachenko I. M. Operator Theory: Advances and Applications. – Basel: Birkhauser Verlag, 2000. – Vol. 33. –P. 118; (c) Kalman G. and Golden K.I. Theory of partial response functions in multicomponent plasmas // Phys. Rev. A. – 1984. – Vol. 29. – P. 844.
21. Morawetz K. Dynamical local field, compressibility, and frequency sum rules for quasiparticles. // Phys. Rev. B. – 2002. – Vol. 66.
–P. 075125.
22. (a) Barriga-Carrasco M. D. Effects of target plasma electron-electron collisions on correlated motion of fragmented H2+ protons //
Phys. Rev. E. – 2006. – Vol. 73. – P. 026401; (b) Barriga-Carrasco M. D. Influence of damping on proton energy loss in plasmas of all degeneracies // Phys. Rev. E. – 2006. – Vol. 7. – P. 016405; (c)
Barriga-Carrasco M. D. Dynamical local field corrections on energy loss in plasmas of all degeneracies// Phys. Rev. E. – 2009. – Vol. 79. –
P. 027401; (d) Barriga-Carrasco M. D. Proton stopping using a full conserving dielectric function in plasmas at any degeneracy// Phys. Rev. E. – 2010. – Vol. 82. – P. 046403.
23. Fortmann C., Wierling A. and Roepke G. Influence of local-field corrections on Thomson scattering in collision-dominated two-component
plasmas // Phys. Rev. E. – 2010. – Vol. 81. – P. 026405.
24. Dabrowski B. Dynamical local-field factor in the response function of an electron gas // Phys. Rev. B. – 1986. Vol. 34.– P. 4989.
25. Kugler A. A. Theory of the local field correction in an electron gas // J. Stat. Phys. – 1975. – Vol. 12. –P. 35-87.
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Arkhipov, Y. V., Ashikbayeva, A. B., Askaruly, A., Davletov, A. E., Dubovtsev, D., & Tkachenko, I. M. (2014). The loss function of dense plasmas and sum rules. International Journal of Mathematics and Physics, 5(1), 53–59. https://doi.org/10.26577/2218-7987-2014-5-1-53-59
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Theoretical Physics and Plasma Physics
