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TRANSVERSE ELECTRIC CONDUCTIVITY OF QUANTUM COLLISIONAL PLASMAS

https://doi.org/10.18384/2224-0209-2012-1-624

Abstract

The article presents the formulae for calculation of transverse dielectric function
and transverse electric conductivity in quantum collisional plasmas under arbitrary degree of
degeneracy of the electron gas. To derive the formulae the Wigner Vlasov Boltzmann kinetic
equation with collision integral in BGK (Bhatnagar, Gross and Krook) form in coordinate
space has been used. The research of various particular cases has been done. The case
of fully degenerated quantum plasma has been studied separately. The article gives the
comparison with Lindhards formula.

About the Authors

А. Латышев

Russian Federation


А. Юшканов

Russian Federation


References

1. Klimontovich Y. The Spectra of Systems of Interacting Particles / Klimontovich Y. and Silin V.P. JETF (Journal Experimental Theoreticheskoi Fiziki), 23, 151 (1952).

2. Lindhard J. On the properties of a gas of charged particles / Lindhard J. Kongelige Danske Videnskabernes Selskab, Matematisk-Fysiske Meddelelser. V. 28, №8 (1954), 1-57.

3. Von Roos O. Boltzmann - Vlasov Equation for a Quantum Plasma / Von Roos O. Phys. Rev. 119. №4 (1960), 1174-1179.

4. Kliewer K.L. Lindhard Dielectric Functions with a Finite Electron Lifetime / Kliewer K.L., Fuchs R. Phys. Rev. 1969. V. 181. №2. P. 552-558.

5. Mermin N. D. Lindhard Dielectric Functions in the Relaxation- Time Approximation / Mermin N.D. Phys. Rev. B. 1970. V. 1, №5. P. 2362-2363.

6. Manfredi G. How to model quantum plasmas / Manfredi G. ArXiv:quant-ph/0505004. 30 pp.

7. Anderson D. Statistical effects in the multistream model for quantum plasmas / Anderson D., Hall B., Lisak M., and Marklund M. Phys. Rev. E 65 (2002), 046417.

8. De Andrґes P. Relaxation-time effects in the transverse dielectric function and the electromagnetic properties of metallic surfaces and small particles / De Andrґes P., Monreal R., and Flores F. Phys. Rev. B. 1986. Vol. 34,№10, 7365-7366.

9. Shukla P.K. Nonlinear aspects of quantum plasma physics / Shukla P. K. and Eliasson B. Uspekhy Fiz. Nauk, 53(1) 2010; [V. 180. No. 1, 55-82 (2010) (in Russian)].

10. Eliasson B. Dispersion properties of electrostatic oscillations in quantum plasmas / Eliasson B. and Shukla P.K. arXiv:0911.4594v1 [physics.plasm-ph] 24 Nov 2009, 9 pp.

11. Bhatnagar P.L. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems / Bhatnagar P.L., Gross E.P., and Krook M. Phys. Rev. 94 (1954), 511-525.

12. Opher M. Krook collisional models of the kinetic susceptibility of plasmas / Opher M., Morales G.J., Leboeuf J.N. Phys. Rev. E. V. 66, 016407, 2002.

13. Gelder van, A.P.Quantum Corrections in the Theory of the Anomalous Skin Effect / Gelder van, A.P. Phys. Rev. 1969. Vol. 187. №3. P. 833-842.

14. Fuchs R. Surface plasmon in a semi-infinite free-electron gas / Fuchs R., Kliewer K.L. Phys. Rev. B. 1971. V. 3. №7. P. 2270-2278.

15. Fuchs R. Optical properties of an electron gas: further studies of a nonlocal description / Fuchs R., Kliewer K.L. Phys. Rev. 1969. V. 185. №3. P. 905-913.

16. Dressel M. Electrodynamics of Solids. Optical Properties of Electrons in Matter / Dressel M., GrЁuner G. Cambridge. Univ. Press. 2003. 487 p.

17. Wierling A. Interpolation between local field corrections and the Drude model by a generalized Mermin approach / Wierling A. arXiv:0812.3835v1 [physics.plasm-ph] 19 Dec 2008.

18. Brodin G. Quantum Plasma Effects in the Classical Regime / Brodin G., Marklund M., Manfredi G. Phys. Rev. Letters. 100, (2008). P. 175001-1 - 175001-4.

19. Manfredi G. Self-consistent fluid model for a quantum electron gas / Manfredi G. and Haas F. Phys. Rev. B 64 (2001), 075316.

20. Wigner E.P. On the quantum correction for thermodynamic equilibrium / Wigner E.P. Phys. Rev. 40 (1932), 749-759.

21. Tatarskii V.I. The Wigner representation of quantum mechanics / Tatarskii V.I. Uspekhy Fiz. Nauk. 26 (1983), 311-327; [Usp. Fis. Nauk. 139 (1983), 587 (in Russian)].

22. Hillery M. Distribution functions in physics: Fundamentals / Hillery M., OConnell R.F., Scully M. O., and Wigner E.P. Phys. Rev. 106 (1984), 121-167.

23. Arnold A. The electromagnetic Wigner equation for an electron with spin / Arnold A. and SteinrЁuck H. Z. Angew. Math. Phys. 40 (1989), 793-815.

24. Kozlov V. V. Vigners function and diffusion in a collisionless medium of quantum particles / Kozlov V.V. and Smolyanov O.G. Teor. Veroyatn. Primen. 51 (2006), №1, 109-125 (In Russian); translation in Theory Probab. Appl. 51 (2007), №1, 168-181.


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