evestnikРоссийский социально-гуманитарный журналRussian Social and Humanitarian Journal2224-0209State University of Education10.18384/2224-0209-2012-1-624evestnik-624Research ArticleСтатьиПОПЕРЕЧНАЯ ЭЛЕКТРИЧЕСКАЯ ПРОВОДИМОСТЬ В КВАНТОВОЙ СТОЛКНОВИТЕЛЬНОЙ ПЛАЗМЕTRANSVERSE ELECTRIC CONDUCTIVITY OF QUANTUM COLLISIONAL PLASMASЛатышевА. В.noemail@neicon.ruЮшкановА. А.noemail@neicon.ru2012300320120185138Copyright © Латышев А.В., Юшканов А.А., 20122012Латышев А.В., Юшканов А.А.Латышев А.В., Юшканов А.А.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.evestnik-mgou.ru/jour/article/view/624

Получены корректные формулы для вычисления по¬перечной электри- ческой проводимости и поперечной диэлектриче¬ской проницаемости в квантовой столкновительной плазме при про¬извольной степени вырождения электронного газа. Для этого ис¬пользовалось кинетическое уравнение Вигнера Власова Больцмана с интегралом столкновений в форме БГК модели (Бхатнагар, Гросс и Крук) в координат- ном пространстве. Исследованы различ¬ные частные случаи. Отдельно рассмотрен случай полностью вырожденнной квантовой плазмы. Приводится сравнение с форму- лой, полученной Линдхардом.

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.

столкновительная плазмауравнение Шредингерауравнение Вигнера Власова Больцманаинтеграл столкновенийпроводимостьпроницаемостьфункция Линдхардаcollisional plasmaSchrödinger equationWigner Vlasov Boltzmann kinetic equationcollision integralconductivitypellucidityLindhard functionReferencesKlimontovich Y. The Spectra of Systems of Interacting Particles / Klimontovich Y. and Silin V.P. JETF (Journal Experimental Theoreticheskoi Fiziki), 23, 151 (1952).Klimontovich Y. The Spectra of Systems of Interacting Particles / Klimontovich Y. and Silin V.P. JETF (Journal Experimental Theoreticheskoi Fiziki), 23, 151 (1952).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.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.Von Roos O. Boltzmann - Vlasov Equation for a Quantum Plasma / Von Roos O. Phys. Rev. 119. №4 (1960), 1174-1179.Von Roos O. Boltzmann - Vlasov Equation for a Quantum Plasma / Von Roos O. Phys. Rev. 119. №4 (1960), 1174-1179.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.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.Mermin N. D. Lindhard Dielectric Functions in the Relaxation- Time Approximation / Mermin N.D. Phys. Rev. B. 1970. V. 1, №5. P. 2362-2363.Mermin N. D. Lindhard Dielectric Functions in the Relaxation- Time Approximation / Mermin N.D. Phys. Rev. B. 1970. V. 1, №5. P. 2362-2363.Manfredi G. How to model quantum plasmas / Manfredi G. ArXiv:quant-ph/0505004. 30 pp.Manfredi G. How to model quantum plasmas / Manfredi G. ArXiv:quant-ph/0505004. 30 pp.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.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.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.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.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)].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)].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.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.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.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.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.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.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.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.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.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.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.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.Dressel M. Electrodynamics of Solids. Optical Properties of Electrons in Matter / Dressel M., GrЁuner G. Cambridge. Univ. Press. 2003. 487 p.Dressel M. Electrodynamics of Solids. Optical Properties of Electrons in Matter / Dressel M., GrЁuner G. Cambridge. Univ. Press. 2003. 487 p.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.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.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.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.Manfredi G. Self-consistent fluid model for a quantum electron gas / Manfredi G. and Haas F. Phys. Rev. B 64 (2001), 075316.Manfredi G. Self-consistent fluid model for a quantum electron gas / Manfredi G. and Haas F. Phys. Rev. B 64 (2001), 075316.Wigner E.P. On the quantum correction for thermodynamic equilibrium / Wigner E.P. Phys. Rev. 40 (1932), 749-759.Wigner E.P. On the quantum correction for thermodynamic equilibrium / Wigner E.P. Phys. Rev. 40 (1932), 749-759.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)].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)].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.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.Arnold A. The electromagnetic Wigner equation for an electron with spin / Arnold A. and SteinrЁuck H. Z. Angew. Math. Phys. 40 (1989), 793-815.Arnold A. The electromagnetic Wigner equation for an electron with spin / Arnold A. and SteinrЁuck H. Z. Angew. Math. Phys. 40 (1989), 793-815.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.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.

The authors declare that there are no conflicts of interest present.