RSS feeds
ÐóññêèéEnglish
Issue 6, 2026
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

1968

 / 

June

←  →

Reviews of topical problems


The vibrational properties of an electron gas


1. Statement of the problem 721
2. Initial equations and their simplification 722
3. Solution of the linearized equations 724
4. Dispersion of longitudinal waves 728
5. Dispersion of longitudinal waves in an electron gas with a Fermi distribution function 730
6. Dispersion of transverse waves 732
7. Summary and conclusion 733

Fulltext pdf (1.2 MB)
Fulltext is also available at DOI: 10.1070/PU1968v010n06ABEH003709
PACS: 52.35.−g, 52.25.Fi (all)
DOI: 10.1070/PU1968v010n06ABEH003709
URL: https://ufn.ru/en/articles/1968/6/a/
Citation: Vlasov A A "The vibrational properties of an electron gas" Sov. Phys. Usp. 10 721–733 (1968)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Îðèãèíàë: Âëàñîâ À À «Î âèáðàöèîííûõ ñâîéñòâàõ ýëåêòðîííîãî ãàçà» ÓÔÍ 93 444–470 (1967); DOI: 10.3367/UFNr.0093.196711f.0444

Cited by (172) ↓ Similar articles (20)

  1. Shi L, Shen Ju, Lu K Sci. China Math. (2026)
  2. Bellingeri C, Coppini F Bernoulli 32 (3) (2026)
  3. Fiorillo D F G, Raffelt G G J. High Energ. Phys. 2026 (1) (2026)
  4. Steinhöfel T, Boltz H-H, Ihle T Eur. Phys. J. Spec. Top. (2026)
  5. Abramov R V J. Phys. A: Math. Theor. 59 (21) 215701 (2026)
  6. Anh B T, Thinh D X, Merz K Nonlinearity 39 (1) 015021 (2026)
  7. Vos M, Grande P L Nuclear Instruments And Methods In Physics Research Section B: Beam Interactions With Materials And Atoms 573 166046 (2026)
  8. Matus P Phys. Rev. B 113 (7) (2026)
  9. Chacón-Lavanderos Ja, Gómez-Vargas I et al Phys. Rev. D 113 (6) (2026)
  10. Kato Y, Mima K, Bulanov S Springer Series On Atomic, Optical, And Plasma Physics Vol. High Power Laser and Plasma SciencePlasma Kinetic Theory130 Chapter 9 (2026) p. 329
  11. McGrae-Menge M C, Pierce J R et al Phys. Rev. Research 8 (1) (2026)
  12. Bell D, Campos P M et al Journal Of Computational Physics 555 114765 (2026)
  13. Zeng T, Li R, Li D Math Methods In App Sciences (2026)
  14. Tahmasebi M Math Finan Econ (2026)
  15. Prömel D J, Scheffels D J. Appl. Probab. 1 (2026)
  16. Bellomo N, Burini D, Liao J Math. Models Methods Appl. Sci. 36 (02) 341 (2026)
  17. Shi L, Shen Ju, Wang B Journal Of Differential Equations 453 113855 (2026)
  18. Giachetti G, Defenu N Phys. Rev. B 111 (21) (2025)
  19. Borzì A, Infante G, Mascali G SIAM J. Appl. Math. 85 (1) 143 (2025)
  20. SHI C, WANG W ANZIAM J. 67 (2025)
  21. Barsuk A A, Paladi F Eur. Phys. J. D 79 (1) (2025)
  22. Bachhawat N, Litvinenko V Phys. Rev. Accel. Beams 28 (10) (2025)
  23. Huang Ya, Li M, Liu W Potential Anal 63 (1) 329 (2025)
  24. Zhao T, Zhen M 2025 44th Chinese Control Conference (CCC), (2025) p. 1704
  25. Cao S H, Munasinghe S et al Physics of Plasmas 32 (4) (2025)
  26. Lobo A, Sayal V K Eur. Phys. J. Plus 140 (2) (2025)
  27. Chizhonkov E V Comput. Math. And Math. Phys. 65 (12) 2959 (2025)
  28. Bresch D, Jabin P-E, Soler Ju Analysis & PDE 18 (4) 1037 (2025)
  29. Cherepanov V V Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya «Fiziko-matematicheskie Nauki» 29 (3) 516 (2025)
  30. Bollweg K-W G, Meyer-Brandis T PUQR 10 (2) 241 (2025)
  31. Li J, Liu W et al Communications In Nonlinear Science And Numerical Simulation 142 108535 (2025)
  32. Barbour N, Dorland W et al J. Plasma Phys. 91 (5) (2025)
  33. Chen Ju, Qiu Zh, Tang Ya Journal Of Differential Equations 423 41 (2025)
  34. Adams M F, Wang P et al SIAM J. Sci. Comput. 47 (2) B360 (2025)
  35. Wang 王 Ya 彦, Wu 吴 Sh 士, Fan 范 P 培 Chinese Phys. B 34 (6) 065201 (2025)
  36. Zhang T, Xu Y et al Qual. Theory Dyn. Syst. 24 (1) (2025)
  37. Wu S, Li Ya et al Journal of Applied Physics 137 (20) (2025)
  38. Kalinin A, Meyer-Brandis T, Proske F Stoch. Dyn. 24 (05) (2024)
  39. Hong W, Hu Sh, Liu W Ann. Appl. Probab. 34 (2) (2024)
  40. Jin Z, Li R Res Math Sci 11 (3) (2024)
  41. Boukaram W, Hong Yu et al The International Journal Of High Performance Computing Applications 38 (6) 585 (2024)
  42. Chizhonkov E V Russian Journal of Numerical Analysis and Mathematical Modelling 39 (1) 13 (2024)
  43. Guzmán J G A, Florinski V et al ApJS 272 (2) 46 (2024)
  44. Hao Z, Zhang X et al Ann. Probab. 52 (2) (2024)
  45. Touati A B, Boutabia H, Redjil A Lobachevskii J Math 45 (3) 1296 (2024)
  46. Snytnikov A V, Ezrokh Yu S Lobachevskii J Math 45 (7) 3416 (2024)
  47. Andreev P A Physics of Plasmas 31 (4) (2024)
  48. Mushtaq H, Singh K et al Sci Rep 14 (1) (2024)
  49. Benilov E S Physics of Fluids 36 (3) (2024)
  50. Dieye M, Diop A et al Stochastics 96 (4) 1388 (2024)
  51. Pongsangangan K, Cosme P et al Phys. Rev. B 110 (4) (2024)
  52. Chizhonkov E V Comput. Math. And Math. Phys. 64 (7) 1537 (2024) [Chijonkov E V Žurnal Vyčislitelʹnoj Matematiki I Matematičeskoj Fiziki 64 (7) 1268 (2024)]
  53. Shen Y, YuChih Ho-Yun, Chen B Phys. Rev. D 110 (12) (2024)
  54. Veretennikov A Stoch. Dyn. 24 (05) (2024)
  55. Lobo A, Sayal V K Physics of Plasmas 31 (9) (2024)
  56. Kalinin A, Meyer-Brandis T, Proske F J Theor Probab 37 (4) 2941 (2024)
  57. Barbu V, Röckner M Probab. Theory Relat. Fields 189 (3-4) 849 (2024)
  58. Chen T, Wang Ch, Liu T International Journal Of Multiphase Flow 172 104705 (2024)
  59. Velozo R A, Velozo R R Commun. Math. Phys. 405 (3) (2024)
  60. Cissé A, Boutayeb M Communications In Nonlinear Science And Numerical Simulation 130 107751 (2024)
  61. Jing Y, Litvinenko V N et al Physics 6 (3) 921 (2024)
  62. Rosenfeld E V Physics of Plasmas 31 (7) (2024)
  63. Bahsoun W, Liverani C, Sélley F M Commun. Math. Phys. 400 (3) 1791 (2023)
  64. Kokovin A O, Kozhevnikov V Yu et al Izvestiâ Akademii Nauk. Rossijskaâ Akademiâ Nauk. Mehanika židkosti I Gaza (6) 183 (2023)
  65. Bobylev A, Potapenko I KRM 16 (1) 20 (2023)
  66. Barbu V, Röckner M Journal Of Functional Analysis 285 (4) 109980 (2023)
  67. Ghosh I, Saxena V, Krishnamachari A 2023 International Conference on Device Intelligence, Computing and Communication Technologies, (DICCT), (2023) p. 520
  68. Bezrodnykh S I, Gordeeva N M Russ. J. Math. Phys. 30 (4) 443 (2023)
  69. Fairushin I I, Mokshin A V Phys. Rev. E 108 (1) (2023)
  70. Litvinenko V N, Jing Y et al Phys. Rev. Accel. Beams 26 (5) (2023)
  71. Kozhevnikov V Yu, Kozyrev A V et al Fluid Dyn 58 (6) 1148 (2023)
  72. Lazarovici D Typicality Reasoning in Probability, Physics, and Metaphysics New Directions In The Philosophy Of Science Chapter 10 (2023) p. 175
  73. Crisan D, Holm D D, Korn P Nonlinearity 36 (9) 4862 (2023)
  74. Chen T, Zhang Ch, Wang L-P Phys. Rev. E 107 (2) (2023)
  75. ÇOKSAK ER Derya Hacettepe Journal of Mathematics and Statistics 52 (4) 983 (2023)
  76. Chen T, Wu L et al International Journal Of Multiphase Flow 164 104451 (2023)
  77. Chizhonkov E V, Frolov A A Russian Journal of Numerical Analysis and Mathematical Modelling 38 (2) 63 (2023)
  78. Skubachevskii A L Diff Equat 59 (11) 1473 (2023)
  79. Guillin A, Le Bris P, Monmarché P Electron. J. Probab. 27 (none) (2022)
  80. Adams M F, Brennan D P et al 2022 IEEE International Parallel and Distributed Processing Symposium (IPDPS), (2022) p. 115
  81. Schilling T Physics Reports 972 1 (2022)
  82. Dieye M, Diop A, Mckibben M A Stoch. Dyn. 22 (05) (2022)
  83. Maquart T, Noël R et al Applied Sciences 12 (9) 4627 (2022)
  84. Kozhevnikov V, Kozyrev A et al Vojnotehnički Glasnik 70 (3) 650 (2022)
  85. Tian J, Anderson G E et al Monthly Notices of the Royal Astronomical Society 514 (2) 2756 (2022)
  86. Vedenyapin V V, Fimin N N, Chechetkin V M Eur. Phys. J. Plus 137 (9) (2022)
  87. Abramov R V Phys. Rev. Fluids 7 (5) (2022)
  88. Pongsangangan K, Grubinskas S, Fritz L Phys. Rev. Research 4 (4) (2022)
  89. Cordonnier A, Leoncini X et al Phys. Rev. E 106 (6) (2022)
  90. Pongsangangan K, Ludwig T et al Phys. Rev. B 106 (20) (2022)
  91. Belov A A, Loza O T et al Discrete And Continuous Models 30 (3) 217 (2022)
  92. Bedrossian Ja Tunisian J. Math. 3 (1) 121 (2021)
  93. Filippov A V J. Exp. Theor. Phys. 132 (1) 148 (2021)
  94. Röckner M, Zhang X Bernoulli 27 (2) (2021)
  95. Kozhevnikov V, Kozyrev A et al Energies 14 (22) 7608 (2021)
  96. Lv L, Zhang Ya, Wang Z Chaos: An Interdisciplinary Journal of Nonlinear Science 31 (5) (2021)
  97. Mezerdi M A Optim Control Appl Methods 42 (4) 1161 (2021)
  98. Kiselev E I Phys. Rev. B 103 (23) (2021)
  99. Gunell H Magnetospheres in the Solar System Geophysical Monograph Series 1 (2021) p. 37
  100. Mezerdi M A, Khelfallah N Random Operators and Stochastic Equations 29 (1) 67 (2021)
  101. Gorelenkov N N, Sharapov S E Encyclopedia of Nuclear Energy (2021) p. 459
  102. Huang X, Song Yu Nonlinear Analysis 203 112167 (2021)
  103. Kiramov D I, Breizman B N Physics of Plasmas 27 (2) (2020)
  104. Bahlali Kh, Mezerdi M A, Mezerdi B Stoch. Dyn. 20 (01) 2050007 (2020)
  105. BEIKIRCH MAXIMILIAN, CRAMER SIMON et al Advs. Complex Syst. 23 (06) 2050017 (2020)
  106. Métivier D, Chertkov M Phys. Rev. E 101 (2) (2020)
  107. Vynnyk O K, Anisimov I O Problems of Atomic Science and Technology 59 (2020)
  108. Shohet G, Price Ja et al Journal Of Computational Physics: X 8 100070 (2020)
  109. Lentz E W, Quinn T R, Rosenberg L J Nuclear Physics B 952 114937 (2020)
  110. Kiselev E I, Schmalian J Phys. Rev. B 102 (24) (2020)
  111. Chen L, Li X et al Journal of Mathematical Physics 61 (6) (2020)
  112. Laribi E, Ogawa Sh et al Fluids 4 (3) 172 (2019)
  113. Rukhadze A A, Silin V P Uspekhi Fizicheskikh Nauk 189 (07) 739 (2019) [Rukhadze A A, Silin V P Phys.-Usp. 62 (7) 691 (2019)]
  114. Woods B J Q Plasma Res. Express 1 (4) 045003 (2019)
  115. Knopf P Math Methods In App Sciences 42 (18) 6369 (2019)
  116. Benilov E S, Benilov M S Phys. Rev. E 99 (1) (2019)
  117. Bauer M, Meyer-Brandis T, Proske F Electron. J. Probab. 23 (none) (2018)
  118. Benilov E S, Benilov M S Phys. Rev. E 97 (6) (2018)
  119. Allanson O Theory of One-Dimensional Vlasov-Maxwell Equilibria Springer Theses Chapter 1 (2018) p. 1
  120. Chen L, Siedentop H Journal of Mathematical Physics 59 (5) (2018)
  121. Golovanov A A, Kostyukov I Yu Physics of Plasmas 25 (10) (2018)
  122. Allanson O, Troscheit S, Neukirch T IMA Journal of Applied Mathematics 83 (5) 849 (2018)
  123. Morse E Nuclear Fusion Graduate Texts In Physics Chapter 3 (2018) p. 39
  124. Jabin P-E, Wang Zh Active Particles, Volume 1 Modeling And Simulation In Science, Engineering And Technology Chapter 10 (2017) p. 379
  125. Sulaiman A H The Near-Saturn Magnetic Field Environment Springer Theses Chapter 1 (2017) p. 1
  126. Silantyev D A, Lushnikov P M, Rose H A Physics of Plasmas 24 (4) (2017)
  127. Benilov E S, Benilov M S Phys. Rev. E 96 (4) (2017)
  128. Kolesnichenko A V KIAM Prepr. (43) 1 (2017)
  129. Pike O Ja Particle Interactions in High-Temperature Plasmas Springer Theses Chapter 2 (2017) p. 17
  130. Dehghan M, Abbaszadeh M Engineering With Computers 33 (4) 961 (2017)
  131. Pulvirenti M, Simonella S Math. Mech. Compl. Sys. 4 (3-4) 255 (2016)
  132. Webb S D Journal of Mathematical Physics 57 (4) (2016)
  133. Wesp Ch, van Hees H et al Phys. Rev. E 91 (4) (2015)
  134. Elizarov A, Litvinenko V Phys. Rev. ST Accel. Beams 18 (4) (2015)
  135. Sykes A G, Bohn J L Phys. Rev. A 91 (1) (2015)
  136. Sasorov P V, Fomin I V J. Exp. Theor. Phys. 120 (6) 1101 (2015)
  137. Jabin P-E Kinetic & Related Models 7 (4) 661 (2014)
  138. Balakin A B, Muharlyamov R K, Zayats A E Eur. Phys. J. D 68 (6) (2014)
  139. Balakin A B, Muharlyamov R K, Zayats A E Class. Quantum Grav. 31 (2) 025005 (2014)
  140. Kalman G J, Donkó Z et al EPL 107 (3) 35001 (2014)
  141. Ivanov A Yu, Andreev P A, Kuz’menkov L S Int. J. Mod. Phys. B 28 (21) 1450132 (2014)
  142. Jenab S M H, Kourakis I Eur. Phys. J. D 68 (8) (2014)
  143. Sereda Yu V, Ortoleva P J The Journal of Chemical Physics 140 (13) (2014)
  144. Andreev P A Annals Of Physics 350 198 (2014)
  145. Lushnikov P M, Rose H A et al Physics of Plasmas 21 (7) (2014)
  146. Hosseini Je S M, Kourakis I Physics of Plasmas 21 (4) (2014)
  147. Pavelka M, Klika V, Grmela M Phys. Rev. E 90 (6) (2014)
  148. Nungesser E J. Phys.: Conf. Ser. 453 012008 (2013)
  149. Sereda Yu V, Ortoleva P J Physica A: Statistical Mechanics And Its Applications 392 (4) 628 (2013)
  150. Chesnokov A A, Khe A K Stud Appl Math 131 (4) 343 (2013)
  151. Andreev P A, Kuz’menkov L S Eur. Phys. J. D 67 (10) (2013)
  152. Elizarov A, Litvinenko V Phys. Rev. ST Accel. Beams 16 (12) (2013)
  153. Thomas A G R, Tzoufras M et al Journal Of Computational Physics 231 (3) 1051 (2012)
  154. Webb S, Litvinenko V N, Wang G Phys. Rev. ST Accel. Beams 15 (8) (2012)
  155. Huang D, Gumbs G, Roslyak O Journal Of Modern Optics 58 (21) 1898 (2011)
  156. Khorashadizadeh S M, Niknam A R, Haghtalab T Physics Of Plasmas 18 (6) 063703 (2011)
  157. Webb S, Wang G, Litvinenko V Phys. Rev. ST Accel. Beams 14 (5) (2011)
  158. Rose H A, Daughton W Physics of Plasmas 18 (12) (2011)
  159. Hosseini Je S M, Kourakis I, Abbasi H Physics of Plasmas 18 (7) (2011)
  160. Johnson R W Mechanics Research Communications 38 (2) 146 (2011)
  161. Johnson R W Mechanics Research Communications 37 (4) 427 (2010)
  162. Tarasov V E Nonlinear Physical Science Vol. Fractional DynamicsFractional Statistical Mechanics0 Chapter 15 (2010) p. 335
  163. Magnus W, Brosens F, Sorée B J Comput Electron 8 (3-4) 307 (2009)
  164. Valenti D, Shubov M International Journal Of Mathematics And Mathematical Sciences 2009 (1) (2009)
  165. Filippov A V, Zagorodny A G et al J. Exp. Theor. Phys. 104 (1) 147 (2007)
  166. Muralidhar Y, Jain P K, Basu B N IEEE Trans. Electron Devices 47 (3) 634 (2000)
  167. Rao S J, Jain P K, Basu B N IEEE Trans. Electron Devices 43 (12) 2290 (1996)
  168. Hong J, Kim Ch Phys. Rev. A 43 (4) 1965 (1991)
  169. Baus M Phys. Rev. A 15 (2) 790 (1977)
  170. Zubarev Yu M, Smirnov V A Fluid Dyn 9 (4) 610 (1974)
  171. Drummond J IRE Trans. Antennas Propag. 10 (1) 4 (1962)
  172. Osborn R IRE Trans. Antennas Propag. 10 (1) 8 (1962)
© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions