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 (166) ↓ Similar articles (20)

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