Issues

 / 

2015

 / 

March

  

Reviews of topical problems


Pekar's ansatz and the strong coupling problem in polaron theory


Institute of Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino, Moscow Region, Russian Federation

The translationally invariant polaron theory of Tulub is discussed in detail which makes no use the Pekar's ansatz (believed to provide the asymptotically exact solution in the strong coupling limit) and fundamentally produces a lower-energy polaron than when using the anzatz. In the case of the bipolaron, the theory yields the best values for bonding energy and for critical stability parameters. A variety of physical implications of the existence of translationally invariant polarons and bipolarons are discussed.

Text can be downloaded in Russian. English translation is available here.
Keywords: Froehlich Hamiltonian, Lee—Low—Pines transformation, weak coupling, Bose condensate, F-center
PACS: 71.38.−k, 74.20.−z, 74.72.−h (all)
DOI: 10.3367/UFNe.0185.201503d.0317
URL: https://ufn.ru/en/articles/2015/3/d/
Citation: Lakhno V D "Pekar's ansatz and the strong coupling problem in polaron theory" Phys. Usp. 58 295–308 (2015)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 29th, November 2013, revised: 10th, December 2014, 20th, May 2014

Оригинал: Лахно В Д «Анзац Пекара и проблема сильной связи в теории полярона» УФН 185 317–331 (2015); DOI: 10.3367/UFNr.0185.201503d.0317

References (83) ↓ Cited by (9) Similar articles (20)

  1. Pekar S I Issledovaniya Po Elektronnoi Teorii Kristallov (M. - L.: GITTL, 1951)
  2. Kuper C G, Whitfield G D (Eds) Polarons And Excitons (Edinburgh: Oliver and Boyd, 1963)
  3. Devreese J T (Ed.) Polarons In Ionic Crystals And Polar Semiconductors (Amsterdam: North-Holland, 1972)
  4. Firsov Yu A Polyarony (M.: Nauka, 1975)
  5. Devreese J T, Peeters F (Eds) Polarons And Excitons In Polar Semiconductors And Ionic Crystals (New York: Plenum Press, 1984)
  6. Lakhno V D (Ed.) Polarons And Applications (Chichester: Wiley, 1994)
  7. Devreese J T, Alexandrov A S Rep. Prog. Phys. 72 066501 (2009)
  8. Kashirina N I, Lakhno V D Usp. Fiz. Nauk 180 449 (2010); Kashirina N I, Lakhno V D Phys. Usp. 53 431 (2010)
  9. Emin D Polarons (Cambridge: Cambridge Univ. Press, 2013)
  10. Kashirina N I, Lakhno V D Matematicheskoe Modelirovanie Avtolokalizovannykh Sostoyanii v Kondensirovannykh Sredakh (M.: Fizmatlit, 2013)
  11. Fröhlich H, Pelzer H, Zienau S Philos. Mag. 41 221 (1950)
  12. Pekar S I Zh. Eksp. Teor. Fiz. 16 341 (1946); Pekar S I Zh. Eksp. Teor. Fiz. 16 335 (1946)
  13. Smondyrev M A Teor. Mat. Fiz. 68 29 (1986); Smondyrev M A Theor. Math. Phys. 68 653 (1986)
  14. Selyugin O V, Smondyrev M A Phys. Status Solidi B 155 155 (1989)
  15. Bogolyubov N N Ukr. Mat. Zhurn. 2 (2) 3 (1950)
  16. Tyablikov S V Zh. Eksp. Teor. Fiz. 21 377 (1951)
  17. Miyake S J J. Phys. Soc. Jpn. 38 181 (1975)
  18. Miyake S J J. Phys. Soc. Jpn. 41 747 (1976)
  19. Adamowski J, Gerlach B, Leschke H Phys. Lett. A 79 249 (1980)
  20. Gerlach B, Löwen H Rev. Mod. Phys. 63 63 (1991)
  21. Höhler G Z. Phys. 140 192 (1955)
  22. Allcock G R Adv. Phys. 5 412 (1956)
  23. Gross E P Phys. Rev. 100 1571 (1955)
  24. Buimistrov V M, Pekar S I Zh. Eksp. Teor. Fiz. 33 1271 (1957); Buimistrov V M, Pekar S I Sov. Phys. JETP 6 977 (1958)
  25. Toyozawa Y Prog. Theor. Phys. 26 29 (1961)
  26. Gross E P Ann. Physics 99 1 (1976)
  27. Landau L D, Pekar S I Zh. Eksp. Teor. Fiz. 18 419 (1948)
  28. Bethe H A Intermediate Quantum Mechanics (New York: W.A. Benjamin, 1964); Bete G Kvantovaya Mekhanika (M.: Mir, 1965)
  29. Bohr N, Rosenfeld L Kgl. Danske Vid. Selsk. Math.-Fys. Medd. 12 (8) 1 (1933); Bor N Izbrannye Nauchnye Trudy Vol. 2 (M.: Nauka, 1971)
  30. Lakhno V D Usp. Fiz. Nauk 168 465 (1998); Lakhno V D Phys. Usp. 41 403 (1998)
  31. Tulub A V Vestn. LGU 15 (22) 104 (1960)
  32. Tulub A V Zh. Eksp. Teor. Fiz. 41 1828 (1961); Tulub A V Sov. Phys. JETP 14 1301 (1962)
  33. Kashirina N I, Lakhno V D, Tulub A V Zh. Eksp. Teor. Fiz. 141 994 (2012); Kashirina N I, Lakhno V D, Tulub A V JETP 114 867 (2012)
  34. Heisenberg W Z. Phys. 65 4 (1930)
  35. Lee T D, Low F E, Pines D Phys. Rev. 90 297 (1953)
  36. Wentzel G Helv. Phys. Acta 15 111 (1942)
  37. Porsch M, Röseler J Phys. Status Solidi 23 365 (1967)
  38. Röseler J Phys. Status Solidi 25 311 (1968)
  39. Smondyrev M A, Fomin V M Polarons And Applications (Ed. V D Lakhno) (Chichester: Wiley, 1994) p. 13
  40. Gunnarsson O, Rösch O J. Phys. Condens. Matter 20 043201 (2008)
  41. Vidmar L et al. Phys. Rev. Lett. 103 186401 (2009)
  42. Meevasana W et al. Phys. Rev. B 74 174524 (2006)
  43. Meevasana W et al. Phys. Rev. Lett. 96 157003 (2006)
  44. Mishchenko A S et al. Phys. Rev. Lett. 100 166401 (2008)
  45. Alexandrov A S, Kornilovitch P E Phys. Rev. Lett. 82 807 (1999)
  46. Holstein T Ann. Physics 8 343 (1959)
  47. Lakhno V D Zh. Eksp. Teor. Fiz. 137 926 (2010); Lakhno V D JETP 110 811 (2010)
  48. Lakhno V D Solid State Commun. 152 621 (2012)
  49. Lakhno V D Zh. Eksp. Teor. Fiz. 143 1033 (2013); Lakhno V D JETP 116 892 (2013)
  50. Verbist G, Peeters F M, Devreese J T Phys. Rev. B 43 2712 (1991)
  51. Adamowski J, Bednarek S J. Phys. Condens. Matter 4 2845 (1992)
  52. Kashirina N I, Lakhno V D, Sychyov V V Phys. Status Solidi B 234 563 (2002)
  53. Kashirina N I, Lakhno V D, Sychyov V V Phys. Rev. B 71 134301 (2005)
  54. Suprun S G, Moizhes B Ya Fiz. Tverd. Tela 24 1571 (1982); Suprun S G, Moizhes B Ya Sov. Phys. Solid State 24 903 (1982)
  55. Kashirina N I, Lakhno V D, Sychyov V V Phys. Status Solidi B 239 174 (2003)
  56. Verbist G et al. Phys. Rev. B 45 5262 (1992)
  57. Vansant P et al. J. Phys. A Math. Gen. 27 7925 (1994)
  58. Vinetskii V L, Meredov O, Yanchuk V A Teor. Eksp. Khimiya 25 641 (1989); Vinetskii V L, Meredov O, Yanchuk V A Theor. Exp. Chem. 25 591 (1989)
  59. Aleksandrov A S, Krebs A B Usp. Fiz. Nauk 162 (5) 1 (1992); Alexandrov A S, Krebs A B Sov. Phys. Usp. 35 345 (1992)
  60. Alexandrov A S, Mott N Polarons And Bipolarons (Singapore: World Scientific, 1995)
  61. Tyablikov S V Metody Kvantovoi Teorii Magnetizma (M.: Nauka, 1975); perevod 1-go izd., Tyablikov S V Methods In The Quantum Theory Of Magnetism (New York: Plenum Press, 1967)
  62. Novozhilov Yu V, Tulub A V Usp. Fiz. Nauk 61 53 (1957)
  63. Novozhilov Y V, Tulub A V The Method Of Functionals In The Quantum Theory Of Fields (New York: Gordon and Beach, 1961)
  64. Klimin S N, Devreese J T Solis State Commun. 152 1601 (2012)
  65. Klimin S N, Devreese J T Solid State Commun. 153 58 (2013)
  66. Lakhno V D Solid State Commun. 152 1855 (2012)
  67. Lakhno V D arXiv:1211.0382
  68. Lakhno V D, Chuev G N Usp. Fiz. Nauk 165 285 (1995); Lakhno V D, Chuev G N Phys. Usp. 38 273 (1995)
  69. Marchand D J J et al. Phys. Rev. Lett. 105 266605 (2010)
  70. Hague J P, Kornilovitch P E, Alexandrov A S Phys. Rev. B 78 092302 (2008)
  71. Mishchenko A S et al. Phys. Rev. B 79 180301(R) (2009)
  72. Ebrahimnejad H, Berciu M Phys. Rev. B 85 165117 (2012)
  73. Lakhno V D Prog. Theor. Exp. Phys. 2014 073I01 (2014)
  74. Schultz T D Phys. Rev. 116 526 (1959)
  75. Kittel Ch Quantum Theory Of Solids (New York: Wiley, 1963); Kittel’ Ch Kvantovaya Teoriya Tverdykh Tel (M.: Nauka, 1967)
  76. Grib A A Usp. Fiz. Nauk 183 1337 (2013); Grib A A Phys. Usp. 56 1230 (2013)
  77. Feynman R P Phys. Rev. 97 660 (1955); Feynman R P Statistical Mechanics (Reading, Mass.: W.A. Benjamin, 1972); Feinman R Statisticheskaya Mekhanika (M.: Mir, 1975)
  78. Rajaraman R Solitons And Instantons: An Introduction To Solitons And Instantons In Quantum Field Theory (Amsterdam: North-Holland, 1982); Radzharaman R Solitony i Instantony v Kvantovoi Teorii Polya (M.: Mir, 1985)
  79. Gerlach B, Löwen H Phys. Rev. B 37 8042 (1988)
  80. Mishchenko A S Usp. Fiz. Nauk 175 925 (2005); Mishchenko A S Phys. Usp. 48 887 (2005)
  81. Kashurnikov V A, Krasavin A V Chislennye Metody Kvantovoi Statistiki (M.: Fizmatlit, 2010)
  82. Landau L D Phys. Z. Sowjetunion 3 644 (1933); Landau L D Sobranie Trudov Vol. 1 (M.: Nauka, 1969) p. 90
  83. Iwao S Lett. Nuovo Cimento 15 331 (1976)

© 1918–2019 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions