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Non-perturbative Description of Quantum Systems pp 331–358Cite as

Systems with Infinite Number of Degrees of Freedom

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Part of the Lecture Notes in Physics book series (LNP,volume 894)

Abstract

This chapter is dedicated to the applications of operator method for the analysis of propagation of electron in ionic crystal, called often as propagation of polaron of a large radius. This task is qualitatively distinguishable from the ones discussed in previous chapters by the fact that Hamiltonian includes the interaction of electron with the system possessing infinite degrees of freedom and describing the phonon field of the lattice vibration. A similar problem arises for the systems, which require the self-consistent description of objects with external media, and the significance of polaron covers much wider area than the description of the interaction between electrons and phonons initially constructed by Fröhlich [1].

Keywords

  • Phonon Field
  • Optical Polaron
  • Strong-coupling Polaron
  • Polaron Ground State
  • Polaron Effective Mass

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. H. Fröhlich, Adv. Phys. 3, 325 (1950)

    CrossRef  ADS  Google Scholar 

  2. Y.A. Firsov, Polarons, Ed. (in Russian) (Nauka, Moscow, 1975)

    Google Scholar 

  3. T.K. Mitra, A. Chatterjee, Mikhopadhyay, Phys. Rep. 153, 91 (1987)

    CrossRef  ADS  Google Scholar 

  4. A.S. Alexandrov, N. Mott, Polarons and Bipolarons (World Scientific, Singapore, 1996)

    CrossRef  Google Scholar 

  5. J.T. Devreese, A.S. Alexandrov, Rep. Progr. Phys. 72, 066501 (2009)

    CrossRef  ADS  Google Scholar 

  6. S.I. Pekar, Zh. Exper. Theor. Fiziki (in Russian) 16, 341 (1946)

    Google Scholar 

  7. N.N. Bogoliubov, Matemat. Zh (in Russian) 2, 3 (1950)

    Google Scholar 

  8. N.N. Bogolubov, Selected Works, v.2, p.499 (in russian) (Navukova Dumka, Kiev, 1972)

    Google Scholar 

  9. S.V. Tyablikov, Zh. Exper. Theor. Fiziki (in Russian) 21, 377 (1952)

    Google Scholar 

  10. I.D. Feranchuk, L.I. Komarov, J. Phys. C Solid State Phys. 15, 1965 (1982)

    CrossRef  ADS  Google Scholar 

  11. R.P. Feynman, Phys. Rev. 97, 660 (1955)

    CrossRef  ADS  MATH  Google Scholar 

  12. A.S. Mishchenko, N.V. Prokof’ev, A. Sakamoto, B.V. Svistunov, Phys. Rev. B 62, 6317 (2000)

    Google Scholar 

  13. I.D. Feranchuk, P.A. Khomyakov, Nonlinear Phenom. Complex Syst. 4, 347 (2001)

    Google Scholar 

  14. I.D. Feranchuk, S.I. Fisher, L.I. Komarov, J. Phys. C Solid State Phys. 18, 5083 (1985)

    CrossRef  ADS  Google Scholar 

  15. B. Gerlach, H. Löwen, Rev. Mod. Phys. 63, 63 (1991)

    CrossRef  ADS  Google Scholar 

  16. G.D. Fillipis, V. Gataudella, V.M. Ramaglia, C.A. Perroni, D. Bersioux, Eur. Phys. J. B 36, 65 (2003)

    CrossRef  ADS  Google Scholar 

  17. I.D. Feranchuk, L.I. Komarov, arxiv.org. cond-mat., 0510510 (2005)

    Google Scholar 

  18. P.A. Khomyakov, Development and Application of the Operator Method for Quantum Systems with many Degrees of Freedom (in Russian), PhD Thesis, Belarusian University, 2001

    Google Scholar 

  19. P.A. Khomyakov, Phys. Rev. B 63, 153405 (2001)

    CrossRef  ADS  Google Scholar 

  20. M.H. Degani, G.A. Farias, Phys. Rev. B 42, 11950 (1990)

    CrossRef  ADS  Google Scholar 

  21. F.M. Peeters, M.A. Smondyrev, Phys. Rev. B 43, 4920 (1991)

    CrossRef  ADS  Google Scholar 

  22. T.D. Lee, F.M. Low, D. Pines, Phys. Rev. 90, 297 (1953)

    CrossRef  ADS  MATH  MathSciNet  Google Scholar 

  23. P.M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953)

    MATH  Google Scholar 

  24. K.P. Huber, G. Gerzberg, Molecular Spectra and Molecular Structure. vol. 4 Constants of Diatomic Molecules (Van Rostrand Reinhold, New York, 1979)

    Google Scholar 

  25. J.T. Devreese, Encyclopedia of Applied Physics, vol. 14 (Wiley-VCH, New York, 1996), p. 383

    Google Scholar 

  26. R. Evrard, Phys. Lett. 14, 295 (1965)

    CrossRef  ADS  Google Scholar 

  27. L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Fizmatgiz, Moscow, 2004)

    Google Scholar 

  28. A.-T. Le, L.I. Komarov, J. Phys. C Cond. Matt. 11, 11679 (1998)

    Google Scholar 

  29. N.N. Bogoliubov, Preprint JINR (in Russian) R-1451, 1 (1963)

    Google Scholar 

  30. N.W. Ashcroft, N.D. Mermin, Solid State Physics (Holt and Rinehart and Winsto, New York, 1976)

    Google Scholar 

  31. A.I. Akhiezer, V.B. Beresteckij, Quantum Electrodynamics, 3rd edn. (Nauka, Moscow, 1969)

    Google Scholar 

  32. L.D. Landau, E.M. Lifshitz, Quantum Electrodynamics, 1st edn. (Pergamon, New York, 1971)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Physics Department, Belarusian State University, Minsk, Belarus

    Ilya Feranchuk

  2. Physics Department, Belarusian National Technical University, Minsk, Belarus

    Alexey Ivanov

  3. Department of Physics, Ho Chi Minh City University of Pedagogy, Ho Chi Minh City, Vietnam

    Van-Hoang Le

  4. Atomicus GmbH, Karlsruhe, Germany

    Alexander Ulyanenkov

Authors
  1. Ilya Feranchuk
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  2. Alexey Ivanov
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  3. Van-Hoang Le
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  4. Alexander Ulyanenkov
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Feranchuk, I., Ivanov, A., Le, VH., Ulyanenkov, A. (2015). Systems with Infinite Number of Degrees of Freedom. In: Non-perturbative Description of Quantum Systems. Lecture Notes in Physics, vol 894. Springer, Cham. https://doi.org/10.1007/978-3-319-13006-4_9

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