Condensed Matter Physics, 2010, vol. 13, No. 2, p. 23703:1-10

Title: The Bogolubov representation of the polaron model and its completely integrable RPA-approximation
  N.N.Bogolubov (jr.) (Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russian Federation,Abdus Salam International Centre for Theoretical Physics, Trieste, Italy) ,
  Ya.A. Prykarpatsky (Institute of Mathematics, Pedagogical University of Cracow, Poland,Drohobych Ivan Franko State Pedagogical University, Lviv region, Ukraine) ,
  A.A. Ghazaryan (The Lomonosov Moscow State University, Department of Physics, Moscow, Russian Federation)

The polaron model in ionic crystal is studied in the Bogolubov representation using a special RPA-approximation. A new exactly solvable approximated polaron model is derived and described in detail. Its free energy at finite temperature is calculated analytically. The polaron free energy in the constant magnetic field at finite temperature is also discussed. Based on the structure of the Bogolubov unitary transformed polaron Hamiltonian there is stated a very important new result: the full polaron model is exactly solvable.

Key words: polaron, polaron model, constant magnetic field, RPA-approximation
PACS: 71.38.+i

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