The unitary operator form of the general Bogolyubov-Tyablikov transformation

É. A. Arinshtein

O. D. Timofeevskaya

Fan Hong-Yi, Jack Vanderlinde

The Bogolyubov transformation (1958) frequently used in dealing with pairing interactions of fermions, is extended to allow for binary coupling between any (even) number of fermions by using a matrix transformation 'coefficient'. The corresponding quasiparticles and quasi-vacuum state are derived. The normally ordered expansion of the unitary generalized Bogolyubov operator is obtained by application of the technique of integration within an ordered product (IWOP) for the fermion system.

Fan Hong-Yi

The formalism of the generalized fermionic Bogolyubov transformation, previously by Fan and VanderLinde (1990), is extended to the bosonic case. The corresponding bosonic quasi-particle and quasi-vacuum state are derived; the bosonic generalized Bogolyubov operator is decomposed as a normal product form by the technique of integration within an ordered product (IWOP).

W S Liu, Paolo Tombesi

The generalized single-mode and two-mode squeeze operators are diagonalized by employing Bogolyubov and Bogolyubov-Valatin transformations, and the unitary operators performing these transformations are derived. The authors find that the eigenvalues are complex exponential functions with the exponential factors of harmonic-oscillator spectra and the eigenstates are a new kind of squeezed number state different from the ordinary squeezed number states.