A New Variational Ansatz in the Polaron Theory

И. Д. Феранчук, L I Komarov

New variational ansatz for the large-radius Fröhlich polaron is considered. The corresponding operator estimation for the energy of polaron proves to be very similar to the result found by Feynman on the basis of the variational principle for the functional integral of the system. It allows us to make clear the problem of ``phase transition'' and to anylize the structure of the localized state of the polaron in the intermediate coupling regime. It is shown that the analogous state exists also for the model of particle-field interaction with the divergent perturbation theory.

Nikolay N. Bogolubov, Nikolay N. Bogolubov

Nikolay N. Bogolubov, Nikolay N. Bogolubov

J. Röseler

Abstract A new translational invariant variational statement is given, which is exact to the order α2 for weak coupling and which is in the limiting case of strong coupling regarding the polaron self‐energy not poorer as‐0.105 α2 h ω. In the limiting case of weak coupling the polaron mass, the contributions to the self‐energy due to the individual components of Fröhlich's Hamiltonian, and up to the order α2 the mean value of virtual phonons in the ground state are exactly calculated.

Nikolay N. Bogolubov, V. N. Plechko

Pang Xiao‐feng

The influences of the squeezing–antisqueezing effect arising from variations of the electron density and motion of polarons and nonadiabatic phonon fluctuations on the properties of the ground state and the binding energy of the polaron in the Holstein model of coupled one-dimensional electron–phonon systems with spin 1/2 in the cases of high and low electron densities have been studied by using the Bogolyubov transformation and a new ansatz for states that includes correlation effects among the one-phonon coherent and two-phonon squeezed and polaronic states. The results obtained show that the squeezing–antisqueezing (correlation) effect results in that the ground state energy of the systems is significantly lowered, and the binding energy of the polaron is considerably increased. Thus, the stability of the systems and of the polaron are obviously enhanced in such a case when compared with the uncorrelated case. This shows that the ground state determined by the new state ansatz is most stable, and the new ansatz introduced here is very relevant for the coupled electron–phonon systems, especially in strongly coupled and largely squeezed cases.