Gross–Tulub polaron functional in the region of intermediate and strong coupling

Abstract

, variational parameters, and the electronphonon interaction parameter α (Fröhlich coupling constant). A simple and exact formula for the recoil energy of the translationally invariant polaron has been derived, which makes it possible to extend the range of admissible values of the parameters of the electron-phonon interaction to the region of extremely strong coupling (α > 10), where. Numerical investigation of different forms of polaron functionals obtained using the field theory methods has been carried out.

Asymptotic dependence of Gross–Tulub polaron ground-state energy in the strong coupling region

“…As was shown in [17], the functionals (10) and (17) . In the same figure, the corresponding dependence for the Feynman polaron energy E F [9] are given for comparison.…”

“…The simple form of the exact functional of translationally invariant polaron was found in [17]. That makes it possible to extend the region of admissible α values for the Gross-Tuloub polaron [6,7] to the strongcoupling region.…”

“…As was shown in [17], the functional (1) was written in [6,7] only for the case when the complex quantity D(s) is located in the first quarter of the complex plane, although the authors of [6,7] do not stipulated this particularity.…”

“…Variation of the exact functional without checking the results of calculations for self-consistency with the range of admissible values of the initial functional can also lead to unreasonably low values of the polaron energy. For example, we vary the Gross-Tulub functional (1) determined, as was shown in [17], only in the first coordinate quarter of the complex plane. Taking (4) into account, we obtain:…”

“…This paper is devoted to investigation of the asymptotic dependence of the polaron energy in the region of the extremely strong coupling. The polaron energy is determined by minimizing the polaron functional obtained in [17].…”