The virial theorem and the ground state problem in polaron theory

Abstract

The virial theorem for the translation invariant theory of a polaron [3] is discussed. It is shown that, in [3], Tulub made a nonoptimal choice of variational parameters in the strong coupling limit, which led to the violation of the virial relations. The introduction of an additional variational parameter to the test function reduces the polaron energy and makes it possible to satisfy the relations of the virial theorem for a strong coupling polaron (the Pekar 1 : 2 : 3 : 4 theorem).

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

“…At the same time, for a two-parameter function (8) numerical verification showed that the known relations 1:3:4 of the virial theorem [21], which do not depend on the electronphonon interaction, are satisfied to within 7 significant digits. For the functional (13), the variation of which leads to a quadratic dependence on the parameter α , the Pekar theorem for the strong coupling polaron 1:2:3:4 holds [19]. We verify the fulfillment of the virial theorem for the functional (20).…”

“…(8), since it was shown in [19] that the one-parameter function f k (5) is not enough flexible to satisfy the virial relations of the polaron theory [1].…”

A translation invariant bipolaron in the Holstein model and superconductivity

“…(2012) a concept of translation invariant polarons and bipolarons was introduced. Under certain conditions these quasiparticles can possess superconducting properties even if they do not form a Bose condensate.…”

“…Papers Tulub (1962), Lakhno (2010, 2012, 2013) and Kashirina et al. (2012) dealt with three-dimensional translation-invariant polarons and bipolarons. In the context of the aforesaid it would be interesting to consider the conditions under which translation invariant bipolarons arise in low-dimensional systems.…”

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

“…has the form: 7], where N and a are the variational parameters. After calculating the integrals included in the expression (11), we obtain: (20)…”