Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1310.0246 · Journal of Experimental and Theoretical Physics

The virial theorem and the ground state problem in polaron theory

N. I. Kashirina, Victor Dmitrievich Lakhno, A. V. Tulub

Published May 1, 2012• 23 citations
arXivHTMLPDF

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).

DOI
10.1134/s1063776112030065

Related papers

2 Pekar’s ansatz and the strong coupling problem in polaron theory

Victor Dmitrievich Lakhno

A detailed consideration is given to the translation-invariant theory of Tulub polaron constructed without the use of Pekar ansatz.A fundamental result of the theory is that the value of the polaron energy is lower than that obtained on the basis of Pekar ansatz which was considered as an asymptotically exact solution in the strong coupling limit.In the case of bipolarons the theory yields the best values of the coupling energy and critical parameters of their stability.Numerous physical consequences of the existence of translation-invariant polarons and bipolarons are discussed.

De Gruyter eBooks•Jul 18, 2022•0 citations

Pekar's ansatz and the strong coupling problem in polaron theory

V D Lakhno

A detailed consideration is given to the translation-invariant theory of Tulub polaron constructed without the use of Pekar ansatz. A fundamental result of the theory is that the value of the polaron energy is lower than that obtained on the basis of Pekar ansatz which was considered as an asymptotically exact solution in the strong coupling limit. In the case of bipolarons the theory yields the best values of the coupling energy and critical parameters of their stability. Numerous physical consequences of the existence of translation-invariant polarons and bipolarons are discussed.

arXiv:1505.01699•Physics-Uspekhi•Mar 8, 2015•31 citations

Reply to “On the cutoff parameter in the translation-invariant theory of the strong coupling polaron”

Serghei N. Klimin, J. T. Devreese

The present work is a reply to the paper [1]. It is proven that the argumentation of Refs. [1] is inconsistent. The variational functional for the polaron ground state energy considered in Ref. [1] contains an incomplete recoil energy. Since the variational functional of Ref. [1] is incomplete, it is not proven to provide a variational upper bound for the polaron ground-state energy. The same conclusion follows also for the bipolaron ground-state energy.

arXiv:1208.1166•Solid State Communications•Oct 16, 2012•10 citations

Comments on “Translation-invariant bipolarons and the problem of high-temperature superconductivity”

Serghei N. Klimin, J. T. Devreese

We comment on the recent results of Refs. [1], [2] on the bipolaron problem derived using an approximation of Gross–Tulub. It is proved that, contrary to the claim made in Refs. [1], [2], the bipolaron ground-state energy calculated there in the strong-coupling approximation has not been shown to constitute a variational upper bound.

arXiv:1204.4142•Solid State Communications•May 21, 2012•9 citations

Large-radius Holstein polaron and the problem of spontaneous symmetry breaking

V. D. Lakhno

A translation-invariant solution is found for a large-radius Holstein polaron whose energy in the strong coupling limit is lower than that obtained by Holstein. The wave function corresponding to this solution is delocalized. A conclusion is made about the absence of a spontaneous symmetry breaking in the quantum system discussed.

arXiv:1403.2920•Progress of Theoretical and Experimental Physics•Jul 1, 2014•7 citations

3 Large-radius Holstein polaron and the problem of spontaneous symmetry breaking

Victor Dmitrievich Lakhno

A translation-invariant solution is found for a large-radius Holstein polaron whose energy in the strong coupling limit is lower than that obtained by Holstein.The wave function corresponding to this solution is delocalized.A conclusion is made about the absence of a spontaneous symmetry breaking in the quantum system discussed.

De Gruyter eBooks•Jul 18, 2022•0 citations
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).
A detailed consideration is given to the translation-invariant theory of Tulub polaron constructed without the use of Pekar ansatz.A fundamental result of the theory is that the value of the polaron energy is lower than that obtained on the basis of Pekar ansatz which was considered as an asymptotically exact solution in the strong coupling limit.In the case of bipolarons the theory yields the best values of the coupling energy and critical parameters of their stability.Numerous physical consequences of the existence of translation-invariant polarons and bipolarons are discussed.
A detailed consideration is given to the translation-invariant theory of Tulub polaron constructed without the use of Pekar ansatz. A fundamental result of the theory is that the value of the polaron energy is lower than that obtained on the basis of Pekar ansatz which was considered as an asymptotically exact solution in the strong coupling limit. In the case of bipolarons the theory yields the best values of the coupling energy and critical parameters of their stability. Numerous physical consequences of the existence of translation-invariant polarons and bipolarons are discussed.