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

physica status solidi (b)

On the Nature of the Self‐Trapping of Different Types of Polarons

P. Nagy, P. Markoš

Published Feb 1, 1989• 5 citations
Publisher

Abstract

Abstract A generalized Huybrechts approximation is developed and used for the calculation of the ground state energy, E, of the polaron as the function of the coupling constant α. A simple criterion for the continuity of ∂E/∂α is given, which enables to discuss the nature of the transition of the polaron from the free state to the localised state in the framework of different approximations.

DOI
10.1002/pssb.2221510217

Related papers

A Simple and Available Approach for Calculating the Ground State Energy of the Acoustic Polaron

Hou Jun-hua

The ground state energy of the acoustic polaron is calculatedby using Huybrechts variational approach.It was verified that the Huybrechts approach is an available approach and is applicable for the whole coupling range.

Jiangxi kexue•Jan 1, 2011•0 citations

Functional Integrals in the Strong Coupling Regime and the Polaron Self‐Energy

Гарий Владимирович Ефимов, Gurjav Ganbold

Abstract A general method of representation of functional integrals in the strong coupling regime is developed. This method is applied to the computing of polaron ground state energy at large coupling constant.

physica status solidi (b)•Nov 1, 1991•18 citations

Mean field theory of a single fröhlich polaron possible existence of phase transitions

Yves Lépine, D. Matz

Abstract New results for the free polaron ground state energy are presented, based on a non‐perturbative Fock approximation mean field theory. From variational calculations a new energy upper bound for all couplings is obtained, whose newness lies in its cylindrical symmetry, thu sbreaking the spherical symmetry of the Fröhlich Hamiltonian. For α (the electron–phonon coupling constant)≦3 a translational invariant state is found, for 3 ≦ α ⪅ 3.8 a two‐dimensional localized state while for α ⪆ 3.8, a three‐dimensional cylindrical localized state is obtained. By linking the variational approach to a dynamical approximation of the Fröhlich Hamiltonian, the possibility is suggested of second‐order phase transitions for the structure of the polaron, in the framework of the Fock approximation.

physica status solidi (b)•Dec 1, 1979•23 citations

Polaron ground-state energy inddimensions

Gurjav Ganbold, Гарий Владимирович Ефимов

The polaron path integral introduced by Feynman is generalized to the case of an electron moving in d space dimensions. A scheme of systematic calculations of the obtained path integral is developed to estimate the ground-state energy of the polaron in the same way for different values of the electron-phonon coupling constant \ensuremath{\alpha}. The leading-order term in this approach yields an upper bound to the polaron self-energy and improves Feynman's variational estimates for d=2 and d=3. A scaling relation between polaron self-energies for different space dimensions is obtained for this term. The next correction to this estimation is calculated by numerical integration for d=2 and d=3.

Physical review. B, Condensed matter•Aug 1, 1994•11 citations

Phase-transition-like behaviour in the problems of different types of polaron

H Shoji, Naoaki Tokuda

The ground state energies and the mean numbers of phonons in the cloud around the electron for the different types of polarons are calculated variationally for the whole range of the electron-phonon coupling. Phase-transition-like behaviour such as abrupt changes of the ground state energy and the mean number of phonons at a certain value of the coupling constant are seen for every case.

Journal of Physics C Solid State Physics•Mar 30, 1981•40 citations

Polaron Theory in Wide and Narrow Electron Bands

Giuseppe Iadonisi, V. Cataudella, D. Ninno

The polaron band theory of Lee, Low and Pines is extended beyond the effective mass approximation to a general form of the electron–phonon interaction within two different self-consistent schemes. In the first one a variational Bloch state depending on the polaron crystalline momentum is used to study polaron features taking into account umklapp processes. In particular, the self-energy and the effective mass at the Γ point of the Brillouin zone are calculated as functions of the electron–phonon coupling constant α. It is found that a sudden transition of these quantities from a large band to a narrow band polaron behaviour occurs at a critical value αc. Such value increases indefinitely with the bare electron band width; moreover the transition becomes sharper. The theory recovers, as particular cases, a) the Lee-Low-Pines regime valid for small α and large electron band width Δ˜(Δ˜ ≫ ħω and b) the Holstein limit for large α and small band width (Δ˜ ≫ ħω). This occurs as result of the competing role of α and Δ˜. In the second scheme, the electron–phonon interaction is considered only in a single elementary cell and the self-trapped polaron state is calculated self-consistently. It is shown that, if only one electronic band is taken into account, such state becomes a Δ function with infinitely negative energy when α is larger than a critical value depending on the electron band width. To avoid this fact, electronic band states of higher energy must be considered. Finally, through the tight-binding method, the polaron band is set up. It is shown that at the Γ point of the Brillouin zone, the contribution of the higher electronic bands prevents the self-energy and the polaron mass to have a sharp increase from the large to the narrow band regime.

physica status solidi (b)•Oct 1, 1997•10 citations
Abstract A generalized Huybrechts approximation is developed and used for the calculation of the ground state energy, E, of the polaron as the function of the coupling constant α. A simple criterion for the continuity of ∂E/∂α is given, which enables to discuss the nature of the transition of the polaron from the free state to the localised state in the framework of different approximations.
Abstract New results for the free polaron ground state energy are presented, based on a non‐perturbative Fock approximation mean field theory. From variational calculations a new energy upper bound for all couplings is obtained, whose newness lies in its cylindrical symmetry, thu sbreaking the spherical symmetry of the Fröhlich Hamiltonian. For α (the electron–phonon coupling constant)≦3 a translational invariant state is found, for 3 ≦ α ⪅ 3.8 a two‐dimensional localized state while for α ⪆ 3.8, a three‐dimensional cylindrical localized state is obtained. By linking the variational approach to a dynamical approximation of the Fröhlich Hamiltonian, the possibility is suggested of second‐order phase transitions for the structure of the polaron, in the framework of the Fock approximation.
The polaron path integral introduced by Feynman is generalized to the case of an electron moving in d space dimensions. A scheme of systematic calculations of the obtained path integral is developed to estimate the ground-state energy of the polaron in the same way for different values of the electron-phonon coupling constant \ensuremath{\alpha}. The leading-order term in this approach yields an upper bound to the polaron self-energy and improves Feynman's variational estimates for d=2 and d=3. A scaling relation between polaron self-energies for different space dimensions is obtained for this term. The next correction to this estimation is calculated by numerical integration for d=2 and d=3.
The polaron band theory of Lee, Low and Pines is extended beyond the effective mass approximation to a general form of the electron–phonon interaction within two different self-consistent schemes. In the first one a variational Bloch state depending on the polaron crystalline momentum is used to study polaron features taking into account umklapp processes. In particular, the self-energy and the effective mass at the Γ point of the Brillouin zone are calculated as functions of the electron–phonon coupling constant α. It is found that a sudden transition of these quantities from a large band to a narrow band polaron behaviour occurs at a critical value αc. Such value increases indefinitely with the bare electron band width; moreover the transition becomes sharper. The theory recovers, as particular cases, a) the Lee-Low-Pines regime valid for small α and large electron band width Δ˜(Δ˜ ≫ ħω and b) the Holstein limit for large α and small band width (Δ˜ ≫ ħω). This occurs as result of the competing role of α and Δ˜. In the second scheme, the electron–phonon interaction is considered only in a single elementary cell and the self-trapped polaron state is calculated self-consistently. It is shown that, if only one electronic band is taken into account, such state becomes a Δ function with infinitely negative energy when α is larger than a critical value depending on the electron band width. To avoid this fact, electronic band states of higher energy must be considered. Finally, through the tight-binding method, the polaron band is set up. It is shown that at the Γ point of the Brillouin zone, the contribution of the higher electronic bands prevents the self-energy and the polaron mass to have a sharp increase from the large to the narrow band regime.