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

Journal of Experimental and Theoretical Physics

Theory of Polarons in Many-valley Crystals I. Weak Interaction Between Electron and Lattice Polarization Field

Stano Pekár

Published May 1, 1969• 0 citations
OpenAlex

Related papers

Theory of Polarons in Many-valley Crystals. II. Strong Interactions Between an Electron and the Polarization Oscillations of the Lattice

Stano Pekár, Valentin I. Sheka, G. V. Dmitrenko

Journal of Experimental and Theoretical Physics•Jan 1, 1973•0 citations

Theory of many-electron interaction in crystals

M. F. Olekseeva, K. D. Tovstyuk

Theoretical and Mathematical Physics•May 1, 1976•1 citation

A generalized functional approach to the polaron problem

Sergey Gorshkov, Victor Dmitrievich Lakhno, K. Rodriges +1 more

It is well known that two qualitatively different pictures arise in the description of the motion of an electron in an ionic crystal. In the first case, when the electron interacts weakly with the ionic lattice of the crystal, its motion is the same as the motion of a free band electron whose energy is shifted downward with respect to the bottom of the conduction band, and the effective mass is replaced by the renormalized mass (weak-coupling polaron). In the other limiting case, when the electron interacts strongly with the ionic crystal, an entire series of different self-consistent states of the electron and lattice, each of which has its own effective mass and radius (strong-coupling polaron), arises. Although the motion of an electron in an ionic crystal is described in both limiting cases with the help of the Pekar-Frohlich Hamiltonian, each case requires its own special methods of analysis. Thus, for example, in the strong-coupling theory a special form of adiabatic perturbation theory has been developed in which the trans-lational degeneracy is removed before the perturbation expansion is made. It has been possible to relate both descriptions within the framework of Feynman's varia-tional approach, in which a smooth upper bound was obtained for the energy of the ground state of the polaron for all values of the electron-phonon coupling constant a (see Fig. 1). We call attention in this connection to Ref. 6, where the thermodynamic properties are calculated with the help of a special method for performing the calculations and for finding averages of T-products. The approach developed there is more convenient for performing specific calculations than is the use of path integrals. It seems to us that it has definite advantages in the construction of general proofs concerning the choice of the approximating Hamiltonians (this is illustrated in Ref. 6 for the example of the linear Bogolyubov model), in the investigation of the characteristics of the behavior of a polaron in external fields, etc.

Soviet physics. Doklady•Oct 1, 1984•0 citations

Polaron Energy Spectrum

David M. Larsen

The energy spectrum of a polaron---an electron interacting with the longitudinal-optical phonons of a polar crystal---is studied with particular attention given to the region where the polaron excitation energy closely approaches the energy of a longitudinal-optical phonon. In this region, existing theories of the polaron spectrum are inadequate; in particular, the usual Rayleigh-Schr\"odinger perturbation theory is shown to be inconsistent. A self-consistent weak-coupling theory is developed, and a variational theory of the polaron spectrum which, for small coupling, reduces to this weak-coupling theory is presented. Whitfield and Puff, and Schultz have conjectured that the polaron energy $E\mathrm{E}p\mathrm{R}$, bends over and becomes horizontal as the polaron momentum $p$ approaches from below the value at which the polaron excitation energy, $E(p)\ensuremath{-}E(0)$, becomes equal to the optical-phonon energy. Using the weak-coupling method of the present paper, this conjecture has been verified to lowest order and next higher order in the coupling constant.

Physical Review•Apr 15, 1966•83 citations

Aspects of Polaron Theory

Nikolay N. Bogolubov, Nikolay N. Bogolubov

WORLD SCIENTIFIC eBooks•Sep 1, 2008•31 citations

The Fröhlich Hamiltonian

Ashok Chatterjee, Soma Mukhopadhyay

The picture of the polaron conceived by Frohlich is again that of a complex consisting of an electron and the lattice distortion induced by it, but unlike the case of Landau-Pekar polaron, the complex can be found anywhere in the lattice. The Frohlich model considers a low-lying or a slow electron so that the de Broglies wavelength is much larger than the lattice constant, and in this limit, the structure of the lattice becomes unimportant and lattice can be considered to be a continuum. In the Frohlich polaron model, one considers an extra slow electron in the conduction band of the crystal that interacts with the fields associated with the aforementioned polarization vectors to give rise to the electron-phonon Hamiltonian relevant for the polaron problem. Because the electron is low-lying, it will have a large de Broglie wave length associated with it.

CRC Press eBooks•Oct 9, 2018•0 citations
It is well known that two qualitatively different pictures arise in the description of the motion of an electron in an ionic crystal. In the first case, when the electron interacts weakly with the ionic lattice of the crystal, its motion is the same as the motion of a free band electron whose energy is shifted downward with respect to the bottom of the conduction band, and the effective mass is replaced by the renormalized mass (weak-coupling polaron). In the other limiting case, when the electron interacts strongly with the ionic crystal, an entire series of different self-consistent states of the electron and lattice, each of which has its own effective mass and radius (strong-coupling polaron), arises. Although the motion of an electron in an ionic crystal is described in both limiting cases with the help of the Pekar-Frohlich Hamiltonian, each case requires its own special methods of analysis. Thus, for example, in the strong-coupling theory a special form of adiabatic perturbation theory has been developed in which the trans-lational degeneracy is removed before the perturbation expansion is made. It has been possible to relate both descriptions within the framework of Feynman's varia-tional approach, in which a smooth upper bound was obtained for the energy of the ground state of the polaron for all values of the electron-phonon coupling constant a (see Fig. 1). We call attention in this connection to Ref. 6, where the thermodynamic properties are calculated with the help of a special method for performing the calculations and for finding averages of T-products. The approach developed there is more convenient for performing specific calculations than is the use of path integrals. It seems to us that it has definite advantages in the construction of general proofs concerning the choice of the approximating Hamiltonians (this is illustrated in Ref. 6 for the example of the linear Bogolyubov model), in the investigation of the characteristics of the behavior of a polaron in external fields, etc.
The energy spectrum of a polaron---an electron interacting with the longitudinal-optical phonons of a polar crystal---is studied with particular attention given to the region where the polaron excitation energy closely approaches the energy of a longitudinal-optical phonon. In this region, existing theories of the polaron spectrum are inadequate; in particular, the usual Rayleigh-Schr\"odinger perturbation theory is shown to be inconsistent. A self-consistent weak-coupling theory is developed, and a variational theory of the polaron spectrum which, for small coupling, reduces to this weak-coupling theory is presented. Whitfield and Puff, and Schultz have conjectured that the polaron energy EEpRE\mathrm{E}p\mathrm{R}EEpR, bends over and becomes horizontal as the polaron momentum ppp approaches from below the value at which the polaron excitation energy, $E(p)\ensuremath{-}E(0)$, becomes equal to the optical-phonon energy. Using the weak-coupling method of the present paper, this conjecture has been verified to lowest order and next higher order in the coupling constant.
The picture of the polaron conceived by Frohlich is again that of a complex consisting of an electron and the lattice distortion induced by it, but unlike the case of Landau-Pekar polaron, the complex can be found anywhere in the lattice. The Frohlich model considers a low-lying or a slow electron so that the de Broglies wavelength is much larger than the lattice constant, and in this limit, the structure of the lattice becomes unimportant and lattice can be considered to be a continuum. In the Frohlich polaron model, one considers an extra slow electron in the conduction band of the crystal that interacts with the fields associated with the aforementioned polarization vectors to give rise to the electron-phonon Hamiltonian relevant for the polaron problem. Because the electron is low-lying, it will have a large de Broglie wave length associated with it.