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WORLD SCIENTIFIC eBooks

Aspects of Polaron Theory - Equilibrium and Nonequilibrium Problems

Nikolay N. Bogolubov, NICKOLAI N. BOGOLUBOV

Published Jan 1, 2008• 8 citations
Publisher

Abstract

Linear Polaron Model Equilibrium Thermodynamic State of Polaron System Kinetic Equations in Polaron Theory.
DOI
10.1142/9789812833990

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Polaron Theory: Model Problems

Nikolay N. Bogolubov

1. Linear Polaron Model 2. Equilibrium Thermodynamic State of the Polaron Systems 3. Kinetic Equations in the Polaron Theory.

•May 1, 2000•5 citations

Kinetic Equations in Polaron Theory

N. N. Bogolubov Jr.

This chapter generalizes works by N.N. Bogolubov and N.N. Bogolubov, Jr. [1,6], and \nis written with the aim of formulating methods of investigation of the electron-phonon \nsystem and the elimination of phonon operators from the corresponding kinetic equations. In particular, a kinetic equation is derived for the interaction of an electron \nwith a phonon field. Moreover, under the proper approximation, the exact Boltzmann equation for the polaron system follows from this kinetic equation. Methods of \ncalculation of the response functions (impedance and admittance), based on the "approximating" Hamiltonian with linear interaction, are also proposed. The equilibrium \ndensity probability function of the particle is also calculated.

CRC Press eBooks•May 17, 2000•0 citations

Some Aspects of Polaron Theory

Nikolay N. Bogolubov, N N Bogolubov

This monograph is an amplification of a set of special lectures delivered by the authors in the Physics Department of Moscow State University. The linear polaron model is studied. It is shown that the system is soluble for arbitrary coupling interaction strength between the electron and lattice vibrations. Detailed calculational techniques for obtaining the correlation, spectral and Green functions are given. The thermodynamic properties of the system are studied within the framework of the functional method.

World Scientific lecture notes in physics•Nov 1, 1988•11 citations

Polaron State at a Finite Temperature

Y. Osaka

We extend the treatment of Feynman for the polaron problem at 0°K to the case at a finite temperature. A variational principle is applied to the free energy of polaron state.

Progress of Theoretical Physics•Sep 1, 1959•105 citations

Relaxation Dynamics of the Holstein Polaron

Denis Golež, J. Bonča, Lev Vidmar +1 more

Keeping the full quantum nature of the problem, we compute the relaxation time of the Holstein polaron in one dimension after it was driven far from the equilibrium by a strong oscillatory pulse. Just after the pulse, the polaron's kinetic energy increases and subsequently exhibits a relaxation-type decrease with simultaneous emission of phonons. In the weak coupling regime, partial tunneling of the electron from the polaron self-potential is observed. The inverse relaxation time is for small values of electron-phonon coupling λ linear with λ, while it deviates downwards from the linear regime at λ>/~0.1/ω(0). The imaginary part of the equilibrium self-energy shows good agreement with the inverse relaxation time obtained from nonequilibrium simulations.

arXiv:1209.2586•Physical Review Letters•Dec 5, 2012•81 citations

Modeling of the Evolution of the Polaron States

И. В. Амирханов, Амирханов Илькизар Валиевич, Земляная Елена Валериевна +10 more

The evolution of polaron in a homogeneous environment is analyzed depending on parameters of the model and initial conditions which are selected in the form of various combinations of stationary polaron states. A computational scheme and results of the numerical modelling are presented. Work supported by RFBR grants 07-07-00313, 08-01-00800, 07-01-00738, 09-01-00770.

Вестник Российского университета дружбы народов. Серия: Математика, информатика, физика•Jun 15, 2010•0 citations
This chapter generalizes works by N.N. Bogolubov and N.N. Bogolubov, Jr. [1,6], and \nis written with the aim of formulating methods of investigation of the electron-phonon \nsystem and the elimination of phonon operators from the corresponding kinetic equations. In particular, a kinetic equation is derived for the interaction of an electron \nwith a phonon field. Moreover, under the proper approximation, the exact Boltzmann equation for the polaron system follows from this kinetic equation. Methods of \ncalculation of the response functions (impedance and admittance), based on the "approximating" Hamiltonian with linear interaction, are also proposed. The equilibrium \ndensity probability function of the particle is also calculated.
This monograph is an amplification of a set of special lectures delivered by the authors in the Physics Department of Moscow State University. The linear polaron model is studied. It is shown that the system is soluble for arbitrary coupling interaction strength between the electron and lattice vibrations. Detailed calculational techniques for obtaining the correlation, spectral and Green functions are given. The thermodynamic properties of the system are studied within the framework of the functional method.
Keeping the full quantum nature of the problem, we compute the relaxation time of the Holstein polaron in one dimension after it was driven far from the equilibrium by a strong oscillatory pulse. Just after the pulse, the polaron's kinetic energy increases and subsequently exhibits a relaxation-type decrease with simultaneous emission of phonons. In the weak coupling regime, partial tunneling of the electron from the polaron self-potential is observed. The inverse relaxation time is for small values of electron-phonon coupling λ linear with λ, while it deviates downwards from the linear regime at λ>/~0.1/ω(0). The imaginary part of the equilibrium self-energy shows good agreement with the inverse relaxation time obtained from nonequilibrium simulations.