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Polaron Theory: Model Problems

Nikolay N. Bogolubov

Published May 1, 2000• 5 citations
OpenAlex

Abstract

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

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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

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CRC Press eBooks•May 17, 2000•0 citations

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Entropy is in Flux

Leo P. Kadanoff

The science of thermodynamics was put together in the Nineteenth Century to describe large systems in equilibrium. One part of thermodynamics defines entropy for equilibrium systems and demands an ever-increasing entropy for non-equilibrium ones. However, starting with the work of Ludwig Boltzmann in 1872, and continuing to the present day, various models of non-equilibrium behavior have been put together with the specific aim of generalizing the concept of entropy to non-equilibrium situations. This kind of entropy has been termed {\em kinetic entropy} to distinguish it from the thermodynamic variety. Knowledge of kinetic entropy started from Boltzmann's insight about his equation for the time dependence of gaseous systems. In this paper, his result is stated as a definition of kinetic entropy in terms of a local equation for the entropy density. This definition is then applied to Landau's theory of the Fermi liquid thereby giving the kinetic entropy within that theory. Entropy has been defined and used for a wide variety of situations in which a condensed matter system has been allowed to relax for a sufficient period so that the very most rapid fluctuations have been ironed out. One of the broadest applications of non-equilibrium analysis considers quantum degenerate systems using Martin-Schwinger Green's functions\cite{MS} as generalized of Wigner functions, $g^$. This paper describes once again these how the quantum kinetic equations for these functions give locally defined conservation laws for mass momentum and energy. In local thermodynamic equilibrium, this kinetic theory enables a reasonable local definition of entropy density. However, when the system is outside of local equilibrium, this definition fails. It is speculated that quantum entanglement is the source of this failure.

arXiv:1403.6162•Mar 24, 2014•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.
The science of thermodynamics was put together in the Nineteenth Century to describe large systems in equilibrium. One part of thermodynamics defines entropy for equilibrium systems and demands an ever-increasing entropy for non-equilibrium ones. However, starting with the work of Ludwig Boltzmann in 1872, and continuing to the present day, various models of non-equilibrium behavior have been put together with the specific aim of generalizing the concept of entropy to non-equilibrium situations. This kind of entropy has been termed {\em kinetic entropy} to distinguish it from the thermodynamic variety. Knowledge of kinetic entropy started from Boltzmann's insight about his equation for the time dependence of gaseous systems. In this paper, his result is stated as a definition of kinetic entropy in terms of a local equation for the entropy density. This definition is then applied to Landau's theory of the Fermi liquid thereby giving the kinetic entropy within that theory. Entropy has been defined and used for a wide variety of situations in which a condensed matter system has been allowed to relax for a sufficient period so that the very most rapid fluctuations have been ironed out. One of the broadest applications of non-equilibrium analysis considers quantum degenerate systems using Martin-Schwinger Green's functions\cite{MS} as generalized of Wigner functions, $g^$. This paper describes once again these how the quantum kinetic equations for these functions give locally defined conservation laws for mass momentum and energy. In local thermodynamic equilibrium, this kinetic theory enables a reasonable local definition of entropy density. However, when the system is outside of local equilibrium, this definition fails. It is speculated that quantum entanglement is the source of this failure.