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Theoretical and Mathematical Physics

Investigation of the polaron model by the method of functional integration

E. A. Kochetov, S.P. Kuleshov, M. A. Smondyrev

Published Oct 1, 1975• 6 citations
Publisher
DOI
10.1007/bf01037638

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Functional variational approach to polaron models

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A general approach to the investigation of polaron systems using path integrals is presented. The basis of the approach is a functional variational method which generalizes Feynman's to the case of a nonvanishing momentum of the system. The characteristics of a free polaron and the behavior of a polaron system in the presence of weak external perturbations are investigated. Questions associated with polaron thermodynamics are considered. The high-temperature behavior of the mean energy and the polaron mass are studied, as is the reaction of a polaron system at finite temperatures to an external perturbation.

•May 1, 1982•2 citations

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Introduction

N. N. Bogolubov Jr.

Despite the apparent simplicity of the formulation, the polaron problem has not yet been solved, and continues to attract much attention. It plays an important role in statistical mechanics and quantum field theory because it can be considered as the simplest example of a nonrelativistic quantum particle interacting with a quantum field. Therefore many sophisticated mathematical techniques have been tested for the first time using this problem as a model. A shining example of this is Feynman's functional integration method, which was applied first to the polaron problem, before becoming one of the main methods used in statistical mechanics and quantum field theory. Moreover, polaron theory is an expanding field of investigation in solid state physics because polarons are not only theoretical constructs but practically observable physical objects (see e.g. [6]).

CRC Press eBooks•May 17, 2000•0 citations

Aspects of Polaron Theory

Nikolay N. Bogolubov, Nikolay N. Bogolubov

WORLD SCIENTIFIC eBooks•Sep 1, 2008•31 citations
A general approach to the investigation of polaron systems using path integrals is presented. The basis of the approach is a functional variational method which generalizes Feynman's to the case of a nonvanishing momentum of the system. The characteristics of a free polaron and the behavior of a polaron system in the presence of weak external perturbations are investigated. Questions associated with polaron thermodynamics are considered. The high-temperature behavior of the mean energy and the polaron mass are studied, as is the reaction of a polaron system at finite temperatures to an external perturbation.
Despite the apparent simplicity of the formulation, the polaron problem has not yet been solved, and continues to attract much attention. It plays an important role in statistical mechanics and quantum field theory because it can be considered as the simplest example of a nonrelativistic quantum particle interacting with a quantum field. Therefore many sophisticated mathematical techniques have been tested for the first time using this problem as a model. A shining example of this is Feynman's functional integration method, which was applied first to the polaron problem, before becoming one of the main methods used in statistical mechanics and quantum field theory. Moreover, polaron theory is an expanding field of investigation in solid state physics because polarons are not only theoretical constructs but practically observable physical objects (see e.g. [6]).