Lectures on quantum statistics. Vol. 1, Quantum statistics.

255 Pages·1967·13.055 MB·English

by  Bogoliubov, N. N.

LECTURES ON QUANTUM STATISTICS
Volume I
Quantum Statistics
LECTURES ON QUANTUM STATISTICS
by N. N. BOGOLIUBOV
(in two volumes)
Volume I
Quantum Statistics
Volume 2
The Model Hamiltonian
LECTURES ON
QUANTUM STATISTICS
VOLUME I
QUANTUM STATISTICS
by N. N. BOGOLIUBOV
Steklov Mathematical Institute
Academy of Science, Moscow, U.S.S.R.
Translated from the Ukranian
English Edition Revised by..}/. N. BOGOL[pBOV
Edited by L. KLEIN and S. tLASS,
Howard University, Washington, D. C.
GORDON AND BREACH, Science Publishers
New York • London • Paris
Copyright© 1967 by
GORDON AND BREACH, Science Publishers, Inc.
150 Fifth Avenue, New York, N. Y. 10011
For Great Britain and Europe:
Gordon and Breach, Science Publishers Ltd.
61 Carey Street, Chauncery Lane
London W.C.2 , England
Library of Congress Catalog Card Number 66-28060
Distribution en France par:
Dunod Editeur
92, rue Bonaparte
Paris 6, France
Distribution in Canada by:
The Ryerson Press
299 Queen Street West
Toronto 2B, Ontario
Printed in the United States of America
EDITOR'S PREFACE
This small volume is a translation of a set of lecture notes
delivered in the Ukranian language by Prof. N. N. Bogoliubov at Kiev
University. These remarkable notes were originally published in the
U.S.S.R. in a limited edition which rapidly became a collector's item.
Today, although these notes are extensively quoted in the literature and
generally considered to be a classic introduction to modern methods
in Quantum Statisical Mechanics, they are unavailable except in a
Japanese language edition.
The editors have carefully checked the text and formulae and
have corrected typographical errors and misprints in the original.
The translation follows closely Professor Bogoliubov's original
Ukranian text.
This book is of far more than historical interest, although first
published over fifteen years ago. It is especially valuable to graduate
students because of the meticulous care with which all details of
calculations and derivations are presented. In addition, research
workers in many fields of modern physics will find that these notes
bring together in a unified and comprehensive treatment many topics
which have appeared in various places in the literature.
In the first chapter, the basic principles of Quantum Statistical
Mechanics are discussed, The I, 2, ... , n, particle density matrices
are also introduced in this chapter and the equations of motion
which lead to the BBGKY hierarchy are derived. Also discussed are
probability distributions in momentum space and fluctuations of
particle number in a region in configuration space.
The second chapter presents a comprehensive treatment of the
method of second quantization based on the original concepts intro
duced by W. A. Fock. The fundamental ideas are introduced and
carefully discussed for the separate cases of Fermi and Bose Statistics
and the connection with the method of statistical operators developed.
Chapter Three contains a discussion of the Bose-Einstein gas and
applications to superfluidity. Landau's theory of superfluidity is pre
sented and a rigorous justification of its postulates from the micro
scopic theory of Bogoliubov is given.
v
The fourth chapter is of particular interest to scientists in solid
state research. It contains a thorough and detailed exposition of the
polar theory of metals. Second quantized notation is used throughout
and operator algebra techniques are utilized. For example, these
techniques are used to develop a perturbation theory method which
leads to an "effective Hamiltonian" £or the polar model of a metal.
In addition, operators are introduced which -permit a calculation of
the electric current associated with the spin waves.
The notation used in this volume is standard, except that every
where h appears it is to he understood as Planck's constant divided
by 211", Thus, the h in this volume is the Ii, of modern texts.
Finally, we would like to thank Professor Bogoliuhov for his
interest in this translation. He has very kindly sent further unpublished
material which discusses more recent developments, including a treat
ment of the Green function method and quasi-averai:res. The editors
plan to publish this material in a second volume which is to he a
companion to the present text.
December 1966 L. S. KLEIN
S. G. GLASS
vi
INTRODUCTION
In recent years new and effective methods have been developed
for the statistical mechanics of quantum systems. Among these is
the method of statistical operators of molecular complexes which is
closely related to the method of second quantization.
Previously, these methods were presented in various places in the
scientific literature and this monograph is the first attempt at a
systematic presentation with applications.
Special attention is given to the application of the above method
to the structure of the molecular theory of superfluidity and to the
theory of. the polar model of a metal.
In addition, as an aid to the reader, introductory chapters are
included on quantum statistics and on the method of second
quantization.
In preparation of the material included in this monograph, the
author has carefully considered the relationship of second quantization
with the method of statistical operators. This relationship has con
siderably simplified the presentation.
Most of the subject matter in this monograph is based upon
material presented in specialized lectures in Statistical Physic!' which
were given by the author in Moscow and Kiev.
N. N. BOGOLIUBOV
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