Table Of ContentQUANTUM STATISTICS
AND THE
MANY - BODY PROBLEM
QUANTUM STATISTICS
AND THE
MANY - BODY PROBLEM
Edited by
Samuel B. Trickey, Wiley P. Kirk,
and
James W. Dufty
University of Florida
Gainesville, Florida
PLENUM PRESS· NEW YORK AND LONDON
Library of Congress Cataloging in Publication Data
Symposium on Quantum Statistics and Many-Body Problems, 1st, Sanibel Island,
Fla., 1975.
Quantum statistics and the many-body problem.
Includes bibliographical references.
1. Liquid helium-Congresses. 2. Superfluidity - Congresses. 3. Quantum statistics
Congresses. 4. Problem of many bodies - Congresses. I. Trickey, Samuel B. II. Kirk,
Wiley P. III. Dufty, James W. IV. Title.
QC145.45.H4S9 1975 530.1'4 75-25547
ISBN-13: 978-1-4684-2210-8 e-ISBN-13: 978-1-4684-2208-5
001: 10.1007/978-1-4684-2208-5
Proceedings of the first Symposium on Quantum Statistics and
Many-Body Problems held on Sanibel Island, January 26-29, 1975
©1975 Plenum Press, New York
Softcover reprint of the hardcover 1st edition 1975
A Division of Plenum Publishing Corporation
227 West 17th Street, New York, N.Y. 10011
United Kingdom edition published by Plenum Press, London
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All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted,
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PREFACE
The present volume represents the great majority of the papers
presented on Sanibel Island at the first Symposium on Quantum
Statistics and Many-Body Problems (January 26-29, 1975). In his
Introductory Remarks, Professor Lawdin outlines the history of the
original Symposia, and the genesis of the conference whose papers
comprise this volume. We join him in his expression of thanks,
and note, additionally, our gratitude to him and to Professors
N. Y. Ohrn, J. R. Sabin, E. D. Adams, and John Daunt.
The papers are grouped somewhat differently from their order
of presentation. It seemed convenient to begin with the six papers
which deal with sound propagation in one form or another, then
have a two-paper diversion into solid Helium. The SHe superf1uid
theme is picked up again with four papers on spin dynamics, orbit
waves, etc., followed by a selection of five papers on a variety of
experimental and theoretical aspects of the SHe superf1uid problem.
Work in the areas of films, mono1ayers, and mixtures is presented
next, followed by two papers on liquid ~He. We conclude with a
selection of six papers on other quantum fluids and general
statistical mechanics.
We are most grateful to the contributors to this volume for
their patience and cooperation; they have had as editors three
utter novices! We have learned much, both scientifically and
editorially. We hope that this volume will be of at least some
help to others as well.
Samuel B. Trickey
Wiley P. Kirk
James W. Dufty
Gainesville, 10 June 1975
v
CONTENTS
INTRODUCTORY REMARKS xi
ATTENUATION AND DISPERSION OF FIRST SOUND NEAR THE
SUPERFLUID TRANSITION OF LIQUID HELIUM 1
F. Pobe11
HYDRODYNAMIC THEORY OF FOURTH SOUND IN A MOVING SUPERFLUID -
A DISCUSSION OF SIZE EFFECTS • 3
D. J. Bergman
THEORY OF SOUND ABSORPTION IN THE SUPERFLUID PHASES OF 3He • 9
P. Wo1f1e
SOUND PROPAGATION AND ANISOTROPY IN LIQUID 3He A 19
D. T. Lawson, H. M. Bozler and D. M. Lee
SOUND PROPAGATION IN NORMAL AND SUPERFLUID 3He • 35
J. B. Ketterson, P. R. Roach, B. M. Abraham
and P. D. Roach
PHONON PROPAGATION IN LIQUID AND SOLID HELIUM 65
V. Narayanamurti and R. C. Dynes
THERMAL BOUNDARY RESISTANCE BETWEEN SOLID 3He AND
CERIUM MAGNESIUM NITRATE 73
L. E. Reinstein and G. O. Zimmerman
NUCLEAR SPIN ORDERING OF SOLID 3He IN A MAGNETIC FIELD 83
R. B. Kummer, E. D. Adams, W. P. Kirk, A. S. Greenberg,
R. M. Mueller, C. V. Britton and D. M. Lee
THEORETICAL SEARCH FOR COLLISIONLESS ORBIT WAVES 91
W. M. Saslow
SPIN DYNAMICS IN SUPERFLUID 3He • 95
R. Combes cot
viii CONTENTS
SPIN WAVES AND MAGNETIZATION OSCILLATION IN SUPERFLUID
3He 101
K. Maki
DISSIPATIVE PROCESSES IN THE NUCLEAR MAGNETIC RESONANCES
OF SUPERFLUID LIQUID 3He 119
V. Ambegaokar
HYDROMAGNETIC EFFECTS IN SUPERFLUID 3He 127
A. L. Fetter
SUPERFLUID DENSITY OF 3He • 139
H. Kojima, D. N. Paulson and J. C. Wheatley
COMMENTS ON THE JOSEPHSON PLASMA RESONANCE IN 3He(A) • 149
A. J. Dahm and D. N. Langenberg
FREE ENERGY FUNCTIONALS FOR SUPERFLUID 3He 155
J. W. Serene and D. Rainer
FLUCTUATIONS ABOVE THE SUPERFLUID TRANSITION IN LIQUID 3He • 163
V. J. Emery
EXCITATIONS IN DILUTE 3He-4He MIXTURES 171
L. Mittag and M. J. Stephen
RIPPLONS AND SUPERFLUIDITY IN 3He MONOLAYERS 177
C.-W. Woo
FILM THICKNESS DETERMINATIONS IN MOVING SATURATED
SUPERFLUID 4He FILMS 185
R. B. Hallock
RECENT EXPERIMENTS ON THE SURFACE OF LIQUID 4He:
ELASTIC SCATTERING OF 4He ATOMS • 195
D. O. Edwards, P. P. Fatouros, G. G. Ihas,
P. Mrozinski, S. Y. Shen and C. P. Tam
THERMAL EXPANSION COEFFICIENT AND UNIVERSALITY NEAR THE
SUPERFLUID TRANSITION OF 4He UNDER PRESSURE • 205
K. H. Mueller, F. Pobell and G. Ahlers
BOGOLIUBOV'S COMPENSATION OF DANGEROUS DIAGRAMS AND THE
EXCITATION SPECTRUM OF He II • 207
D. H. Kobe
ELECTRON-HOLE DROPLETS IN GERMANIUM AND SILICON 215
M. Combes cot
CONTENTS
SUPERFLUIDITY IN NEUTRON STARS 221
G. Baym
THE HOT INTERACTING NEUTRON GAS • 231
J.-R. Buchler and S. A. Coon
A GENERAL THEORY FOR SUPER PHENOMENA IN PHYSICS 239
A. J. Coleman
C-NUMBER REPRESENTATION FOR MULTILEVEL SYSTEMS AND THE
QUANTUM-CLASSICAL CORRESPONDENCE 249
R. Gilmore, C. M. Bowden and L. M. Narducci
NONZERO TEMPERATURE VARIATIONAL PRINCIPLE APPLIED TO LOW
TEMPERATURE LIQUID SODIUM . 271
R. L. Coldwell, M. A. Pokrant and A. A. Broyles
LIST OF CONTRIBUTORS 279
INDEX 283
INTRODUCTORY REMARKS
The Quantum Theory Project at the University of Florida was
begun in 1960 as the American part of a new University of Uppsa1a -
University of Florida exchange program in quantum sciences. From
1963 to the present, a series of annual International Symposia on
the Quantum Theory of Atoms, Molecules, and Solids has been
organized by the Quantum Theory Project and its sister project, the
Quantum Chemistry Group, University of Uppsa1a. These January
meetings at Sanibel Island typically attract 250 researchers from
allover the world. It has been customary to dedicate the odd-year
symposia to one of the outstanding pioneers in the quantum theory
of matter: Professors E. A. Hy11eraas (1963), R. S. Mulliken (1965),
J. C. Slater (1967), H. Eyring (1969), J. H. Van Vleck (1971),
E. U. Condon (1973) and L. H. Thomas (1975).
For some years the Sanibel Symposia included sessions devoted
to Quantum Statistics and to Quantum Biology. In January. 1974,
Quantum Biology became the subject of a three-day Symposium in its
own right. The success of this new Symposium prompted Professor
L. H. Nosanow (then Chairman of the Department of Physics and
Astronomy at University of Florida) to suggest an experiment with
Quantum Statistics. Thus, it was decided to arrange a special
three-day session on Quantum Statistics and Many-Body Problems as
the last of the 1975 series of Symposia. The Quantum Statistics
Symposium was from the beginning a joint venture between the Quantum
Theory Project and the Department of Physics and Astronomy of the
University of Florida.
The Editors of these Proceedings were therefore asked to under
take the detailed organization of the new Symposium, with Professor
Trickey as Associate Director. We were fortunate to have Professor
David M. Lee of Cornell University as a Visiting Professor at the
University of Florida during the academic year 1974-'75, and we are
most grateful to Dr. Lee for utilizing so many of his international
contacts and putting so much time and effort into the organization
of this Symposium. Because of the interests of the organizers, it
finally turned out to be appropriate to focus the Symposium on
Quantum Fluids, with particular emphasis on superf1uid 3He•
xii INTRODUCTORY REMARKS
On behalf of all the organizers, I take this opportunity to
express our gratitude to various units of the University of Florida
for financial support of this meeting: the Office of Academic
Affairs, the Division of Continuing Education, the Graduate School,
the College of Arts and Sciences, and the Department of Physics and
Astronomy.
Many of the practical details of the Symposium were handled by
faculty, post-doctoral associates, and graduate students of the
Quantum Theory Project and of the Department of Physics and
Astronomy. Their efforts, as well as those of their fine secre
tarial staffs, are hereby gratefully acknowledged. We are further
indebted to the owners of the Island Beach Club, Mr. Walter P.
Condon, Trustee, and the manager, Mr. Robert J. Houser, and their
staff for their efforts to provide a pleasant and effective
environment for the Symposium on Sanibel Island.
Per-Olov Lowdin
Professor and Head Graduate Research Professor
Department of Quantum Chemistry Quantum Theory Project
University of Uppsala University of Florida
Uppsala, Sweden Gainesville, Florida
Member of Nobel Committee in Physics
ATTENUATION DISPERSION OF FIRST SOUND NEAR THE SUPERFLUID
Al~D
TRANSITION OF LIQUID HELIUM
F. Pobe11
Institut fur Festkorperforschung, Kernforschungsan1age
517 Ju1ich, W. Germany
Summary: The superf1uid phase transition of liquid helium has
been investigated in recent years in great detail and with very
high prec1s10n. In this paper acoustic investigations of this
phase transition will be discussed.
Low frequency measurements of the velocity u of first sound
near TAl have been found to agree with the fo110win~ Pippard
Buckingham-Fairbank re1ation2 as modified by Ahlers
u(T)-u(TA) = A1 / Cp+A2t+A3t 1-0 (1)
(C : specific heat; t=II-T/TAI; a: critical exponent of C ).
p p
Williams and Rudnick~ have measured the attenuation
(600 kHz ~ w/2n ~ 3.17 Mhz), and Thomlinson and Pobel15 have inves
tigated the dispersion (5.4 kHz ~ w/2n ~ 208 kHz) of first sound in
~He near TA (l~K ~ Ir-TAI ~ 5 mK). Both are asymmetric around TA
with a peak on the low temperature side. The measured attenuation
and dispersion are discussed as arising from the Landau-Kha1atnikov
relaxation process occurring only below TA, and from a fluctuation
process occurring on both sides of the A-transition. The data can
only be compared to the relaxation process because no detailed
prediction for the contribution arising from fluctuations is
available at present.
Recently these experiments have been extended to 3He-~He mix
tures.6- 8 The low-frequency velocity could again be fit to Eq. 1.6
The dispersion D and attenuation a have been measured in mixtures
containing up to 40% 3He and at 2.25 kHz ~ w/2n ~ 594 kHz.7,s Both
