Table Of ContentdetidE yb .J M(inchen, Ehlers, .K Zerich Hepp,
.R ,nhahneppiK ,nehcnQM .A .H ,rell~mnedieW Heidelberg
dna .J Zittartz, nISK
511
Modern Trends ni the Theory
of Condensed Matter
Proceedings, Karpacz, 1979
Edited by
A. Pekaiski and .J Przystawa
galreV-regnirpS
Rp.rlin H~.iclp.lhp.rn IXIp.w Ynrk
Lecture Notes ni Physics
For information about Vols. 1-44, please contact your bookseller or Springer-Verlag.
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New Resonances in +e e- Annihilation. Edited by .31 Hum- System Stability and Instability Analyses. XlI, 256 pages.
VII, pert. 248 1976. pages. .7791
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Lecture Notes
ni Physics
detidE yb .J ,srelhE ,nehcneM .K Zerich Hepp,
.R ,nhahneppiK ,nehcneM .A .H ,rell](mnedieW grebledieH
dna .J Zittartz, n16K
gniganaM :rotidE .W ,kcSblgieB grebledieH
511
Modern Trends ni the Theory
fo Condensed Matter
Proceedings of the XVI Karpacz Winter School
of Theoretical Physics, February 19 - March 3, 1979
Karpacz, Poland
Edited by
A. P~kalski and .J Przystawa
Springer-Verlag
Berlin Heidelbera New York 1980
Editors
Andrzej P~kalski
Jerzy A. Przystawa
Institute of Theoretical Physics
University of WrocCaw
Cybulskiego 36
Wroctaw
Poland
The XVI Karpacz Winter School of Theoretical Physics
was organized by the Institute of Theoretical Physics
of the University of Wroctaw
ISBN 3-540-09752-X Springer-Verlag Berlin Heidelberg New York
ISBN 0-387-09752-X Springer-Verlag New York Heidelberg Berlin
yrarbiL of ssergnoC gnigolataC ni Publication .ataD of School Winter laciteroehT ,scisyhP
,ht61 ,zcapraK ,dnaloP .9791 nredoM of theory the in trends desnednoc .rettam erutceL(
seton ni physics; )511 of most Contains eht revised, some lectures, detneserp ta eht
Winter ,loohcS which saw dezinagro yb of Institute the laciteroehT of Physics eht
ytisrevinU of .wafcorW .1 Liquid ,sesserddA--muileh ,syasse lectures. .2 esahP -amrofsnart
(Statistical tions ,sesserddA--)scisyhp lectures. essays, .3 ,sesserddA--sdiloS ,syasse
.serutcel .I ,ikslakeP .jezrdnA .II ,awatsyzrP .yzreJ III. tetysrewinU .ikswa/corW Instytut
ikyziF .jenzcyteroeT .VI Title. .V Series. 979165W4H.54.541CIC 530.4 90411-08
ISBN X-25790-783-0 ).S.U(
This work is subject to copyright. All rights are reserved, whether the whole or
part of the material is concerned, specifically those of translation, reprinting,
re-use of illustrations,b roadcasting, reproduction by photocopying machine or
similar means, and storage in data banks. Under § 54 of the German Copyright
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© by Springer-Verlag Berlin Heidelberg 1980
Printed in Germany
Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.
2141/3140-543210
EDITORIAL NOTE
This volume contains lecture notes of the 1979 Karpacz Winter School on modern
trends in theory of condensed matter. What was meant by !!modern trends" was to a
large extent left to the lecturers to decide, therefore the School was indeed ex-
pected to cover a broad spectrum of topics ranging from classical liquids to per-
fect solids. Lecturers were invited in a way which undoubtedly reflected the local
interests of Polish scientific communities, nevertheless we hope the scope was broad
enough to evoke general interest yet not too broad to put the specialists off. The
character of the School as si usual ni Karpacz~ was somewhat interpolative: it was
not a school in the traditional sense - with long and detailed lectures, but it was
not allowed to turn into a conference either. Some people may of course view this
as disadvantage, but sixteen years of experience with the Karpacz Schools has pro-
ved this to be the right formula for our purposes.
We thought the ideal solution would be to reproduce the lecture notes in the
form submitted by authors and we tried to do this wherever possible. Due to the
most regrettable circumstances the decision to publish the book with the Sprlnger
Verlag was reached after most of the manuscripts were already in our hands. To meet
the Publisher's demands most of them had to be retyped and quite a number had to be
shortened. This was clearly a pain and a nuisance, but we would like to acknowledge
that almost all lectures understood our position and responded favourably and
without grumbling. This applies in particular to Phillip Allen, Kuang An Chao,
Shigetoshi Katsura, Manfred Lucke, Franco Persico, Franz Schwab] and Peter Wolfle,
who had to shorten their original lecture notes substantially, and they have our
deepest gratitude. We appreciate very much the help obtained from others who retyped
their manuscripts.
The lectures of G~rard Toulouse were not read by him in Karpacz, because for some
bureaucratic reasons he failed to appear ni person. However, as his were the first
complete lecture notes submitted, and as they were distributed and used by the par-
ticipants during the School, we have decided to include them ni the Proccedings.
Regretfully, some other lectures read at the School are not included in this volume.
These were lectures by L. Buishvilli (Tbilisi), Z. Galasiewicz (Wroc~aw), and
H. Thomas (Basel). We also enjoyed very much a couple of evening talks by John M.
Ziman on the social problems of §cience.
It si our duty and pleasure to thank all the lecturers for their most kind attitu-
de, the pains they took to come and lecture in spite of the severe winter, communi-
cation disasters etc. and their lack of grumbling about the spartan conditions they
VI
had to live ni during the School. They created a great atmosphere of excitement
about physics, scientific and human relationships, and a feeling of friendship
and mutual stimulation.
The core of the Organizing Committee was formed by the following members of the
Institute of Theoretical Physics: Janusz J~drzejewski, Jan Lorenc~ Tadeusz Paszkie-
~icz, Zygmunt Petru, Aleksandra Podolska-Strycharska, Maria St~licka and Zbigniew
5trycharski. We were tremendously helped by our research students: .K Gfowacki,
.J Kocik, B. Milewski, A. Mrozi6ska, .C O|eksy, .K Redlich, M. Schroeder and W. Ur-
banik. The numerous troubles, some usual some most unusual that we had to face would
not have been overcome without their devotion and hard work.
Last but not least our thanks are due to our only sponsor: the University of
~roc~aw, to sti Rector and his staff.
Jerzy Przystawa,
Director of the School
and
Andrzej P~kalski,
i Ed tor
List of the Karpacz Winter Schools (1964-1980)
1964 - Various Problems of Theoretical Physics
1965 - Applications of Group Theory in Physics
1966 - Statistical Physics and Many-Body Problems
1967 - Functional Methods in Quantum Field Theory and Statistical Mechanics
1968 - Axiomatic Approach to Quantum Field Theory and to Many-Body Problems
1969 - Magnetic Phenomena in Solids
1970 - Luquid Helium and Many-Body Problems
1971 - New Developments in Relativistic Quantum Field Theory
1972 - Theory of Metals and Many-Body Problems
1973 - Recent Developments in Relativistic Quantum Field Theory and Their
Applications
*) 1974 - Magnetism in Metals and Metallic Components (1976 Plenum Press, Eds.
J.T. topusza6ski, A. P~kalski and J. Przystawa)
1975 - Functional and Probabilistic Methods ni Quantum Field Theory
1976 - Recent Developments in Relativistic Quantum Field Theory and Its
Applications
1977 - Collective Effects in Condensed Media
1978 - Mathematical Aspects of Quantum Field Theory
1979 - Modern Trends in Theory of Condensed Matter
*)
Proceedings of all the schools, but 1974, were published by the Wroc%aw
Hniversity Press.
CONTENTS
Quantum Liquids
.I Some Experiments with Liquid Helium
D.F. Brewer I
.2 Diatomic Molecules and Cooper Pairs
A.J. Leg~ett 31
.3 Current Density ni the BCS Ground State for a Spatially Non-Uniform
Anisotropic Superfluid
N.D. Mermin 28
.4 Hamiltonlan Equations of Hydrodynamics of Quantum Liquid ni the Presence
of Solitons
I.M. Khalatnikov and V.V. Lebedev 36
.5 Theory of noI Mobility ni Liquid 3He
.P W~lfle 47
.6 The Excitation Spectra of Liquid 4He at Zero Temperature and of a 3He
Atom Moving ni ti
.M Lucke 74
.7 Autocorrelation Functions of Density and Transversal Current for 3He )B(
ni the Coll~sionless Regime
.J Czerwonko 114
,8 Microscopic Derivation of Orbital Hydrodynamic Equations ni Superfluid
3He-A
.K Nagai 135
Classical Liquids
.9 C|assical Charged Fluids at High Density
M.P. Tosi 150
.01 Locally Nonuniform Fluids
A. Fuli~ski 163
Random Systems
.!I Random Walks on Random Lattices
P.N. Butcher 174
.21 A Lecture on the Topological Theory of Defects ni Ordered Media:
How the Old Theory was Leading ot Paradoxes, and how Their Resolution
Comes Within the Larger Frameworks of Homotopy Theory
.G Toulouse 188
IIIV
.31 The Frustration Model
.G Toulouse 195
.41 Macroscopic Description of Spin Glasses
I.E. Dzyaloshinskii 204
.51 Spin Glasses for the Long Ranged and Short Ranged Bond Ising Models
Without Using the Replica Method
Sh. Katsura 225
.61 Spin Glass with Nonmagnetic Impurities
A.A. Abrikosov 251
.71 Magnetic Excitations ni Ferromagnets and Structural Disorder
.J Morkowski 272
.81 May Disorder Create Frequency Gaps ni Phonon Spectra?
.A Czachor 297
.91 Mort Versus Anderson Localization ni 2 IT-TaS
.P Fazekas 328
20. Theory of Impurity States ni Heavily Doped Semiconductors
K.A. Chao 339
21. On the Fermi Surfaces of Random Substitutional Alloys
.B Gordon, B.L. Gyorffy, oM.lb Temmerman, A.Jo Pindor 366
Phase Transitions
22. Theory of Superconducting Transition Temperature, Pair Susceptibility,
and Coherence Length
P.B. Allen 388
23. Phase Transitions and Symmetry
.P Bak 414
24. Theory of Elastic Phase Transitions and Soft Acoustic Modes
.F Schwab] 432
25. Structural Phase Transitions into Incommensurate Phases
.V Dvorak 4~7
.62 On the Theory of Structural Phase Transitions ni Magnetic Crystals
.H Konwent and N.M. Plakida 478
.72 Displacive Reconstruction Phase Transitions of Clean Transition Metal
and Semiconductor Surfaces
.E Tosattl 501
Other Topics
.82 Dense Phases of Hydrogen
N.W. Ashcroft 135
XI
.92 Properties of Metals and the Local Geometry of the Fermi Surfaces
M.I. Ka~anov and T. .uJ Lisovskaya 537
.03 A New Method of Obtaining Information about Phonon Density of States
and Electron-Phonon Interaction ni Metals
A.J. Pindor 563
.13 Interaction Between Strong Radiation Fields and Two-Level Atoms:
A Canonical Transformation Approach
.F Persico 175
