Statistical Mechanics Made Simple - D. Mattis (World, 2003).pdf

(2274 KB) Pobierz
smms.dvi
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: Suite 202, 1060 Main Street, River Edge, NJ 07661
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
Library of Congress Cataloging-in-Publication Data
Mattis, Daniel Charles, 1932–
Statistical mechanics made simple : a guide for students and researchers / Daniel C. Mattis.
p. cm.
Includes bibliographical references and index.
ISBN 981-238-165-1 -- ISBN 981-238-166-X (pbk.)
1. Statistical mechanics. I. Title.
QC174.8.M365 2003
530.13--dc21
2003042254
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Copyright © 2003 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to
photocopy is not required from the publisher.
Printed in Singapore.
668308368.029.png 668308368.030.png 668308368.031.png 668308368.032.png 668308368.001.png 668308368.002.png 668308368.003.png 668308368.004.png 668308368.005.png 668308368.006.png 668308368.007.png 668308368.008.png 668308368.009.png 668308368.010.png 668308368.011.png 668308368.012.png 668308368.013.png 668308368.014.png 668308368.015.png 668308368.016.png
Publishers’ page
668308368.017.png 668308368.018.png 668308368.019.png
Contents
Preface
ix
Introduction: Theories of Thermodynamics, Kinetic Theory and
Statistical Mechanics
xiii
Chapter 1 Elementary Concepts in Statistics
and Probability 1
1.1. TheBinomialDistribution..................... 1
1.2. LengthofaWinningStreak.................... 3
1.3. BrownianMotionandtheRandomWalk............. 4
1.4. PoissonversusNormal(Gaussian)Distributions......... 5
1.5. CentralLimitTheorem(CLT)................... 9
1.6. MultinomialDistributions,StatisticalThermodynamics..... 12
1.7. TheBarometerEquation...................... 14
1.8. OtherDistributions......................... 14
Chapter 2 The Ising Model and the Lattice Gas 17
2.1. SomeBackgroundandMotivation................. 17
2.2. First-PrinciplesStatisticalTheoryofParamagnetism...... 18
2.3. MoreonEntropyandEnergy ................... 21
2.4. SomeOtherRelevantThermodynamicFunctions ........ 21
2.5. Mean-FieldTheory,StableandMetastableSolutions...... 23
2.6. TheLatticeGas........................... 26
2.7. TheNearest-NeighborChain:Thermodynamicsin1D ..... 26
2.8. TheDisorderedIsingChain .................... 28
2.9. OtherMagneticSystemsinOneDimension ........... 28
v
668308368.020.png 668308368.021.png 668308368.022.png
vi
Statistical Mechanics Made Simple
Chapter 3 Elements of Thermodynamics 31
3.1. TheScopeofThermodynamics .................. 31
3.2. EquationsofStateandSomeDefinitions............. 32
3.3. MaxwellRelations ......................... 35
3.4. ThreeImportantLawsofThermodynamics ........... 35
3.5. TheSecondDerivativesoftheFreeEnergy............ 38
3.6. PhaseDiagramsforthevanderWaalsGas............ 39
3.7. Clausius–ClapeyronEquation................... 43
3.8. PhaseTransitions.......................... 46
3.9. TheCarnotCycle.......................... 49
3.10. Superconductivity . . . . ...................... 51
Chapter 4Statistical Mechanics 55
4.1. TheFormalism—andaFalseStart ............... 55
4.2. Gibbs’ParadoxandItsRemedy.................. 58
4.3. TheGibbsFactor.......................... 59
4.4. TheGrandEnsemble........................ 60
4.5. Non-IdealGasandthe2-BodyCorrelationFunction ...... 62
4.6. TheVirialEquationofState.................... 64
4.7. WeaklyNon-IdealGas....................... 65
4.8. Two-bodyCorrelations....................... 68
4.9. ConfigurationalPartitionFunctionin1D............. 73
4.10. OneDimensionversusTwo .................... 75
4.11. Two Dimensions versus Three: The Debye–Waller Factors . . . 77
Chapter 5 The World of Bosons 83
5.1. TwoTypesofBosonsandTheirOperators............ 83
5.2. NumberRepresentationandtheMany-BodyProblem ..... 86
5.3. TheAdiabaticProcessandConservationofEntropy ...... 88
5.4. Many-BodyPerturbations..................... 89
5.5. Photons ............................... 90
5.6. Phonons............................... 93
5.7. Ferromagnons............................ 96
5.8. ConservedBosonsandtheIdealBoseGas............ 99
5.9. Natureof“Ideal”Bose–EinsteinCondensation..........101
5.10. IdealBose-EinsteinCondensationinLowDimensions......104
5.11. ConsequencesofaHardCoreRepulsionin1D..........106
5.12. Bosonsin3DSubjecttoWeakTwo-BodyForces ........109
5.13. SuperfluidHelium(HeII) .....................114
668308368.023.png 668308368.024.png 668308368.025.png
Contents
vii
Chapter 6 All About Fermions: Theories of Metals,
Superconductors, Semiconductors 119
6.1. Fermi–DiracParticles........................119
6.2. SlaterDeterminant:TheGroundState..............120
6.3. IdealFermi–DiracGas.......................121
6.4. IdealFermi–DiracGaswithSpin .................123
6.5. FermiIntegrals ...........................124
6.6. ThermodynamicFunctionsofanIdealMetal...........125
6.7. QuasiparticlesandElementaryExcitations............128
6.8. Semiconductor Physics: Electrons and Holes . . . . . . .....130
6.9. n-Type Semiconductor Physics: The Statistics . . . . . .....131
6.10. CorrelationsandtheCoulombRepulsion.............132
6.11. Miscellaneous Properties of Semiconductors . . . . . . .....135
6.12. Aspects of Superconductivity: Cooper Pairs . . . . . . .....137
6.13. AspectsofBCSTheory ......................140
6.14. Contemporary Developments in Superconductivity . . .....146
Chapter 7 Kinetic Theory 149
7.1. ScopeofThisChapter.......................149
7.2. Quasi-Equilibrium Flows and the Second Law . . . . . .....150
7.3. The Collision Integral . ......................151
7.4. Approach to Equilibrium of a “Classical” Non-Ideal Gas . . . . 154
7.5. ANewLookat“QuantumStatistics” ..............156
7.6. MasterEquation:ApplicationtoRadioactiveDecay.......158
7.7. BoltzmannEquation........................160
7.8. ElectricalCurrentsinaLow-DensityElectronGas .......162
7.9. DiffusionandtheEinsteinRelation................165
7.10. Electrical Conductivity of Metals . . . . . ............165
7.11. ExactlySolved“Backscattering”Model .............166
7.12. Electron-PhononScattering ....................169
7.13. ApproximatingtheBoltzmannEquation.............170
7.14. CrossedElectricandMagneticFields...............171
7.15. Propagation of Sound Waves in Fluids . . ............173
7.16. TheCalculationsandTheirResult ................178
Chapter 8 The Transfer Matrix 183
8.1. TheTransferMatrixandtheThermalZipper..........183
8.2. OpeningandClosinga“ZipperLadder”orPolymer ......186
8.3. The Full Zipper ( N> 2)......................190
668308368.026.png 668308368.027.png 668308368.028.png

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin