Elementary lectures in statistical mechanics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2000
|
| Series: | Graduate texts in contemporary physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 430 S. graph. Darst. |
| ISBN: | 0387989188 |
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Record in the Search Index
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| adam_text | GEORGE DJ. PHILLIES ELEMENTARY LECTURES IN STATISTICAL MECHANICS WITH 51
ILLUSTRATIONS SPRINGER CONTENTS PREFACE V REFERENCES VII I FUNDAMENTALS:
SEPARABLE CLASSICAL SYSTEMS 1 LECTURE 1. INTRODUCTION 3 1.1 HISTORICAL
PERSPECTIVE 4 1.2 BASIC PRINCIPLES 6 1.3 AUTHOR S SELF-DEFENSE 8 1.4
OTHER READINGS 9 REFERENCES 10 LECTURE 2. AVERAGING AND STATISTICS 11
2.1 EXAMPLES OF AVERAGES 12 2.2 FORMAL AVERAGES 16 2.3 PROBABILITY AND
STATISTICAL WEIGHTS 18 2.4 MEANING AND CHARACTERIZATION OF STATISTICAL
WEIGHTS 22 2.5 IDEAL TIME AND ENSEMBLE AVERAGES 23 2.6 SUMMARY 25
PROBLEMS 25 REFERENCES 27 X CONTENTS LECTURE 3. ENSEMBLES: FUNDAMENTAL
PRINCIPLES OF STATISTICAL MECHANICS 28 3.1 ENSEMBLES 28 3.2 THE
CANONICAL ENSEMBLE 30 3.3 OTHER ENSEMBLES 32 3.4 NOTATION AND
TERMINOLOGY: PHASE SPACE 36 3.5 SUMMARY 37 PROBLEMS 37 REFERENCES 38
LECTURE 4. THE ONE-ATOM IDEAL GAS 39 4.1 THE CLASSICAL ONE-ATOM ENSEMBLE
39 4.2 THE AVERAGE ENERGY 42 4.3 MEAN-SQUARE ENERGY 43 4.4 THE
MAXWELL-BOLTZMANN DISTRIBUTION 43 4.5 REDUCED DISTRIBUTION FUNCTIONS 46
4.6 DENSITY OF STATES 48 4.7 CANONICAL AND REPRESENTATIVE ENSEMBLES 49
4.8 SUMMARY 51 PROBLEMS 51 REFERENCES 53 ASIDE A. THE TWO-ATOM IDEAL GAS
55 A.L SETTING UP THE PROBLEM 55 A.2 AVERAGE ENERGY 57 A.3 SUMMARY 58
PROBLEMS 58 LECTURE 5. N-ATOM IDEAL GAS 59 5.1 ENSEMBLE AVERAGE FOR
AF-ATOM SYSTEMS 59 5.2 ENSEMBLE AVERAGES OF E AND E 2 62 5.3
FLUCTUATIONS AND MEASUREMENTS IN LARGE SYSTEMS 64 5.4 POTENTIAL ENERGY
FLUCTUATIONS 73 5.5 COUNTING STATES 74 5.6 SUMMARY 78 PROBLEMS 78
REFERENCES 79 LECTURE 6. PRESSURE OF AN IDEAL GAS 80 6.1 P FROM A
CANONICAL ENSEMBLE AVERAGE 80 6.2 P FROM THE PARTITION FUNCTION 83 6.3 P
FROM THE KINETIC THEORY OF GASES 84 6.4 REMARKS 87 PROBLEMS 88
REFERENCES 89 CONTENTS XI ASIDE *. HOW DO THERMOMETERS WORK?*THE
POLYTHERMAL ENSEMBLE 90 B.L INTRODUCTION 90 B.2 THE POLYTHERMAL ENSEMBLE
92 B.3 DISCUSSION 95 PROBLEMS 96 REFERENCES 96 LECTURE 7. FORMAL
MANIPULATIONS OF THE PARTITION FUNCTION 98 7.1 THE EQUIPARTITION THEOREM
98 7.2 FIRST GENERALIZED EQUIPARTITION THEOREM 101 7.3 SECOND
GENERALIZED EQUIPARTITION THEOREM 102 7.4 ADDITIONAL TESTS;
CLARIFICATION OF THE EQUIPARTITION THEOREMS . 104 7.5 PARAMETRIC
DERIVATIVES OF THE ENSEMBLE AVERAGE 107 7.6 SUMMARY 108 PROBLEMS 109
REFERENCES 109 ASIDE C. GIBBS S DERIVATION OF Q = ***(-***) 111
REFERENCES 114 LECTURE 8. ENTROPY 115 8.1 THE GIBBS FORM FOR THE ENTROPY
116 8.2 SPECIAL CASES 118 8.3 DISCUSSION 121 PROBLEMS 122 REFERENCES 122
LECTURE 9. OPEN SYSTEMS; GRAND CANONICAL ENSEMBLE 123 9.1 THE GRAND
CANONICAL ENSEMBLE 124 9.2 FLUCTUATIONS IN THE GRAND CANONICAL ENSEMBLE
133 9.3 DISCUSSION 136 PROBLEMS 136 REFERENCES 137 II SEPARABLE QUANTUM
SYSTEMS 139 LECTURE 10. THE DIATOMIC GAS AND OTHER SEPARABLE QUANTUM
SYSTEMS 141 10.1 PARTITION FUNCTIONS FOR SEPARABLE SYSTEMS 142 10.2
CLASSICAL DIATOMIC MOLECULES 144 10.3 QUANTIZATION OF ROTATIONAL AND
VIBRATIONAL MODES 145 10.4 SPIN SYSTEMS 150 10.5 SUMMARY 153 PROBLEMS
154 REFERENCES 156 XII CONTENTS LECTURE 11. CRYSTALLINE SOLIDS 157 11.1
CLASSICAL MODEL OF A SOLID 158 11.2 EINSTEIN MODEL 159 11.3 DEBYE MODEL
160 11.4 SUMMARY 167 PROBLEMS 167 REFERENCES 168 ASIDE D. QUANTUM
MECHANICS 169 D.L BASIC PRINCIPLES OF QUANTUM MECHANICS 169 D.2 SUMMARY
177 PROBLEMS 178 REFERENCES 178 LECTURE 12. FORMAL QUANTUM STATISTICAL
MECHANICS 180 12.1 CHOICE OF BASIS VECTORS 180 12.2 REPLACEMENT OF SUMS
OVER ALL STATES WITH SUMS OVER EIGENSTATES 183 12.3 QUANTUM EFFECTS ON
CLASSICAL INTEGRALS 186 12.4 SUMMARY 188 PROBLEMS 188 REFERENCES 189
LECTURE 13. QUANTUM STATISTICS 190 13.1 INTRODUCTION 190 13.2 PARTICLES
WHOSE NUMBER IS CONSERVED 191 13.3 NONINTERACTING FERMI-DIRAC PARTICLES
195 13.4 PHOTONS 197 13.5 HISTORICAL ASIDE: WHAT DID PLANCK DO? 201 13.6
LOW-DENSITY LIMIT 205 PROBLEMS 205 REFERENCES 206 ASIDE E.
KIRKWOOD-WIGNER THEOREM 208 E.L MOMENTUM EIGENSTATE EXPANSION 208 E.2
DISCUSSION 213 PROBLEMS 214 REFERENCES 214 LECTURE 14. CHEMICAL
EQUILIBRIA 215 14.1 CONDITIONS FOR CHEMICAL EQUILIBRIUM 215 14.2
EQUILIBRIUM CONSTANTS OF DILUTE SPECIES FROM PARTITION FUNCTIONS 220
14.3 DISCUSSION 222 PROBLEMS 222 CONTENTS XIII REFERENCES 222 III
INTERACTING PARTICLES AND CLUSTER EXPANSIONS 223 LECTURE 15. INTERACTING
PARTICLES 225 15.1 POTENTIAL ENERGIES; SIMPLE FLUIDS 226 15.2 SIMPLE
REDUCTIONS; CONVERGENCE 229 15.3 DISCUSSION 232 PROBLEMS 232 REFERENCES
232 LECTURE 16. CLUSTER EXPANSIONS 233 16.1 SEARCH FOR AN APPROACH 233
16.2 AN APPROXIMANT 236 16.3 FLAWS OF THE APPROXIMANT 237 16.4
APPROXIMANT AS A MOTIVATOR OF BETTER APPROACHES 238 PROBLEMS 239
REFERENCES 239 LECTURE 17. E VIA THE GRAND CANONICAL ENSEMBLE 240 17.1 S
AND THE DENSITY 240 17.2 EXPANSION FOR P IN POWERS OF Z OR P 241 17.3
GRAPHICAL NOTATION 244 17.4 THE PRESSURE 247 17.5 SUMMARY 247 PROBLEMS
248 REFERENCES 249 LECTURE 18. EVALUATING CLUSTER INTEGRALS 250 18.1 B 2
; SPECIAL CASES 250 18.2 MORE GENERAL TECHNIQUES 253 18.3 #-BONDS 259
18.4 THE LAW OF CORRESPONDING STATES 260 18.5 SUMMARY 261 PROBLEMS 262
REFERENCES 263 LECTURE 19. DISTRIBUTION FUNCTIONS 264 19.1 MOTIVATION
FOR DISTRIBUTION FUNCTIONS 264 19.2 DEFINITION OF THE DISTRIBUTION
FUNCTION 267 19.3 APPLICATIONS OF DISTRIBUTION FUNCTIONS 270 19.4
REMARKS 273 19.5 SUMMARY 274 PROBLEMS 274 XIV CONTENTS LECTURE 20. MORE
DISTRIBUTION FUNCTIONS 276 20.1 INTRODUCTION 276 20.2 CHEMICAL POTENTIAL
276 20.3 CHARGING PROCESSES 278 20.4 SUMMARY 281 PROBLEMS 281 REFERENCES
281 LECTURE 21. ELECTROLYTE SOLUTIONS, PLASMAS, AND SCREENING 282 21.1
INTRODUCTION 282 21.2 THE DEBYE-HUCKEL MODEL 282 21.3 DISCUSSION 288
PROBLEMS 288 REFERENCES 288 IV CORRELATION FUNCTIONS AND DYNAMICS 289
LECTURE 22. CORRELATION FUNCTIONS 291 22.1 INTRODUCTION; CORRELATION
FUNCTIONS 291 22.2 THE DENSITY OPERATOR: EXAMPLES OF STATIC CORRELATION
FUNCTIONS 293 22.3 EVALUATION OF CORRELATION FUNCTIONS VIA SYMMETRY:
TRANSLATIONAL INVARIANCE 295 22.4 CORRELATION FUNCTIONS OF VECTORS AND
PSEUDOVECTORS; OTHER SYMMETRIES 298 22.5 DISCUSSION AND SUMMARY 300
PROBLEMS 300 REFERENCES 301 LECTURE 23. STABILITY OF THE CANONICAL
ENSEMBLE 302 23.1 INTRODUCTION 302 23.2 TIME EVOLUTION: TEMPORAL
STABILITY OF THE CANONICAL ENSEMBLE . 304 23.3 APPLICATION OF THE
CANONICAL ENSEMBLE STABILITY THEOREM ... 311 23.4 TIME CORRELATION
FUNCTIONS 315 23.5 DISCUSSION 317 PROBLEMS 318 REFERENCES 318 ASIDE F.
THE CENTRAL LIMIT THEOREM 320 F.L DERIVATION OF THE CENTRAL LIMIT
THEOREM 322 F.2 IMPLICATIONS OF THE CENTRAL LIMIT THEOREM 325 F.3
SUMMARY 326 PROBLEMS 326 REFERENCES 327 CONTENTS XV LECTURE 24. THE
LANGEVIN EQUATION 328 24.1 THE LANGEVIN MODEL FOR BROWNIAN MOTION 328
24.2 A FLUCTUATION-DISSIPATION THEOREM ON THE LANGEVIN EQUATION . 330
24.3 MEAN-SQUARE DISPLACEMENT OF A BROWNIAN PARTICLE 332 24.4 CROSS
CORRELATION OF SUCCESSIVE LANGEVIN STEPS 334 24.5 APPLICATION OF THE
CENTRAL LIMIT THEOREM TO THE LANGEVIN MODEL 335 24.6 SUMMARY 337
PROBLEMS 337 REFERENCES 338 LECTURE 25. THE LANGEVIN MODEL AND DIFFUSION
339 25.1 NECESSITY OF THE ASSUMPTIONS RESULTING IN THE LANGEVIN MODEL
339 25.2 THE EINSTEIN DIFFUSION EQUATION: A MACROSCOPIC RESULT .... 342
25.3 DIFFUSION IN CONCENTRATED SOLUTIONS 343 25.4 SUMMARY 345 PROBLEMS
346 REFERENCES 346 LECTURE 26. PROJECTION OPERATORS AND THE MORI-ZWANZIG
FORMALISM 347 26.1 TIME EVOLUTION OF PHASE POINTS VIA THE LIOUVILLE
OPERATOR . . . 348 26.2 PROJECTION OPERATORS 350 26.3 THE MORI-ZWANZIG
FORMALISM 354 26.4 ASIDES ON THE MORI-ZWANZIG FORMALISM 359 PROBLEMS 363
REFERENCES 363 LECTURE 27. LINEAR RESPONSE THEORY 365 27.1 INTRODUCTION
365 27.2 LINEAR RESPONSE THEORY 365 27.3 ELECTRICAL CONDUCTIVITY 368
27.4 DISCUSSION 371 PROBLEMS 371 REFERENCES 371 V A RESEARCH PROBLEM 373
ASIDE G. SCATTERING OF LIGHT, NEUTRONS, X-RAYS, AND OTHER RADIATION 375
G.L INTRODUCTION 375 G.2 SCATTERING APPARATUS; PROPERTIES OF LIGHT 376
G.3 TIME CORRELATION FUNCTIONS 382 PROBLEMS 386 REFERENCES 386 XVI
CONTENTS LECTURE 28. DIFFUSION OF INTERACTING PARTICLES 388 28.1 WHY
SHOULD WE CARE ABOUT THIS RESEARCH PROBLEM? 389 28.2 WHAT SHALL WE
CALCULATE? 389 28.3 MODEL FOR PARTICLE DYNAMICS 391 28.4 FIRST CUMULANT
FOR G M (K, T) 394 28.5 SUMMARY 398 PROBLEMS 399 REFERENCES 399 LECTURE
29. INTERACTING PARTICLE EFFECTS 401 29.1 REDUCTION TO RADIAL
DISTRIBUTION FUNCTIONS 402 29.2 NUMERICAL VALUES FOR K X AND K S 405
29.3 DISCUSSION 409 PROBLEMS 411 REFERENCES 412 LECTURE 30. HIDDEN
CORRELATIONS 413 30.1 MODEL-INDEPENDENT RESULTS 413 30.2 EVALUATION OF
THE DERIVATIVES 415 30.3 RESOLUTION OF THE ANOMALY 418 30.4 DISCUSSION
419 PROBLEMS 421 REFERENCES 422 INDEX 423
|
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| indexdate | 2024-07-09T18:38:14Z |
| institution | BVB |
| isbn | 0387989188 |
| language | English |
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| spelling | Phillies, George D. J. 1947- Verfasser (DE-588)1113124997 aut Elementary lectures in statistical mechanics George D. J. Phillies New York [u.a.] Springer 2000 XVI, 430 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in contemporary physics Mecânica estatística larpcal Mécanique statistique ram Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008890277&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Phillies, George D. J. 1947- Elementary lectures in statistical mechanics Mecânica estatística larpcal Mécanique statistique ram Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd |
| subject_GND | (DE-588)4056999-8 |
| title | Elementary lectures in statistical mechanics |
| title_auth | Elementary lectures in statistical mechanics |
| title_exact_search | Elementary lectures in statistical mechanics |
| title_full | Elementary lectures in statistical mechanics George D. J. Phillies |
| title_fullStr | Elementary lectures in statistical mechanics George D. J. Phillies |
| title_full_unstemmed | Elementary lectures in statistical mechanics George D. J. Phillies |
| title_short | Elementary lectures in statistical mechanics |
| title_sort | elementary lectures in statistical mechanics |
| topic | Mecânica estatística larpcal Mécanique statistique ram Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd |
| topic_facet | Mecânica estatística Mécanique statistique Statistical mechanics Statistische Mechanik |
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