Microcanonical thermodynamics: phase transitions in "small" systems
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2001
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| Schriftenreihe: | World Scientific lecture notes in physics
66 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 269 S. graph. Darst. |
| ISBN: | 9810242158 |
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| adam_text | WORLD SCIENTIFIC LECTURE NOTES IN PHYSICS - VOL. 66 MICROCANONICAL
THERMODYNAMICS PHASE TRANSITIONS IN SMALL SYSTEMS DIETER H. E. GROSS
HAHN MEITNER INSTITUT, BERLIN WORLD SCIENTIFIC SINGAPORE * NEW JERSEY *
LONDON * HONG KONG CONTENTS PREFACE VII 0.1 WHO IS ADDRESSED, AND WHY
VII 0.2 A NECESSARY CLARIFICATION VIII 0.3 ACKNOWLEDGMENT IX CHAPTER 1
INTRODUCTION 1 1.1 PHASE TRANSITIONS AND THERMODYNAMICS IN SMALL
SYSTEMS. . . 1 1.2 BOLTZMANN GIVES THE KEY 4 1.3 MICRO-CANONICAL
THERMODYNAMICS DESCRIBES NON-EXTENSIVE SYS- TEMS 7 1.3.1 AT PHASE
TRANSITIONS OF FIRST ORDER THE SYSTEM BECOMES INHOMOGENEOUS 8 1.3.2
CONSERVED QUANTITIES ARE THE NATURAL CONTROL PARAMETERS. 9 1.3.3
MICRO-CANONICAL THERMODYNAMICS OFFERS A NEW, EFFEC- TIVE, AND NATURAL
WAY TO CALCULATE THE BASIC PARAMETERS OF PHASE TRANSITIONS 10 1.3.4
FRAGMENTATION A NEW TRANSITION IN FINITE SYSTEMS. ... 12 1.3.5 LONG
RANGE FORCES DEMAND THE USE OF THE MICRO-CANONICAL ENSEMBLE 12 1.4 SOME
REALISTIC SYSTEMS: NUCLEI AND ATOMIC CLUSTERS 13 1.4.1 WHY
MICRO-CANONICAL METROPOLIS MONTE CARLO AND NOT MOLECULAR DYNAMICS? 13
1.4.2 THE SIGNIFICANCE OF THE FREEZE-OUT VOLUME. OR HOW CAN A FINITE
DECAYING SYSTEM BECOME EQUILIBRIZED? 13 1.5 PLAN OF THIS BOOK. . . 14
XII CONTENTS CHAPTER 2 THE MECHANICAL BASIS OF THERMODYNAMICS: 19 2.1
BASIC DEFINITIONS 19 2.2 THE THERMODYNAMIC LIMIT, THE GLOBAL CONCAVITY
OF S(E,N). ... 21 2.3 PHASE TRANSITIONS MICRO-CANONICALLY 22 2.3.1
MICRO-CANONICAL SIGNALS OF PHASE TRANSITIONS 27 2.3.2 THE INTERPHASE
SURFACE TENSION 29 2.4 SECOND LAW OF THERMODYNAMICS AND BOLTZMANN S
ENTROPY ... 29 2.4.1 CONVEX ENTROPY * VIOLATION OF THE SECOND LAW ? . .
. . 31 2.4.2 THE RISE OF BOLTZMANN S ENTROPY OF A NON-EQUILIBRIUM SYSTEM
IN CONTRAST TO THE CONSTANCY OF GIBBS ENTROPY . 32 2.4.3 WEINHOLD S
GEOMETRICAL INTERPRETATION OF THERMODYNAMICS 34 CHAPTER 3
MICRO-CANONICAL THERMODYNAMICS OF PHASE TRAN- SITIONS STUDIED IN THE
POTTS MODEL. 35 3.1 INTRODUCTION 35 3.2 THE SURFACE TENSION IN THE POTTS
MODEL. [GEZ50] 36 3.2.1 FINITE-SIZE SCALING, ADVANTAGE OF
MICRO-CANONICAL COM- PARED TO CANONICAL SCALING 40 3.2.2 THE SPECIFIC
HEAT IN THE MICRO-CANONICAL ENSEMBLE. ... 41 3.3 THE TOPOLOGY OF THE
ENTROPY SURFACE S(E, N) FOR POTTS LATTICE GASES [GV99] 45 3.3.1
QUALITATIVE CONSIDERATIONS 45 3.3.1.1 THE ISING MODEL 45 3.3.1.2 LATTICE
GAS MODEL 48 3.3.1.3 DILUTED Q = 3 POTTS MODEL: 48 3.3.2 SIMULATION
METHOD 50 3.3.3 RESULTS 51 3.3.3.1 ON THE TOPOLOGY OF CURVATURES 56
3.3.3.2 THE ORDER PARAMETER OF THE PHASE TRANSITION. . 59 3.3.3.3 THE
INFORMATION LOST IN THE GRAND-CANONICAL EN- SEMBLE 60 3.3.4 CONCLUSION
63 3.4 ON THE ORIGIN OF ISOLATED CRITICAL POINTS AND CRITICAL LINES . .
. . 66 3.4.1 THE ISING MODEL WITH THE CLUSTER PAIR APPROXIMATION. . 68
3.4.1.1 MICRO-CANONICAL CLASSIFICATIONS OF THE PHASE TRAN- SITIONS 74
3.4.1.2 FERRO-MAGNETIC (FM) ISING MODEL 79 CONTENTS XIII 3.4.1.3
ANTI-FERRO MAGNETIC (AFM) ISING MODEL , THE LINE OF SECOND ORDER
TRANSITION SIGNALIZES A FIRST ORDER TRANSITION IN THE NON-CONSERVED
ORDER PA- RAMETER A 83 3.4.1.4 CONCLUSION 86 3.4.2 ORDINARY Q = 3 POTTS
MODEL IN THE PLAQUETTE APPROXIMA- TION 86 CHAPTER 4 LIQUID-GAS
TRANSITION AND SURFACE TENSION UNDER CONSTANT PRESSURE . 93 4.1
ANDERSEN S CONSTANT PRESSURE ENSEMBLE 93 4.2 MICRO-CANONICAL ENSEMBLE
WITH GIVEN PRESSURE; THE ENTHALPY. . 94 4.2.1 PISTON UNDER CONSTANT
EXTERNAL FORCE II 95 4.3 LIQUID-GAS TRANSITION IN REALISTIC METAL
SYSTEMS 97 4.3.1 THE MICRO-CANONICAL LIQUID-GAS TRANSITION AT CONSTANT
PRESSURE 97 4.3.2 THE LIQUID-GAS TRANSITION OF SODIUM, POTASSIUM, AND
IRON [GMOO] 100 4.3.3 A MORE REALISTIC ASSUMPTION FOR THE TREATMENT OF
THE SUR- FACE DEGREE OF FREEDOM OF SMALL LIQUID SODIUM CLUSTERS. 108
4.3.4 APPROACHING THE CRITICAL POINT 110 4.4 THE RELATION TO THE METHOD
OF THE GIBBS-ENSEMBLE 110 4.5 ALTERNATIVE MICROSCOPIC METHODS TO
CALCULATE THE SURFACE TENSION. 112 4.6 CRITICISM AND NECESSARY
IMPROVEMENTS OF THE COMPUTATIONAL METHOD. 113 4.7 CONCLUSION 114 CHAPTER
5 STATISTICAL FRAGMENTATION UNDER REPULSIVE FORCES OF LONG RANGE. 119
5.1 INTRODUCTION 119 5.2 THREE DIMENSIONAL STRESS OF LONG RANGE : THE
COULOMB FORCE. . 121 5.2.1 NUCLEAR FRAGMENTATION 121 5.2.1.1 WHICH
MECHANISM LEADS TO EQUILIBRATION ? WHAT CAN WE LEARN FROM NUCLEAR
FRICTION? [GLD92] 121 5.2.1.2 SIMULTANEOUS OR SEQUENTIAL STATISTICAL
FRAG- MENTATION ? 123 5.2.1.3 PHASE TRANSITION TOWARDS FRAGMENTATION. .
. . 132 5.2.1.4 NEW EXPERIMENTAL EVIDENCE FOR PHASE TRANSI- TION IN
NUCLEAR EVAPORATION DATA 134 XIV CONTENTS 5.2.1.5 DETERMINATION OF THE
MICRO HEAT CAPACITY FROM THE FLUCTUATIONS OF THE KINETIC ENERGIES OF THE
FRAGMENTS 141 5.2.1.6 THE ORDER PARAMETER OF MULTIFRAGMENTATION. . 143
5.2.1.7 N-FRAGMENT CORRELATIONS 144 5.2.1.8 IMF-IMF CORRELATION
FUNCTIONS : 145 5.2.1.9 EXCITATION ENERGY DEPENDENCE : 146 5.2.1.10 HOW
TO DISTINGUISH DIFFERENT MULTIFRAGMENTA- TION MODES BY THE SHAPES OF THE
CORRELATION FUNCTION: 149 5.2.1.11 PLANETARY AND SOUP EVENTS : 149
5.2.1.12 BINARY-MULTIFRAGMENTATION EVENTS : 151 5.2.1.13 SUMMARY ON
IMF-IMF CORRELATIONS ,154 5.2.2 FRAGMENTATION OF MULTIPLY CHARGED ATOMIC
CLUSTERS: . . . 156 5.2.2.1 INTRODUCTION 156 5.2.2.2 FIRST EXAMPLE:
SODIUM CLUSTERS 158 5.2.2.3 THE MICROSCOPIC - MACROSCOPIC APPROACH: HOW
TO DETERMINE THE INTERNAL LEVEL-DENSITY IN THE STRONGLY ENHARMONIC
REGIME NEAR THE MELTING PHASE-TRANSITION ? 160 5.2.2.4 EVAPORATION RATE
AND E MAX : 162 5.2.2.5 PHASE TRANSITION TO CLUSTER FRAGMENTATION. . .
166 5.2.2.6 MASS AND CHARGE CORRELATION FUNCTIONS 168 5.2.2.7 FISSION OF
DOUBLY CHARGED ANTIMONY CLUSTERS COMPARED TO ALKALI CLUSTERS 171 5.2.2.8
CONCLUSIONS FOR THE STATISTICAL FRAGMENTATION OF HOT ATOMIC CLUSTERS:
176 5.3 TWO DIMENSIONAL STRESS OF LONG RANGE: RAPIDLY ROTATING HOT NU-
CLEI [BG95B] 178 5.4 CONCLUSION 186 CHAPTER 6 THE COLLAPSE TRANSITION IN
SELF-GRAVITATING SYSTEMS FIRST MODEL-STUDIES. 191 6.1 1 - AND 2 - DIM.
HAMILTONIAN MEAN FIELD MODEL, A CARICATURE OF PHASE TRANSITIONS UNDER
SELF-GRAVITATION 192 6.1.1 SADDLE POINT APPROXIMATION FOR LARGE N 194
6.1.2 1-DIMENSIORIAL MODEL 196 6.1.3 2-DIMENSIONAL MODEL 197 CONTENTS XV
6.1.4 CONCLUSION 201 6.2 COLLAPSE OF NON-EXTENSIVE (GRAVITATING) SYSTEMS
UNDER CONSERVED ANGULAR MOMENTUM 203 6.2.1 CELL DISCRETIZATION 205 6.2.2
MEAN FIELD APPROXIMATION 207 6.2.3 THE THIRRING MODEL WITH ANGULAR
MOMENTUM 208 APPENDIX A ON THE HISTORICAL DEVELOPMENT OF STATISTICAL NU-
CLEAR MULTIFRAGMENTATION MODELS. 215 A.I MATHEMATICAL PARTITION VS.
QUANTUM PARTITION 219 APPENDIX B THE MICRO-CANONICAL ENSEMBLE OF
NA-CLUSTERS. 221 B.I MICRO-CANONICAL METROPOLIS SAMPLING 226 B.2 THE
BASIC MICRO-CANONICAL WEIGHTS 228 B.2.1 THE WEIGHT W V : 229 B.2.2 THE
WEIGHT W M : 229 B.2.3 THE WEIGHT W NZ * 230 B.2.4 THE WEIGHT W R : 231
B.2.5 SAMPLING OF THE EXCITATION ENERGIES {EJ} 1 AND THE AS- SOCIATED
WEIGHTS W Q D, W QT , AND W Q B 232 B.2.6 DIMERS AND TRIMERS: I 233
B.2.7 BULK FRAGMENTS: 233 B.2.8 DECOMPOSITION OF IP, THE WEIGHT W P I
235 B.3 THE METROPOLIS PASS. 238 APPENDIX C SOME GENERAL TECHNICAL
ASPECTS OF MICRO- CANONICAL MONTE CARLO SIMULATION ON A LATTICE. 241
C.0.1 DIRECT SAMPLING METHOD: 241 C.0.2 2. METHOD USING A GRID OF LOCAL
PATCHES C.F. FIG.(C.L) . 242 C.0.3 USING AN AUXILIARY WEIGHT WQ(AI, ...,
AQ) 243 CO.4 ITERATIVE IMPROVEMENT OF THE AUXILIARY WEIGHT W O (A U
...,A Q ) 243 C.I EXAMPLE: THE DILUTED POTTS MODEL 246 BIBLIOGRAPHY 249
INDEX 265
|
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| physical | XV, 269 S. graph. Darst. |
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| spelling | Gross, Dieter H. E. Verfasser aut Microcanonical thermodynamics phase transitions in "small" systems by Dieter H. E. Gross Singapore [u.a.] World Scientific 2001 XV, 269 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier World Scientific lecture notes in physics 66 Thermodynamik (DE-588)4059827-5 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Mikrokanonische Gesamtheit (DE-588)4444250-6 gnd rswk-swf Thermodynamik (DE-588)4059827-5 s Phasenumwandlung (DE-588)4132140-6 s Mikrokanonische Gesamtheit (DE-588)4444250-6 s DE-604 Statistische Mechanik (DE-588)4056999-8 s World Scientific lecture notes in physics 66 (DE-604)BV000819327 66 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009396930&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gross, Dieter H. E. Microcanonical thermodynamics phase transitions in "small" systems World Scientific lecture notes in physics Thermodynamik (DE-588)4059827-5 gnd Phasenumwandlung (DE-588)4132140-6 gnd Statistische Mechanik (DE-588)4056999-8 gnd Mikrokanonische Gesamtheit (DE-588)4444250-6 gnd |
| subject_GND | (DE-588)4059827-5 (DE-588)4132140-6 (DE-588)4056999-8 (DE-588)4444250-6 |
| title | Microcanonical thermodynamics phase transitions in "small" systems |
| title_auth | Microcanonical thermodynamics phase transitions in "small" systems |
| title_exact_search | Microcanonical thermodynamics phase transitions in "small" systems |
| title_full | Microcanonical thermodynamics phase transitions in "small" systems by Dieter H. E. Gross |
| title_fullStr | Microcanonical thermodynamics phase transitions in "small" systems by Dieter H. E. Gross |
| title_full_unstemmed | Microcanonical thermodynamics phase transitions in "small" systems by Dieter H. E. Gross |
| title_short | Microcanonical thermodynamics |
| title_sort | microcanonical thermodynamics phase transitions in small systems |
| title_sub | phase transitions in "small" systems |
| topic | Thermodynamik (DE-588)4059827-5 gnd Phasenumwandlung (DE-588)4132140-6 gnd Statistische Mechanik (DE-588)4056999-8 gnd Mikrokanonische Gesamtheit (DE-588)4444250-6 gnd |
| topic_facet | Thermodynamik Phasenumwandlung Statistische Mechanik Mikrokanonische Gesamtheit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009396930&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT grossdieterhe microcanonicalthermodynamicsphasetransitionsinsmallsystems |