Statistical mechanics: from first principles to macroscopic phenomena
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 283 S. graph. Darst. |
| ISBN: | 052182575x 9780521825757 |
Internformat
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| 100 | 1 | |a Halley, James Woods |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Statistical mechanics |b from first principles to macroscopic phenomena |c J. Woods Halley |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
| 300 | |a XI, 283 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mécanique statistique | |
| 650 | 7 | |a Statistische mechanica |2 gtt | |
| 650 | 4 | |a Statistical mechanics | |
| 650 | 0 | 7 | |a Statistische Mechanik |0 (DE-588)4056999-8 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804134574777696256 |
|---|---|
| adam_text | Contents
Preface
page
ix
Introduction
1
Part I Foundations of equilibrium statistical mechanics
5
1
The classical distribution function
7
Foundations of equilibrium statistical mechanics
7
Liouville s theorem
14
The distribution function depends only on additive constants of the
motion
16
Microcanonical distribution
20
References
24
Problems
24
2
Quantum mechanical density matrix
27
Microcanonical density matrix
33
Reference
34
Problems
34
3
Thermodynamics
37
Definition of entropy
37
Thermodynamic potentials
38
Some thermodynamic relations and techniques
42
Constraints on thermodynamic quantities
46
References
49
Problems
49
4
Semiclassical limit
51
General formulation
51
The perfect gas
52
Problems
56
vi
Contents
Part
II
States
of matter in equilibrium statistical physics
57
5
Perfect gases
59
Classical perfect gas
60
Molecular ideal gas
62
Quantum perfect gases: general features
69
Quantum perfect gases: details for special cases
71
Perfect
Bose gas
at low temperatures
74
Perfect Fermi gas at low temperatures
78
References
81
Problems
81
6
Imperfect gases
85
Method I for the classical virial expansion
86
Method II for the virial expansion: irreducible linked clusters
95
Application of
cumulants
to the expansion of the free energy
102
Cluster expansion for a quantum imperfect gas (extension of
method I)
108
Gross-Pitaevskii-Bogoliubov theory of the low temperature weakly
interacting
Bose gas
115
References
122
Problems
122
7
Statistical mechanics of liquids
125
Definitions of «-particle distribution functions
126
Determination of g(r) by neutron and x-ray scattering
128
BBGKY hierarchy
133
Approximate closed form equations for g(r)
135
Molecular dynamics evaluation of liquid properties
136
References
143
Problems
144
8
Quantum liquids and solids
145
Fundamental postulates of Fermi liquid theory
146
Models of magnets
150
Physical basis for models of magnetic insulators: exchange
150
Comparison of Ising and liquid-gas systems
153
Exact solution of the paramagnetic problem
153
High temperature series for the Ising model
154
Transfer matrix
157
Monte Carlo methods
158
References
159
Problems
160
Contents
vii
9 Phase
transitions:
static
properties
161
Thermodynamic considerations
161
Critical points
166
Phenomenology of critical point singularities: scaling
167
Mean field theory
172
Renormalization group: general scheme
177
Renormalization group: the Landau-Ginzburg model
181
References
189
Problems
189
Partili
Dynamics
193
10
Hydrodynamics and definition of transport coefficients
195
General discussion
195
Hydrodynamic equations for a classical fluid
196
Fluctuation-dissipation relations for hydrodynamic transport
coefficients
199
References
214
Problems
214
11
Stochastic models and dynamical critical phenomena
217
General discussion of stochastic models
217
Generalized
Langevin
equation
217
General discussion of dynamical critical phenomena
221
References
242
Problems
242
Appendix: solutions to selected problems
243
Index
281
|
| adam_txt |
Contents
Preface
page
ix
Introduction
1
Part I Foundations of equilibrium statistical mechanics
5
1
The classical distribution function
7
Foundations of equilibrium statistical mechanics
7
Liouville's theorem
14
The distribution function depends only on additive constants of the
motion
16
Microcanonical distribution
20
References
24
Problems
24
2
Quantum mechanical density matrix
27
Microcanonical density matrix
33
Reference
34
Problems
34
3
Thermodynamics
37
Definition of entropy
37
Thermodynamic potentials
38
Some thermodynamic relations and techniques
42
Constraints on thermodynamic quantities
46
References
49
Problems
49
4
Semiclassical limit
51
General formulation
51
The perfect gas
52
Problems
56
vi
Contents
Part
II
States
of matter in equilibrium statistical physics
57
5
Perfect gases
59
Classical perfect gas
60
Molecular ideal gas
62
Quantum perfect gases: general features
69
Quantum perfect gases: details for special cases
71
Perfect
Bose gas
at low temperatures
74
Perfect Fermi gas at low temperatures
78
References
81
Problems
81
6
Imperfect gases
85
Method I for the classical virial expansion
86
Method II for the virial expansion: irreducible linked clusters
95
Application of
cumulants
to the expansion of the free energy
102
Cluster expansion for a quantum imperfect gas (extension of
method I)
108
Gross-Pitaevskii-Bogoliubov theory of the low temperature weakly
interacting
Bose gas
115
References
122
Problems
122
7
Statistical mechanics of liquids
125
Definitions of «-particle distribution functions
126
Determination of g(r) by neutron and x-ray scattering
128
BBGKY hierarchy
133
Approximate closed form equations for g(r)
135
Molecular dynamics evaluation of liquid properties
136
References
143
Problems
144
8
Quantum liquids and solids
145
Fundamental postulates of Fermi liquid theory
146
Models of magnets
150
Physical basis for models of magnetic insulators: exchange
150
Comparison of Ising and liquid-gas systems
153
Exact solution of the paramagnetic problem
153
High temperature series for the Ising model
154
Transfer matrix
157
Monte Carlo methods
158
References
159
Problems
160
Contents
vii
9 Phase
transitions:
static
properties
161
Thermodynamic considerations
161
Critical points
166
Phenomenology of critical point singularities: scaling
167
Mean field theory
172
Renormalization group: general scheme
177
Renormalization group: the Landau-Ginzburg model
181
References
189
Problems
189
Partili
Dynamics
193
10
Hydrodynamics and definition of transport coefficients
195
General discussion
195
Hydrodynamic equations for a classical fluid
196
Fluctuation-dissipation relations for hydrodynamic transport
coefficients
199
References
214
Problems
214
11
Stochastic models and dynamical critical phenomena
217
General discussion of stochastic models
217
Generalized
Langevin
equation
217
General discussion of dynamical critical phenomena
221
References
242
Problems
242
Appendix: solutions to selected problems
243
Index
281 |
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| index_date | 2024-07-02T13:21:45Z |
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| isbn | 052182575x 9780521825757 |
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| spelling | Halley, James Woods Verfasser aut Statistical mechanics from first principles to macroscopic phenomena J. Woods Halley 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 XI, 283 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mécanique statistique Statistische mechanica gtt Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014178950&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Halley, James Woods Statistical mechanics from first principles to macroscopic phenomena Mécanique statistique Statistische mechanica gtt Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd |
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| title | Statistical mechanics from first principles to macroscopic phenomena |
| title_auth | Statistical mechanics from first principles to macroscopic phenomena |
| title_exact_search | Statistical mechanics from first principles to macroscopic phenomena |
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| title_full | Statistical mechanics from first principles to macroscopic phenomena J. Woods Halley |
| title_fullStr | Statistical mechanics from first principles to macroscopic phenomena J. Woods Halley |
| title_full_unstemmed | Statistical mechanics from first principles to macroscopic phenomena J. Woods Halley |
| title_short | Statistical mechanics |
| title_sort | statistical mechanics from first principles to macroscopic phenomena |
| title_sub | from first principles to macroscopic phenomena |
| topic | Mécanique statistique Statistische mechanica gtt Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd |
| topic_facet | Mécanique statistique Statistische mechanica Statistical mechanics Statistische Mechanik |
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