Basic statistical physics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2010
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 229 S. graph. Darst. |
| ISBN: | 9789814293259 9814293253 |
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MARC
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| 245 | 1 | 0 | |a Basic statistical physics |c Nandita Rudra ; P. Rudra |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2010 | |
| 300 | |a XVII, 229 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-019012190 | ||
Record in the Search Index
| _version_ | 1804141229774995456 |
|---|---|
| adam_text | Contents
Preface
vii
Notations
and Fundamental Constants
xi
1.
Basic Concepts
1
1.1
Introduction
..........................
І
1.2
Master Equation and Hypothesis of Equal
á-priori
Probability
........................... 3
1.2.1
Example of
3
Level Systems
.............. 4
1.3
Phase Space, Phase Point, Phase Trajectory
......... 4
1.4
Statistical Distribution Function and Ergodic
Hypothesis
........................... 5
1.5
Statistical Fluctuation and Statistical Independence
.... 7
1.6
Statistical Fluctuation and Generalized Susceptibility
... 11
1.7
Generalized Ornstein-Zernicke Relation
........... 13
1.8
Problems
............................ 15
2.
Motion of Systems in Phase Space
17
2.1
Integral Invariants
....................... 17
2.2
Classical Liouville s Equation
................. 20
2.3
Role of Energy
......................... 22
2.4
Quantum Mechanical Density Matrix
............ 22
2.5
Quantum Liouville s Equation
................ 24
2.6
Problems
............................ 26
3.
States in Statistical Physics
27
xUi
xiv
BASIC STATISTICAL PHYSICS
3.1
Microscopic and Macroscopic States
............. 27
3.2
Statistical Weight and Density of States
........... 28
3.3
Examples: Non-interacting One- and N-Particle
Systems and Spin-1/2 Particles
................ 29
3.4
Entropy and Boltzmann s Principle
............. 31
3.5
Boltzmann s
Н
-Theorem ...................
34
3.6
Problems
............................ 35
4.
Statistical Ensembles
37
4.1
Introduction
.......................... 37
4.2
Microcanonical Distribution Function
............ 37
4.3
Canonical (Gibbs) Distribution Function
........... 39
4.3.1
Thermodynamic Temperature and Distribution
Function
........................ 39
4.3.2
Spin-1/2 Particles and Negative Temperature
.... 40
4.3.3
Partition Function and Different Thermodynamic
Functions
........................ 41
4.3.4
System of Linear Harmonic Oscillators in Canonical
Ensemble
........................ 42
4.3.5
Energy Fluctuation in Canonical Ensemble and
Equivalence of Canonical and Microcanonical
Ensembles
........................ 43
4.4
Grandcanonical Distribution Function
............ 44
4.4.1
Dependence of Thermodynamic Functions on Number
of Particles
....................... 44
4.4.2
Chemical Potential and Distribution Function
.... 47
4.4.3
Density Fluctuation in Grandcanonical Ensemble and
Equivalence of Grandcanonical and Canonical
Ensembles
........................ 49
4.5
Problems
............................ 50
5.
Ideal Gas
51
5.1
Boltzmann Distribution
.................... 51
5.2
Partition Function, Free Energy and Equation of State
... 52
5.3
Specific Heat: Translational, Vibrational and Rotational
Components
........................... 55
5.4
Degeneracy Temperature
................... 59
5.5
Problems
............................ 61
Contents xv
6. Chemical
Reaction Equilibrium
63
6.1
Conditions of Chemical Equilibrum
............. 63
6.2
Law of Mass Action
...................... 65
6.3
Heat of Reaction and Direction of Reaction
......... 66
6.4
Ionization Equilibrium
.................... 68
6.5
Saha Formula
......................... 70
6.6
Problems
............................ 71
7.
Real Gas
73
7.1
Free Energy, Virial Equation of State
............. 73
7.2
Second Virial Coefficient and Applicability of Virial
Equation
............................ 76
7.3
Model Calculation and van-der-Waal s Equation of State
. 78
7.4
Joule-Thomson Expansion and Inversion Temperature
... 80
7.5
Problems
............................ 83
8.
Strong Electrolytes
85
8.1 Debye-Hückel
Approximation, Debye Length
........ 85
8.2
Screened Coulomb Potential
................. 88
8.3
Equation of State and Osmotic Pressure
.......... 89
8.4
Problems
............................ 90
9.
Quantum Statistics
91
9.1
Bose
and Fermi Distributions
................. 91
9.2
Quantum Gases of Elementary Particles: Number Density
and Chemical Potential, Energy Density, Equation of State
94
9.3
Black Body Radiation and Planck s Law
........... 98
9.4
Lattice Specific Heat and Phonons
.............. 100
9.5
Degenerate
Bose Gas, Bose
Condensation
.......... 103
9.6
Liquid He and Superfluidity
................. 106
9.6.1
Systematics of Liquid 4He
.............. 106
9.6.2
Landau s 2-Fluid Model
................
Ill
9.6.3
Systematics of Liquid 3#e
.............. 117
9.7
Degenerate Fermi Gas, Degeneracy Pressure, Specific Heat
118
9.8
Magnetism of Free
Fermions
................. 124
9.8.1
Preamble
........................ 124
9.8.2
Landau Diamagnetism
................. 124
9.8.3
Pauli Paramagnetism
................. 127
xvi
BASIC
STATISTICAL PHYSICS
9.9
Interacting Fermi System: Fermi Liquid Theory
..... 129
9.10
Relativistic Degenerate Fermi Gas
............. 133
9.11
Problems
........................... 136
10.
Bose-Einstein Condensate
139
10.1
Introduction
......................... 139
10.2
Trapping of Atoms
..................... 140
10.3
Cooling of Atoms
...................... 142
10.4
Problems
........................... 145
11.
Statistical Astrophysics
147
11.1
Introduction
......................... 147
11.2
Stars: Stability and Evolution
............... 148
11.3
High Temperature Dense Matter
............. 152
11.4
Neutron Stars and Black Holes
............... 154
11.5
Problems
........................... 156
12.
Phase Transitions
157
12.1
Systematics of Phase Transitions
............. 157
12.2
Ehrenfest s Classification of Phase Transitions
...... 159
12.3
Order Parameter, Continuous and Discontinuous
Transitions
.......................... 160
12.4
Landau s Theory of Continuous Phase Transitions
.... 163
12.5
Continuity of Entropy and Discontinuity of Specific Heat
165
12.6
Generalized Susceptibility
................. 167
12.7
Critical Exponents and Fluctuations of Order Parameter
170
12.8
Ising Model
.......................... 173
12.8.1
Zero-Field l-Dimensional Case
........... 175
12.8.2
Non-Zero-Field l-Dimensional Case
........ 175
12.8.3
Multi-Dimensional Case
............... 177
12.8.4
2-Dimensional Ising System
............ 178
12.9
Problems
........................... 181
13.
Irreversible Processes
183
13.1
Introduction
......................... 183
13.2
Linear Response Theory
(Kubo
Formalism)
........ 184
13.2.1
Mechanical Process
................. 184
13.2.2
Thermal Process
................... 189
Contents xvii
13.3
Symmetry Relations
.................... 191
13.4
Fluctuation-Dissipation Theorem
.............. 192
13.5
Problems
........................... 196
14.
Mathematical Appendix
197
14.1
Beta and Gamma Functions
................ 197
14.2
Dirac Delta Function (Distribution)
............ 198
14.3
Functional Derivative
.................... 200
14.4
Mathematical Identities
................... 201
14.5
Multiple Summation
..................... 202
14.6 Pauli
Matrices
........................ 203
14.7
Probability Theory
...................... 203
14.7.1
Elementary Results of Probability Theory
..... 203
14.7.2
Statistical Distributions
............... 204
14.7.3
Central Limit Theorem
............... 207
14.8
Quantum Mechanics, A Retrospect
............ 209
14.9
Riemann, Bernoulli and Fourier
.............. 210
14.9.1
Riemann s C-Function
................ 210
14.9.2
Bernoulli Numbers and Polynomials
........ 211
14.9.3
Fourier Series
..................... 212
14.9.4
Integrals of Quantum Statistics
........... 214
14.10
Sanskrit Transliteration
................... 216
14.11
Stirling s Theorem
..................... 217
14.12
Summation and Integration
................ 219
14.13
Volume of an N-Dimensional Sphere
........... 220
Bibliography
223
Index
225
|
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| author | Rudra, Nandita Rudra, P. |
| author_facet | Rudra, Nandita Rudra, P. |
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| indexdate | 2024-07-09T22:12:33Z |
| institution | BVB |
| isbn | 9789814293259 9814293253 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-019012190 |
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| spelling | Rudra, Nandita Verfasser aut Basic statistical physics Nandita Rudra ; P. Rudra New Jersey [u.a.] World Scientific 2010 XVII, 229 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistical physics Statistische Physik (DE-588)4057000-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Statistische Physik (DE-588)4057000-9 s DE-604 Rudra, P. Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019012190&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rudra, Nandita Rudra, P. Basic statistical physics Statistical physics Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4057000-9 (DE-588)4123623-3 |
| title | Basic statistical physics |
| title_auth | Basic statistical physics |
| title_exact_search | Basic statistical physics |
| title_full | Basic statistical physics Nandita Rudra ; P. Rudra |
| title_fullStr | Basic statistical physics Nandita Rudra ; P. Rudra |
| title_full_unstemmed | Basic statistical physics Nandita Rudra ; P. Rudra |
| title_short | Basic statistical physics |
| title_sort | basic statistical physics |
| topic | Statistical physics Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Statistical physics Statistische Physik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019012190&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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