Statistical physics: an introductory course
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2006
|
| Edition: | 1. publ., repr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Hebr. übers. |
| Physical Description: | XII, 565 S. Ill., graph. Darst. |
| ISBN: | 981023192X 9810234767 9789810234768 |
Staff View
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| 100 | 1 | |a Amit, Daniel J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Statistical physics |b an introductory course |c Daniel J. Amit ; Yosef Verbin |
| 250 | |a 1. publ., repr. | ||
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2006 | |
| 300 | |a XII, 565 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016266586 | ||
Record in the Search Index
| _version_ | 1804137302333587456 |
|---|---|
| adam_text | Contents
Preface
xi
Part I The Kinetic Theory of Gases
1
Introduction
3
Chapter
1
Velocity and Position Distributions of Molecules in a Gas
6
1.1
Avogadro s law, or the equation of state of an ideal gas
1.2
Temperature and thermal equilibrium
9
1.3
Equipartition of energy per molecule and its constituent
parts
—
a fundamental problem
13
1.4
The density in an isothermal atmosphere
—
the Boltzmann
factor in the potential energy
20
1.5
The Maxwell-Boltzmann distribution
24
1.6
Averages and distributions
28
Chapter
2
Brownian Motion
32
2.1
Historical background
32
2.2
Characteristic scales of Brownian motion
33
2.3
Random walk
35
2.4
Brownian motion, random force and friction: the
Langevin
equation
37
2.5
Solving the
Langevin
equation: approximations and orders
of magnitude
41
2.6
Applications and implications
44
Chapter
3
Transport Coefficients
49
3.1
Introduction
49
3.2
The mean free path and mean free time
50
3.3
Self-diffusion
56
3.4
The mobility coefficient
61
3.5
The connection between the diffusion coefficient and the
mobility
63
3.6
Viscosity and thermal conductivity
64
3.7
Appendix: a more detailed calculation of the diffusion
coefficient
68
Self-assessment exercises
71
vj Contents
Solutions to exercises in the text
4
Solutions to self-assessment exercises
10?
Part II Statistical Physics with Paramagnets
119
Introduction
121
Chapter
0
Essential Background in Thermodynamics
124
0.1
The first law
124
0.2
The second law and the entropy
128
0.3
Thermodynamic potentials
129
0.4
The third law
133
Chapter
1
Thermodynamics with Magnetic Variables
134
1.1
Introduction
134
1.2
The first law in magnetic variables
136
Chapter
2
Microscopic States and Averages
138
2.1
Magnetic states, angular momentum and paramagnetism
138
2.2
Microscopic states,
observables
141
2.3
Probabilities and averages
143
Chapter
3
Isolated Paramagnet
—
Microcanonical Ensemble
147
3.1
Number of states and probabilities
147
3.2
Calculating averages and correlations
149
3.3
Numerical examples and Stirling s formula
152
Chapter
4
Isolated Paramagnet
—
Subsystems and Temperature
156
4.1
Microscopic states and thermodynamic equilibrium
156
4.2
β
and the temperature
157
4.3
Sharpness of the maximum
158
4.4
Identification of temperature and entropy
161
4.5
Negative temperature
163
4.6
Summary
164
Chapter
5
Paramagnet at a Given Temperature
165
5.1
The canonical ensemble
165
5.2
The partition function and thermodynamic quantities
167
5.3
Susceptibility and specific heat of a paramagnet
170
5.4
Paramagnet with
J
> 1/2 173
Contents
vii
Chapter
6
Order, Disorder and Entropy
174
Chapter
7
Comparison with Experiment
177
Summary
178
Self-assessment exercises
180
Solutions to exercises in the text
183
Solutions to self-assessment exercises
213
Part III Statistical Physics and Thermodynamics
223
Introduction
225
Chapter
1
The Canonical Ensemble and Thermodynamics
226
1.1
The partition function and the internal energy
226
1.2
Thermodynamic work
228
1.3
Entropy, free energy, the first and second laws
233
1.4
The paramagnet
—
revisited
236
1.5
On the statistical meaning of the free energy
237
Chapter
2
Harmonic Oscillator and Einstein Solid
243
2.1
Microscopic states
243
2.2
Partition function for oscillators
245
2.3
Einstein s solid
248
Chapter
3
Statistical Mechanics of Classical Systems
253
3.1
Statistical mechanics of a single particle
253
3.2
Statistical mechanics of a classical gas
258
Chapter
4
Statistical Mechanics of an Ideal Gas
261
4.1
The ideal gas
261
4.2
Mixtures of ideal gases
—
Dalton s law
263
4.3
Maxwell-Boltzmann distribution and equipartition
265
4.4
Ideal gas of quantum particles
268
Chapter
5
The Gibbs Paradox and the Third Law
275
5.1
Two difficulties
275
5.2
The Gibbs paradox and its resolution
276
5.3
Remarks on the third law of thermodynamics
281
5.4
Summary
283
ущ
Contents
Chapter
6
Fluctuations and Thermodynamic Quantities
284
6.1
Paramagnet: fluctuations in the magnetization
284
6.2
Energy fluctuations and the specific heat
286
6.3
Summary
287
Self-assessment exercises
288
Solutions to exercises in the text
292
Solutions to self-assessment exercises
322
Part IV From Ideal Gas to Photon Gas
337
Introduction
339
Chapter
1
An Ideal Gas of Molecules with Internal Degrees of Freedom
340
1.1
Center of mass and internal motions
340
1.2
Kinematics of a diatomic molecule
342
1.3
Gas of general composite molecules
346
1.4
Diatomic gas: classical treatment
352
1.5
Diatomic molecules: vibration and rotation
356
1.6
The equipartition principle and its violation
361
1.7
Diatomic gas
—
quantum calculation
363
Chapter
2
Gases in Chemical Reactions
366
2.1
Conditions for chemical equilibrium
366
2.2
The law of mass action
368
2.3
Dissociation in a diatomic gas
373
Chapter
3
Phonon Gas and the Debye Model
376
3.1
Sound waves in a crystal
376
3.2
Vibrational modes, phonons and enumeration of states
379
3.3
The Debye model
382
Chapter
4
Thermodynamics of Electromagnetic Radiation
385
4.1
General considerations of radiation at thermal equilibrium
385
4.2
Radiation density
387
4.3
Black body radiation
390
4.4
Absorption and emission of radiation
— Kirchhoff
s law
394
4.5
Role of black body radiation in modern physics
398
Appendix Calculation of Some Integrals
401
Contents
ix
Self-assessment exercises
403
Solutions to exercises in the text
406
Solutions to self-assessment exercises
434
Part V Of
Fermions
and Bosons
451
Introduction
453
Chapter
1
Grand Canonical Ensemble
454
1.1
Definitions and motivation
454
1.2
Connection to thermodynamics
455
Chapter
2
Statistical Mechanics of Identical Quantum Particles
458
2.1
Classification of states
—
occupation numbers
458
2.2
Quantum statistics
—
many-particle states
460
2.3
Thermodynamics of
fermions
and bosons
461
2.4
Average occupation numbers
463
Chapter
3
Electrical Conductivity in Metals
466
3.1
The
Drude
model
466
3.2
A critique of the
Drude
model
470
3.3
The
Sommerfeld
model
471
3.4
Electrons at high and low temperatures
474
3.5
Metals at room temperature
478
3.6
Thermodynamics of the
Sommerfeld
model
479
Chapter
4
Boson Gas
485
4.1
Bose-Einstein distribution
485
4.2
Chemical potential at low temperatures
486
4.3
Bose-Einstein condensation
488
4.4
Superfluidity
490
4.5
Bose-Einstein condensation in helium
493
4.6
Viscosity of a superfluid
497
4.7
Fermi liquid and superconductivity
503
Appendix Calculation of Some Integrals
509
Self-assessment exercises
512
Solutions to exercises in the text
514
Solutions to self-assessment exercises
536
Index
547
|
| adam_txt |
Contents
Preface
xi
Part I The Kinetic Theory of Gases
1
Introduction
3
Chapter
1
Velocity and Position Distributions of Molecules in a Gas
6
1.1
Avogadro's law, or the equation of state of an ideal gas
1.2
Temperature and thermal equilibrium
9
1.3
Equipartition of energy per molecule and its constituent
parts
—
a fundamental problem
13
1.4
The density in an isothermal atmosphere
—
the Boltzmann
factor in the potential energy
20
1.5
The Maxwell-Boltzmann distribution
24
1.6
Averages and distributions
28
Chapter
2
Brownian Motion
32
2.1
Historical background
32
2.2
Characteristic scales of Brownian motion
33
2.3
Random walk
35
2.4
Brownian motion, random force and friction: the
Langevin
equation
37
2.5
Solving the
Langevin
equation: approximations and orders
of magnitude
41
2.6
Applications and implications
44
Chapter
3
Transport Coefficients
49
3.1
Introduction
49
3.2
The mean free path and mean free time
50
3.3
Self-diffusion
56
3.4
The mobility coefficient
61
3.5
The connection between the diffusion coefficient and the
mobility
63
3.6
Viscosity and thermal conductivity
64
3.7
Appendix: a more detailed calculation of the diffusion
coefficient
68
Self-assessment exercises
71
vj Contents
Solutions to exercises in the text
'4
Solutions to self-assessment exercises
10?
Part II Statistical Physics with Paramagnets
119
Introduction
121
Chapter
0
Essential Background in Thermodynamics
124
0.1
The first law
124
0.2
The second law and the entropy
128
0.3
Thermodynamic potentials
129
0.4
The third law
133
Chapter
1
Thermodynamics with Magnetic Variables
134
1.1
Introduction
134
1.2
The first law in magnetic variables
136
Chapter
2
Microscopic States and Averages
138
2.1
Magnetic states, angular momentum and paramagnetism
138
2.2
Microscopic states,
observables
141
2.3
Probabilities and averages
143
Chapter
3
Isolated Paramagnet
—
Microcanonical Ensemble
147
3.1
Number of states and probabilities
147
3.2
Calculating averages and correlations
149
3.3
Numerical examples and Stirling's formula
152
Chapter
4
Isolated Paramagnet
—
Subsystems and Temperature
156
4.1
Microscopic states and thermodynamic equilibrium
156
4.2
β
and the temperature
157
4.3
Sharpness of the maximum
158
4.4
Identification of temperature and entropy
161
4.5
Negative temperature
163
4.6
Summary
164
Chapter
5
Paramagnet at a Given Temperature
165
5.1
The canonical ensemble
165
5.2
The partition function and thermodynamic quantities
167
5.3
Susceptibility and specific heat of a paramagnet
170
5.4
Paramagnet with
J
> 1/2 173
Contents
vii
Chapter
6
Order, Disorder and Entropy
174
Chapter
7
Comparison with Experiment
177
Summary
178
Self-assessment exercises
180
Solutions to exercises in the text
183
Solutions to self-assessment exercises
213
Part III Statistical Physics and Thermodynamics
223
Introduction
225
Chapter
1
The Canonical Ensemble and Thermodynamics
226
1.1
The partition function and the internal energy
226
1.2
Thermodynamic work
228
1.3
Entropy, free energy, the first and second laws
233
1.4
The paramagnet
—
revisited
236
1.5
On the statistical meaning of the free energy
237
Chapter
2
Harmonic Oscillator and Einstein Solid
243
2.1
Microscopic states
243
2.2
Partition function for oscillators
245
2.3
Einstein's solid
248
Chapter
3
Statistical Mechanics of Classical Systems
253
3.1
Statistical mechanics of a single particle
253
3.2
Statistical mechanics of a classical gas
258
Chapter
4
Statistical Mechanics of an Ideal Gas
261
4.1
The ideal gas
261
4.2
Mixtures of ideal gases
—
Dalton's law
263
4.3
Maxwell-Boltzmann distribution and equipartition
265
4.4
Ideal gas of quantum particles
268
Chapter
5
The Gibbs Paradox and the Third Law
275
5.1
Two difficulties
275
5.2
The Gibbs paradox and its resolution
276
5.3
Remarks on the third law of thermodynamics
281
5.4
Summary
283
ущ
Contents
Chapter
6
Fluctuations and Thermodynamic Quantities
284
6.1
Paramagnet: fluctuations in the magnetization
284
6.2
Energy fluctuations and the specific heat
286
6.3
Summary
287
Self-assessment exercises
288
Solutions to exercises in the text
292
Solutions to self-assessment exercises
322
Part IV From Ideal Gas to Photon Gas
337
Introduction
339
Chapter
1
An Ideal Gas of Molecules with Internal Degrees of Freedom
340
1.1
Center of mass and internal motions
340
1.2
Kinematics of a diatomic molecule
342
1.3
Gas of general composite molecules
346
1.4
Diatomic gas: classical treatment
352
1.5
Diatomic molecules: vibration and rotation
356
1.6
The equipartition principle and its violation
361
1.7
Diatomic gas
—
quantum calculation
363
Chapter
2
Gases in Chemical Reactions
366
2.1
Conditions for chemical equilibrium
366
2.2
The law of mass action
368
2.3
Dissociation in a diatomic gas
373
Chapter
3
Phonon Gas and the Debye Model
376
3.1
Sound waves in a crystal
376
3.2
Vibrational modes, phonons and enumeration of states
379
3.3
The Debye model
382
Chapter
4
Thermodynamics of Electromagnetic Radiation
385
4.1
General considerations of radiation at thermal equilibrium
385
4.2
Radiation density
387
4.3
Black body radiation
390
4.4
Absorption and emission of radiation
— Kirchhoff
's law
394
4.5
Role of black body radiation in modern physics
398
Appendix Calculation of Some Integrals
401
Contents
ix
Self-assessment exercises
403
Solutions to exercises in the text
406
Solutions to self-assessment exercises
434
Part V Of
Fermions
and Bosons
451
Introduction
453
Chapter
1
Grand Canonical Ensemble
454
1.1
Definitions and motivation
454
1.2
Connection to thermodynamics
455
Chapter
2
Statistical Mechanics of Identical Quantum Particles
458
2.1
Classification of states
—
occupation numbers
458
2.2
Quantum statistics
—
many-particle states
460
2.3
Thermodynamics of
fermions
and bosons
461
2.4
Average occupation numbers
463
Chapter
3
Electrical Conductivity in Metals
466
3.1
The
Drude
model
466
3.2
A critique of the
Drude
model
470
3.3
The
Sommerfeld
model
471
3.4
Electrons at high and low temperatures
474
3.5
Metals at room temperature
478
3.6
Thermodynamics of the
Sommerfeld
model
479
Chapter
4
Boson Gas
485
4.1
Bose-Einstein distribution
485
4.2
Chemical potential at low temperatures
486
4.3
Bose-Einstein condensation
488
4.4
Superfluidity
490
4.5
Bose-Einstein condensation in helium
493
4.6
Viscosity of a superfluid
497
4.7
Fermi liquid and superconductivity
503
Appendix Calculation of Some Integrals
509
Self-assessment exercises
512
Solutions to exercises in the text
514
Solutions to self-assessment exercises
536
Index
547 |
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| index_date | 2024-07-02T19:29:43Z |
| indexdate | 2024-07-09T21:10:08Z |
| institution | BVB |
| isbn | 981023192X 9810234767 9789810234768 |
| language | English |
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| physical | XII, 565 S. Ill., graph. Darst. |
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| publisher | World Scientific |
| record_format | marc |
| spelling | Amit, Daniel J. Verfasser aut Statistical physics an introductory course Daniel J. Amit ; Yosef Verbin 1. publ., repr. Singapore [u.a.] World Scientific 2006 XII, 565 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aus d. Hebr. übers. 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 Verbin, Yosef Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016266586&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Amit, Daniel J. Verbin, Yosef Statistical physics an introductory course Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4057000-9 (DE-588)4123623-3 |
| title | Statistical physics an introductory course |
| title_auth | Statistical physics an introductory course |
| title_exact_search | Statistical physics an introductory course |
| title_exact_search_txtP | Statistical physics an introductory course |
| title_full | Statistical physics an introductory course Daniel J. Amit ; Yosef Verbin |
| title_fullStr | Statistical physics an introductory course Daniel J. Amit ; Yosef Verbin |
| title_full_unstemmed | Statistical physics an introductory course Daniel J. Amit ; Yosef Verbin |
| title_short | Statistical physics |
| title_sort | statistical physics an introductory course |
| title_sub | an introductory course |
| topic | Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Statistische Physik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016266586&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT amitdanielj statisticalphysicsanintroductorycourse AT verbinyosef statisticalphysicsanintroductorycourse |